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Apr 19, 1986 - 6.9 Surface chemistry and paper structure enhancing water ...... Stamm concluded (42) that diffusion in wood may occur as vapour transport.

STUDIES OF WATER TRANSPORT IN PAPER DURING SHORT CONTACT TIMES

Pekka Salminen

Laboratory of Paper Chemistry Department of Chemical Engineering Abo Akademi 1988

STUDIES OF WATER TRANSPORT IN PAPER DURING SHORT CONTACT TIMES

Pekka Salminen

Thesis for the Degree of Doctor of Technology to be presented with due permission of the Faculty of Chemical Engineering at Abo Akademi for public criticism in Auditorium A of Gadolinia Building on October 3, 1988, at 12 noon.

Laboratory of Paper Chemistry Department of Chemical Engineering Abo Akademi 1988

ERRATA

PAGE

WHERE

INSTEAD OF

SHOULD BE

7

line 9

M. Se,

M. Se.,

28

line 14

r,ST,PO,PE and 'rJ.

r, h,PO,PE and 'rJ.

30

eq. (3.16)

35

line 29

(PE=6.9 MPa)

39

line 3

was used

(PE=6.9 MPa) were used

43

line 10

Fig. 5.1

Fig. 5.2

58

Fig. 5.19

PH

58

Fig. 5.20

72

line 7

PH , quality A.

pH pH , PE = 0 atm, quality A.

78

Fig. 6.22

SPS

Clay

78

Fig. 6.23

SPS

Clay

82

Fig. 6.26

to paper

to Cellophane

82

line 1

cellophane

Cellophane

83

Fig. 7.1

(PPS 1O )

(PPS lO , J.tm)

83

line 15

10

84

Fig. 7.2

(PPS 20 )

84

line 2

86 91 91

(PEr 2

+ 2'Ycos(})

kg/m 2 kg/m2

(PEr 2 + 2r'Ycos(})

10 kg/cm2 (PPS 20 , J.tm) 20 kg/cm2

line 16

20 square time

square root time

ref. 11

Paper of

Paper Magazine of

ref. 14

Svensk papperstidning

Svensk Papperstidning

Studies of water transport in paper during short contact times

STUDIES OF WATER TRANSPORT IN PAPER DURING SHORT CONTACT TIMES

Pekka Salminen

Laboratory of Paper Chemistry Department of Chemical Engineering Abo Akademi 1988

ISBN 951-649-459-5

Painola Abo 1988

PREFACE This study has been carried out at the Laboratory of Paper Chemistry at Abo Akademi during the years 1985-1988. I am deeply indepted to the head of the Laboratory, Professor Dan Eklund for his invaluable aid, criticism and continuous encouragement throughout the course of this work. I also wish to express my appreciation to my colleagues at the Chemical Engineering Department for many inspiring discussions and valuable advice. My special thanks go to Mr M. Stal, M. Se., and Mr. P. Sandas, M. Se, for the assistance provided in the experimental work. I am also indepted to Ms. M. Arponen, Valmet Paper Machinery Inc., for drawing the figures in the manuscript. The financial support from The Academy of Finland, Metsa-Serla, and Magnus Ehrnrooths Stifte;se is gratefully acknowledged. I also express my gratitude for the means provided by The Research Institute of the Abo Akademi Foundation for printing the dissertation. Finally, my deepest thanks go to my wife Susanne for her understanding attitude during the work.

Abo, June 1988 Pekka Salminen

Contents

9

CONTENTS SYMBOLS AND SOME DEFINITIONS ................................. 11 1. INTRODUCTION ........................................................ . 15 2. THE THEORY OF WATER TRANSPORT .......................... 17 2.1 Short introduction to liquid transport in porous material .................. 17 2.2 Water transport in paper ................................................... 19

3. FURTHER CONSIDERATIONS ON THE MECHANISM OF WATER TRANSPORT IN PAPER .. ., ....... .,., ........ .,.,.,.,.,.,., ... ., .,23 3.1 Dynamic character of capillary pressure ., .... ., ..... ., .... ., ..... ., .. .,., .. 23 3.1.1 Effect of penetration velocity on the advancing contact angle ........ 24 3.1.2 Interactions ahead of the liquid front between water and the fibre wall ......................................................................... 25 3.2 Counter pressure of air ..................................................... 27 3.2.1 The air is compressed ................................................. 27 3.2.2 The air is removed .................................................... 29 3.3 Expansion of fibre network ................................................. 30 3.3.1 Effect on the transport velocity of the liquid front ................... 31 3.3.2 Effect on the cross section of the penetrating liquid front ............ 31 3.4 Liquid transport through vapour phase .... ., .... ., . .,.,.,., . .,.,.,.,.,.,., 31 3.5 External pressure ........................................................... 33 4. MEASUREMENT OF LIQUID SORPTION ......................... 35 4.1.1 Static systems ........................................................ 35 4.1.2 Dynamic systems ..................................................... 36 4.2 The new experimental method ............................................. 37

10

Studies of water transport in paper during short contact times

5. THE INFLUENCE OF LIQUID CHARACTERISTICS ON THE TRANSPORT RATE ........................................................ 41 5.1 External pressure ........................................................... 41 5.2 Temperature ................................................................ 44 5.3 Viscosity .................................................................... 48 5.4 Surface tension ............................................................. 50 5.5 Salt concentration .......................................................... 55 5.6 pH of the liquid ............................................................ 57

6. THE INFLUENCE OF PAPER CHARACTERISTICS ON THE WATER TRANSPORT ...................................................... 59 6.1 The mechanical pressure exerted on the paper ............................. 59 6.2 Grammage .................................................................. 61 6.3 Beating ..................................................................... 64 6.4 Calendering ................................................................. 66 6.5 Sizing ....................................................................... 68 6.6 Self-sizing ................................................................... 70 6.7 Moisture content ........................................................... 74 6.8 Filler addition .............................................................. 77 6.9 Surface chemistry and paper structure enhancing water transport through vapour phase ............................................................... 79 6.9.1 Capillary pressure opposes liquid movement .......................... 79 6.9.2 The pore structure is not of capillary dimensions .................... 81

7. CONCLUDING REMARKS ON WETTING OF A PAPER SURFACE ............................................................................ 83 7.1 Extrapolation of contact time to zero ...................................... 83 7.2 The concept of wetting delay ............................................... 85

8. SUMMARY ................................................................ 87 REFERENCES ................................................................ 91

Symbols and some definitions

SYMBOLS AND SOME DEFINITIONS

Symbols Roman letters

A a

b c

D dc/dx E

f h Kt k

kA kR kp L LI/2

1 Mt

Moo N P pvap pair

pc

PF

PD PE PO PI r

surface area length of slit opening width of slit opening concentration diffusion coefficient concentration gradient of vapour fractional degree of saturation function pore length slope of penetration curve at time t constant parameter absorption coefficient surface roughness coefficient characteristic air transport coefficient length half-thickness of a specimen penetration depth of liquid front total amount of diffusing substance at time t total amount of diffusing substance after infinite time number of capillaries per surface area pressure vapour pressure pressure drop due to air transport pressure difference across a curved liquid surface pressure drop due to liquid flow mechanical pressure external pressure atmospheric pressure air pressure in a capillary capillary radius

11

Studies of water tmnsport i.n paper during short contact times

12

u

V VG

V/A v LlZ z

effective capillary radius wet capillary radius dry capillary radius thickness of a molecular interaction zone temperature time wetting delay measurement time in a sorption experiment molecular interaction time web velocity liquid volume measurement volume in a sorption experiment absorbed liquid volume per unit area of paper surface transport velocity of a liquid front increase in paper thickness wall thickness of liquid applicator

Greek letters a

'Y

'YE 'Yt

.,.,T

o Os OD

coefficient for velocity dependence of contact angle surface tension of liquid equilibrium surface tension dynamic surface tension at surface of age t viscosity of liquid at temperature T contact angle between liquid and solid static contact angle dynamic contact angle

Some definitions Capillary pressure: Pressure difference across a curved liquid surface in a capillary. Transport velocity of a liquid front: The velocity at which a liquid front moves in a capillary. Transport rate of liquid: Amount of liquid absorbed by paper per unit time. Zero pressure liquid transport: Liquid transport under the influence of no external pressure.

Symbols and some definitions

13

Pressure penetration: Liquid transport under the influence of an external pressure (unless otherwise indicated, PE = 0.5 atm). Hydrophilic character of paper: An expression used to characterize the surface chemistry of the fibre matrix with reference to the rate of capillary water transport in paper. A hydrophilic paper is here defined as one having a pore system which is saturated in less than one second in the sorption apparatus used, whereas the corresponding contact time to saturate a hydrophobic paper is of the magnitude of at least ten seconds. Washburn equation: Equation (2.5).

Introduction

15

1. INTRODUCTION It has been recognized for a long time that water transport is an important consideration in the use of paper. For example, the use of paper as a packaging material often requires special water sorption characteristics. The interaction between water and paper in various converting processes also emphasizes the need to understand the water transport process. Today, the transport of aqueous liquids in paper can be regarded as one of the key factors in the control of coating, surface sizing and printing processes. The penetration of the water phase of aqueous coating colours into paper causes expansion of the fibre matrix and a reduction in strength properties. This lowers the quality of the coated paper and may lead to runnabil~ty problems. On the other hand, an increase in the solids content of the colour often causes rheology related problems. In surface sizing, the desired penetration depth of the size is usually a compromise between strength properties and cost. In printing technology, the offset process and the increased use of water-based printing inks has raised various water sorption related problems as, for example, insufficient dimensional stability and runnability. Different pressurt and contact time situations exist in converting processes for paper and board, and the effect of these factors on the transport of aqueous liquids needs to be known. In addition, the succesful control of water penetration in industrial wetting processes requires knowledge of the sorption determining variables of the liquid as well as of the paper. The primary objective of this work has been to obtain a basic understanding of the water transport mechanisms. The experimental work is therefore limited mainly to variables which are directly related to the fundamental aspects of the sorption process. The practical aspects of the water transport have been discussed elsewhere (1-6) by the author, and parts of the present work have been published in that connection. However, in order to get a more unified presentation of water transport fundamentals, the published material has been revised and supplemented to come out in the present form.

17

The theory of water transport

2. THE THEORY OF WATER TRANSPORT Water transport in paper has been a subject of numerous publications and a complete discussion of the voluminous literature is not within the scope of this work. However, an attempt is made to present a condensed and critical discussion of the studies of current interest. This discussion will then give the background for the theoretical considerations put forward in the next chapter.

2.1 Short introduction to liquid transport in porous material A prerequisite for liquid transport in porous material is the presence of a driving potential. The most common examples are capillary pressure, external pressure, vapour pressure, concentration gradient and temperature gradient. Several driving potentials may be present at the same time which makes the transport mechanism rather complex. The classical liquid transport model is based on the work of Lucas (7) and Washburn (8). In this model it is assumed that liquid penetrates in an open pore with a constant pore radius and that the pressure drop due to air transport and inertial effects are negligible. The driving potential is the sum of the external pressure, PE, and the pressure difference across a curved surface, in the present work referred to as capillary pressure, pc. The capillary pressure has been expressed with the Young-Laplace equation:

(2.1 )

Pc where, = surface tension of the liquid, () the solid phase and r = pore radius.

= contact

angle between the liquid and

These pressures are opposed by the pressure drop due to liquid flow, PF'

(2.2) where 'f/ = viscosity of the liquid, I velocity.

= penetration distance, v = dll dt = penetration

18

Studies of water transport in paper during short contact times

The pressure equilibrium at the liquid front will then be:

(2.3)

PE+PC which gives PE

+ -2,eosO -1'-

81Jl(dlldt) 1'2

(2.4)

The solution to this differential equation states that the penetration distance is proportional to the square root of the time, Vi:

(2.5) Henceforth, the term "classical capillary transport model" will be used to refer to the modification of this equation in which the external pressure is taken to be zero. If the liquid penetrates in a porous material with N parallel capillaries per surface area A, then the Washburn equation can be expressed in the following form:

V A

(2.6)

In air, a vapour phase is formed above the liquid surface. Therefore, this vapour phase can be the cause of liquid transport as well. When the concentration gradient of the vapour, deldx, is the driving force, Pick,s second law gives the relationship between the rate of concentration change, del dt, and the concentration gradient: de dt

(2.7)

where D is the diffusion coefficient. Assuming that the diffusion coefficient is a constant, the suggested appropriate solution (9) to this differential equation states that the amount of liquid absorbed at the early stage of the diffusion process is proportional to the square root of time:

E

(2.8)

where Mt denotes the total amount of diffusing substance at time t, Moo the corresponding quantity after infinite time, E the fractional degree of saturation, and Ll/2 the half-thickness of the specimen.

The theory of water transport

19

2.2 Water transport in paper The following four mechanisms for water transport in paper have been proposed by Nissan (10): • Diffusion transport of vapour in the pores • Capillary transport of liquid in the pores • Surface diffusion in the pores • Water transport through the fibres Of these, Verhoeff, Hart and Gallay (11) considered capillary penetration in the pores and diffusion transport within the fibres to be the most important. They suggested that the water transport in unsized sheets is so rapid that the two mechanisms could not be separated, but concluded that diffusion within the fibres is the primary transport mechanism in sized paper grades. The experimental results suggested that the rate of the transport process increases with beating, but is unaffected by calendering and viscosity of the liquid. Reaville and Hine (12), on the other hand, suggested that the rate of water transport is determined by surface diffusion taking place ahead of the liquid front. The primary transport process is regarded as a condensation of the vapour phase in the hydrophilic parts of the pore walls, followed progressively by reevaporation and condensation up the pore. Simultaneous with this mechanism is a lateral penetration into the fibre. Water transport in sized papers has also been studied by Wink and Van den Akker (13). Their conclusion was that the rate of penetration is governed by a local decrease in the contact angle ahead of the liquid boundary. The process consists of a molecular adsorption from the liquid and vapour phases to the fibre wall. The water penetration is associated with changes in the fibre structure and surface, caused by condensation of vapour and water transport into the fibres. It was suggested that the liquid penetration is a linear function of the contact time between water and paper, because the molecular processes ahead of the liquid front are the rate determining step. The linear correlation was verified by means of a fluorescence size test. It was also found that the viscosity of the liquid did not affect the penetration rate within the viscosity range studied. This result supports the conclusion that the rate of water penetration is not determined by the simple pressure equilibrium between pressure drop due to liquid flow and constant capillary pressure as could be deduced by the Washburn equation. The slow measurement technique did not allow measurements on unsized papers.

20

Studies of water transport in paper during short contact times

Bristow (14) was able to measure water penetration at considerably shorter contact times. The non-linearity between the obtained sorption values and the square root of contact time was explained by the concept wetting delay, i.e. there is a wetting time, t k , before the water starts to penetrate into the paper. After this wetting delay, the water sorption was suggested to follow the square root relationship indicated in the Washburn model. An extrapolation of the water sorption curves to zero contact time resulted in values that noticeably exceeded zero, and which correlated well with the surface roughness of the papers used in the study. It was therefore suggested that the extrapolated sorption volume corresponds to the extremely rapid filling of the surface roughness volume of the paper, k R • The relationship between water sorption and contact time could hence be expressed as:

V A

(2.9)

where kA is the absorption coefficient of the paper. The water sorption curves presented later (15-19) also give a visual impression of slower penetration in the beginning of the sorption process, provided that the sorption values are plotted on the square root time scale. However, sorption curves on a linear time scale (20) do not support the wetting delay theory. The physical significance of the wetting delay is not well understood. Generally, a contact between two plane surfaces is formed instantaneously when the attraction forces are higher than the repulsive. The wetting delay could thus refer to a situation where this condition is not valid. However, Zisman (21) has indicated that there is always some adhesion between a liquid and a solid phase. In other words, the criteria for wetting of a plane solid surface is always met and the wetting of a plane surface is instantaneous. The wetting delay has also been suggested (15,22) as being the time required to fill the porous structure of the paper surface. This explanation is trivial; it is obvious that time is needed to move a liquid volume from one place to another. On the other hand, this movement is governed by the same mechanisms as the water movement within the paper. It can be regarded as flow from the bulk of the liquid to the paper and can be seen on the liquid penetration curve. It was previously indicated that Bristow (14) showed this flow to be extremely rapid. Lepoutre, Inoue and Aspler (23) refer to the work of Kaelble (24) when they present an explanation for the wetting delay. They assumed that the water molecules diffuse into the fibre, and lower the glass transition temperature of the amorphous cellulose in the surface, thereby allowing polar hydroxyl groups to rotate outwards. As a result, the fibre surface energy is increased and the interfacial energy decreased. The time required to increase the capillary pressure in this way corresponds to the wetting delay. It is, however, obvious that a similar mechanism has to precede the water transport

21

The theory of water transport

within the pore system of the paper as well. If the mechanism takes place in a limited zone ahead of the liquid front, the conclusion of Wink and Van den Akker is reached. In this case, the localized reduction of the contact angle ahead of the liquid front determines the capillary pressure, and the pressure drop of liquid flow is of minor importance. As discussed previously, the liquid sorption will then be a linear function of the contact time. Bristow has shown (25,26) that the influence of swelling must be taken into account when water transport phenomena in cellulosic material is discussed. He separated the total water sorption into a pore sorption part describing the transport in the existing pores, and a fibre sorption part depending on the water taken up by the fibre material. It was suggested that the fibre sorption component can be estimated from thickness swelling data. Experimental results were analysed in relation to an idealised parallelogram with the liquid absorption plotted against the increase in sheet thickness. The results indicated that in unsized papers water is transported simultaneously in both pores and fibres, whereas diffusion within the fibres predominates for water transport in sized fibre systems. Also Hoyland (27) explains the differences between the experimental data and Washburn equation with swelling of the fibre matrix. The total water penetration depth is influenced by the water penetration in the fibres and thus a correction factor has to be added to the Washburn equation. The transport of water in the pores is believed to be determined by various diffusion-governed processes, which decrease the contact angle to zero. These processes are vapour diffusion, surface diffusion and water penetn.tion into the fibres. The following mathematical model for the penetration of water into paper was suggested:

k/::,.Z

(2.10)

where /::,.Z is the increase in the thickness at time t, and k is a constant. The model is unquestionably a progress in the theory of water transport. It has, however, some uncertainty: • If the penetration process is controlled by diffusion dependent processes, as is assumed, the mathematical model of Washburn is not feasible. This model has been derived for the pressure equilibrium between (~onstant capillary pressure and pressure drop due to liquid flow. If the transport velocity is regulated by contact angle determining processes ahead of the liquid front, the penetration process is, as will be discussed in chapter

22

Studies of water transport in paper during short contact times

3.1.2, proportional to time in a higher power than 0.5, and the penetration process is controlled by factors not included in the Washburn model. • The pore radius is undoubtedly dependent on the degree of fibre swelling, and it cannot be taken as a constant. The influence on the pore radius concurrently causes changes in the pore volume and the pressure drop due to liquid flow. The concept of dynamic capillary pressure has been discussed by Schubert (28). Assuming that the liquid transport takes place with a sharply defined wetting front, an approximation equation and experimental data is given for the relationship between the dynamic capillary pressure and the mean transport velocity. Although the experimental work is carried out with materials other than paper, this study suggests that the rate of capillary transport in paper is not adequately predicted by the simple equilibrium between static capillary pressure and pressure drop due to liquid flow. The influence of various dynamic contact angle determining processes has to be considered as well.

Further considemtions on the mechanism of water tmnsport in paper

23

3. FURTHER CONSIDERATIONS ON THE MECHANISM OF WATER TRANSPORT IN PAPER The aim of this chapter is to expand the discussion of the water transport mechanisms to include aspects that have received little attention in the context of water transport in paper. The main objective is to explain the differences between the actual water penetration in paper and that predicted by the classical capillary transport model. These differences are suggested to be due to the omission of the following factors: • Dynamic character of the capillary pressure • Counter pressure of air • Expansion of the fibre network • Liquid transport through the vapour phase • External pressure

3.1 Dynamic character of capillary pressure In the mathematical models for water transport in paper presented in the literature it is assumed that the contact angle between water and the fibre wall as well as the capillary pressure are independent of time and penetration velocity. However, the dynamic capillary pressure is probably influenced by molecular processes at the wetting zone and ahead of the liquid front, Fig. 3.1.

Fig. 3.1 Schematic view of liquid front in a paper pore.

24

Studies of water transport in paper during short contact times

The causes of the time and velocity dependence of the capillary pressure can thus be divided into two groups: (1) Effect of penetration velocity on the advancing liquid front and (2) the interactions between water (vapour phase) molecules and fibre wall ahead of the liquid front.

3.1.1 Effect of penetration velocity on the advancing liquid front The experimental work of Rose and Heins (29) clearly showed the velocity dependence of an advancing contact angle during liquid transport in a capillary. A linear relationship between transport velocity and COSOD was obtained for the liquid penetration. Cherry and Holmes (30) used the Eyring theory of viscous flow to propose a mechanism for the dynamic wetting process. This process is considered to be an activated flow process, where the activation energy is dependent on liquid viscosity and surface tension forces. Hoffman suggested (31) that the forming of the dynamic contact angle involves motion of molecules from one preferred site to another at the interface between liquid, gas and solid phases. The speed at which the contact line moves across the solid substrate is enhanced by the imbalance of energy, which is proportional to the difference between static and dynamic contact angles, (COSOD - cosOs). Using the Eyring model, a relationship between the advancing velocity and the difference between static and dynamic contact angles is obtained. A similar theoretical derivation has been made by Strom (32). He concludes that the effect of liquid viscosity and transport velocity on the dynamic contact angle is established and suggests the following general formula:

(3.1 ) where v is transport velocity, a is a coefficient including the effect of surface flow and unknown factors and A is the surface occupied by one mole. The experimental work on the concept of dynamic contact angle has been done with comparably viscous liquids and systems having a well defined geometry. The theories have not been applied to water transport in paper. Hence, at this stage, the velocity dependence of the capillary pressure cannot be treated mathematically. Nevertheless, considering the pressure equilibrium between the dynamic capillary pressure and the pressure drop due to liquid flow, the following relationship between penetration depth and time can be proposed:

0.5::; k < 1.0

(3.2)

If the dynamic contact angle is equal to the static contact angle, the capillary pressure is independent of the transport velocity and the penetration depth is proportional to the square root of the contact time between paper and liquid. On the other

Further considerations on the mechanism of water transport in paper

25

hand, if the dynamic contact angle increases with penetration velocity, the power of the rate function is higher than 0.5. With increasing velocity dependence of the dynamic contact angle, the exponent k approaches 1.0. In addition, the theoretical models suggest that viscosity also has an influence on the dynamic contact angle. The dynamic capillary pressure is generally reduced by the viscosity of the liquid.

3.1.2 Interactions ahead of the liquid front between water and the fibre wall The dynamic capillary pressure is also influenced by sorption of water molecules from the vapour phase on to the fibre wall, as well as by surface chemical changes in the fibres caused by the water molecules diffusing in the fibre network ahead of the liquid front. These processes are time dependent and will therefore contribute to the dynamic character of the capillary pressure. Diffusion will be discussed below in more detail, but its effects on the dynamic capillary pressure between the liquid phase and the fibre wall will be considered briefly in this context. Luner and Sandell (33) have shown that the contact angle between water and cellulose is dependent on the air humidity. With increasing humidity, water molecules adsorb on the cellulose surface and a mono- or multilayer of water forms on the cellulose surface. As a result, the contact angle between the cellulose surface and liquid water is decreased. A similar adsorption from vapour phase to fibre surface may influence the contact angle even during dynamic conditions III a paper pore (3,13). The changes in the chemical structure of the fibre surfaces caused by the water molecules diffusing ahead of the liquid front are probably more complex. The motion in the fibre surface allowing polar hydroxyl groups to rotate outwards (23) has already been discussed (see chapter 2.2), but other modifications in the fibre surface may influence the dynamic contact angle as well.

It should be pointed out that the magnitude of the discussed interaction between water molecules and the fibre surface is likely to be dependent on the number of molecules ahead of the liquid front. As a consequence, the effect of molecular interactions ahead of the liquid front is strongly dependent on the vapour pressure and temperature of the liquid. In addition, as mentioned above, the effect of the molecular interactions on the dynamic capillary pressure is certainly affected by the interaction time between the water molecules and the fibre surface. In order to evaluate this interaction time, tA, the thickness of the interaction zone has to be determined. Two cases can be distinguished:

26

Studies of water transport .in paper during short contact times

• Sharply defined interaction zone • Diffuse interaction zone 1. Sharply defined interaction zone

If the thickness of the interaction zone, s, is constant and small in comparison to the paper thickness, the interaction time is dependent on the penetration velocity of the liquid front, v:

s v

=

(3.3)

The model is probably valid for molecule adsorption from the vapour phase to the fibre surface. Eklund and Salminen (3) have discussed this process assuming that the a~sorption is of the Langmuir type. However, the validity of the Langmuir model is restricted, and the relationship between the surface concentration and capillary pressure unknown. Therefore, only the boundary values for the power of the velocity function could be determined:

=

f(tk)

0.5::; k::; 1.0

(3.4)

When the penetration velocity is determined by the equilibrium between constant capillary pressure and the pr~ssure drop due to liquid flow, the water penetrates into the paper according to the Washburn equation, i.e. k = 0.5. On the other hand, if the interaction between water molecules and fibres ahead of the liquid front is the velocity determining step, the transport rate is independent of the location of the liquid boundary. Consequently, a linear relationship between the penetration depth and the contact time is obtained. This is the case described by Wink and Van den Akker (13) for localized reduction of contact angle from () 2: 90· to () < 90·. For unsized papers, however, the pressure equilibrium between dynamic capillary pressure and the pressure drop due to liquid flow probably corresponds to a rate function which is between these two boundary cases.

If the penetration velocity is high (hydrophilic paper), the time of interaction, tA is short, and the pressure drop due to the liquid flow is high. As a result, the exponent k approaches 0.5. At low penetration velocities, the effect of the pressure drop is diminished and the importance of the interaction between the water molecules and the fibre surface is accentuated. The relationship between penetration depth and contact time becomes more linear.

Further considerations on the mechanism of water transport in paper

27

2. Diffuse interaction zone

If the thickness of the interaction zone is not constant or it is of the same order as the paper thickness, the dynamic character of the capillary pressure is not dependent on the transport velocity of the liquid front only, but also on the contact time between the liquid and the paper. In this case, the equation (3.3) is not valid, and no maximum value for the power of the rate function can be determined:

=

f(tk)

k

~

0.5

(3.5)

The square root relationship is obtained for constant capillary pressure. Otherwise, the increased time and velocity dependence of the capillary pressure and the diminished role of the pressure drop due to liquid flow increase the power of the rate function in a manner discussed above.

3.2 Counter pressure of air In the capillary transport theories proposed in the literature, it is assumed that the capillary system is open at both ends, and that the pressure drop caused by the air transport can be neglected. This, however, is seldom the case for paper. According to Baird and Irubesky (34), only 1.6 % of the pores in paper are in contact with both sides of the paper. In many practical cases, the air transport is prevented by an impervious surface pressed against the other side of the paper. In addition, during dynamic wetting, the contact area between the paper and the liquid is often restricted by compression causing surfaces under pressure, and air transport in the plane of the paper is prevented. All these factors lead to the concept that air could be trapped in the pore system of the paper causing a counter pressure. Two cases can be distinguished: • The air is compressed • The air is removed

3.2.1. The air is compressed This model is founded on the assumption that the trapped air in the closed pore system, Fig. 3.2, causes a counter pressure which is a function of the penetration

28

Studies of water transport in paper during short contact times

depth of the liquid.

T I I

r I

I

1. ~

-----------1

---------- h

Fig. 3.2 Schematic view of pressure balance in a closed pore Neglecting the inertial and slip effects, a pressure balance at the liquid front gives:

po + PE + Pc

=

PF +Pl

(3.6)

where Po = atmospheric pressure, PE = external liquid pressure, pc = capillary pressure, PF = pressure drop of liquid flow and Pl = air pressure in capillary. Combination with the laws of Boyle, Hagen-Poisseule and Young-Laplace

=

Pl

(3.7)

po

8'fJvl

PF

Pc

h h-l

(3.8)

~

=

(3.9)

where h is the length of the pore gives (35) an equation of the form:

(3.10) where kl - k6 are known functions of" cosO, r,

ST,

po, PE and 'fJ.

Further considerations on the mechanism of water tmnsport in paper

29

It is obvious that when the surface tension forces are the only driving forces in the system, the counter pressure caused by the compressed air soon exceeds the capillary forces. Even with the maximum capillary pressure (cose = 1), the equation states that only 59 % of the pore volume (r=l /-lm) can be filled with water. The penetration volume is of course increased when the external pressure is increased, but never reaches saturation. It can be concluded that the counter pressure of compressed air is of such a magnitude that the influence of air must follow some other model. The pressure penetration rate, on the other hand, may be influenced by the compressed air. 3.2.2. The air is removed The derivation of this model is based on the assumption that the air is removed in the x- and y-directions, i.e. perpendicular to the z-direction of the water penetration, Fig. 3.3. In this case, it is assumed that the pressure drop due to air transport is uninfluenced by the place of the liquid boundary in the pore system. I I

L I I

1

Fig. 3.3 Schematic view of air removal through a channel Assume that the air is removed through a channel with the length L and the area A. Darcys law gives:

V t

where

f

=

k

A

L

pair

(3.11 )

is the air flow and k is a constant.

v

T pair

(3.12)

(3.13)

30

Studies of water transport in paper during short contact times

PI

=

Po + Pair

(3.14)

The pressure equilibrium at the liquid front

(3.15) gives

=

.jkJ,r8 + 1677(PEr2 + 2'YcosO)t - kpr 4 877

(3.16)

where k p is a constant characterizing the pressure drop due to air transport in the system. If the pressure drop due to air transport is low, i.e. kp is small, equation (3.16) converts into the Washburn equation. At high values of kp , the pressure drop due to air transport will dominate, and a more linear relationship between water transport and time is obtained. In addition, this model gives a lower penetration velocity for the liquid front than the models neglecting the pressure drop due to air transport.

3.3 Expansion of fibre network It is well known that the presence of water influences the dimensions of a cellulosic fiber matrix. Penetration of water molecules into the fibre wall causes breaking of the intrafibre hydrogen bonds and dimension changes of the fibre. On the other hand, debonding of the interfibre hydrogen bonds faciliates modifications in the pore system between the fibres. Skowronski, Bichard and Lepoutre (36-39) have showed that these processes are closely linked with the redistribution of the internal stresses originating from the preceeding papermaking stages. The expansion of the paper can influence the water transport rate in two different ways: • by the effect on the transport velocity of the liquid front • by the effect on the cross section of the penetrating water front

Further considerations on the mechanism of water transport in paper

31

3.3.1. Effect on the transport velocity of the liquid front It has been suggested above in chapter 3.1 that the capillary transport rate is primarily determined by the equilibrium between the dynamic capillary pressure and the pressure drop due to liquid flow. These two pressures are dependent on the capillary dimensions and thus influenced by the expansion of the fibre network. Chatterjee proposed (40) that the pressure drop due to liquid flow is determined by the "wet" pore radius, rw, whereas the capillary pressure is characterized by the dry capillary radius, rD. If the pore system reacts instantaneously to water, the square root relationship between time and penetration depth would be valid. However, the pore radius in the Washburn equation must in this case be substituted by the effective radius, rE:

(3.17) On the other hand, if the capillary transport velocity primarily is determined by molecular interaction ahead of the liquid front between water and fibre wall , the effect of fibre network expansion and fibre sorption on the transport velocity of the liquid front would be negligible.

3.3.2. Effect on the cross section of the penetrating water front The amount of liquid absorbed by a paper is not only dependent on the transport velocity, but also on the cross section of the penetrating water front. Therefore, all changes in the pore system will influence the amount of water absorbed by the paper. Water penetration into the fibres, i.e. fibre sorption, also has an influence on the absorbed amount of water. Even if the amount of absorbed water is always influenced by the expansion of the fibre network and the fibre sorption, the power of the rate function between the amount of absorbed liquid and time is unaffected if the fibre network expands instantaneously.

It is however doubtful if the expansion of the fiber network can be regarded as instantaneous during the initial stages of penetration. The time dependent expansion of the fiber network and fibre sorption is likely to increase the power of the rate function.

3.4 Liquid transport through vapour phase The driving potential for capillary transport is the dynamic capillary pressure. According to the Young-Laplace equation, the capillary pressure is negative when the

32

~

>

Studies of water tmnsport in paper during short contact times

contact angle between the liquid phase and the solid exceeds 90 degrees, and consequently the capillary pressure then opposes the transport of liquid in the pore system. In this case, the water transport cannot be due to capillary pressure. Water transport via the vapour phase, on the other hand, is independent ofthe surface tension forces between the liquid and fibres. In hydrophobic papers, water transpor~ :1 via the vapour phase may therefore be the main transport mechanism.

V)

A review of the studies made on the steady state water vapor transport in paper has been presented by Corte (41). It is generally recognized that surface diffusion plays an important part in this transport process. The water molecules do not leave the surface of the fibres but move from one hydrophilic spot to another. The adsorption of water vapour on cellulose is the main mechanism that controls the movement of water vapor through paper. The unsteady state water vapor transport 10 paper is not well understood. In wood science, however, several detailed studies of this transport process can be found. Stamm concluded (42) that diffusion in wood may occur as vapour transport through the coarse capillary structure or as bound water through the cell walls. The question of the true driving potential for diffusion of bound water has been a subject for several investigations. For example, in addition to the concentration gradient of the Ficks second law, a spreading pressure gradient (43) and a chemical potential gradient (44) have been proposed as the true driving forces for bound water transport. Osmotic pressure induced water transport has also been discussed in the literature (45-49). Scallan concluded in a review (46) that the osmotic pressure differential between the fibre wall and the external medium may be overcome only by additional water being drawn into the cell wall. This water .transport into the fibres, referred to as electrolytic swelling, is thus dependent on the difference in total ion concentration between the inter~or and exterior of the fibres. The rate of osmotic pressure-induced water transport is then probably controlled by a complicated balance between the acidic group content, nature of counter ions, pH and ionic strength of the external medium. It is easy to comprehend that the unsteady state diffusion of water in paper is complicated by factors similar to those in water transport in wood. Diffusion can take place in the pores, on the fibre surfaces or within the fibres. The driving potentials for these transport mechanisms may be different and it is useless at this time to suggest any particular function for the diffusion transport. Practical experience, however, suggests that the diffusion rate is increased with increasing vapour pressure and decreasing moisture content in paper. The diffusion takes place from a higher moisture concentration to a lower and its role is accentuated at high temperatures.

Further considerations on the mechanism of water transport in paper

33

3.5 External pressure In many industrial wetting processes, the water penetrates into the paper under the influence of a considerable external pressure. Surprisingly, this driving potential has received only little attention during the many decades of study of water transport phenomena. In most investigations, the external pressure is not considered at all. During capillary transport under the influence of an external pressure, the driving potential is the sum of dynamic capillary pressure and external pressure. Of course, external pressure does not increase the dynamic capillary pressure. On the contrary, an increased penetration velocity caused by an increased external pressure will increase the dynamic contact angle between liquid and fibre wall, and hence cause a decrease in the dynamic capillary pressure (see chapters 3.1.1-3.1.2). The capillary pressure determining contact angle can then be higher than 90 degrees, and the external pressure will be the main driving potential. The importance of the molecular interactions ahead of the liquid front is also likely to be reduced during rapid pressure penetration. The pressure drop due to liquid flow, on the other hand, is increased by the transport velocity. At high external pressure, the transport velocity therefore is determined by the pressure equilibrium between external pressure, comparatively constant capillary pressure and the pressure drop due to liquid flow. As the external pressure increases, the importance of surface chemistry related forces diminishes.

It can be suggested that the importance of the factors which complicate the capillary transport theory (see chapters 3.1-3.4) is diminished when the external pressure is increased. The effect of the expansion of the fibre network is lower during the rapid pressure penetration. Water is primarily transported through the pores and the effect of fibre sorption and diffusion is minimized as well. Consequently, the power of the rate function is determined by the pressure drop due to liquid flow and the penetration volume will be proportional to the square root of contact time. At a high enough external pressure, the velocity controlling variables are the viscosity of the liquid and the pore structure of the paper.

Measurement of liquid sorpticm

35

4. MEASUREMENT OF LIQUID SORPTION The systems for the measurement of liquid sorption can be divided into static and dynamic. A static system consists of a stationary paper sample and a liquid applicator, as well as of a system for the measurement of the contact time between the paper and the liquid. Liquid transport into the paper is indicated by the physical changes (weight, fluorescence, reflectance, transmittance, electrical conductivity etc.) caused by the liquid. In a dynamic system, the liquid sorption is determined by the volume of liquid that a moving paper surface takes up from a liquid applicator. The contact time between liquid and paper is a function of the transport velocity of the paper and the dimensions of the liquid applicator. A short review of the most frequently used water sorption measurement systems is presented below. This is followed by a description of the experimental method used in this study.

4.1.1 Static systems The Cobb-test (50) is a practical method for determining the liquid uptake of a paper under a time period longer than 30 s. Because the main interest in water penetration is fon.sed on considerably S'horter contact times, the Cobb-test is used mainly for testing the hydrophobicity of paper and board. The fluorescencing effect of some dyes (13) has been utilizied by Wink and Van den Akker. The dye is applied on the paper surface and the concentration dependent intensity of the fluorescence is measured. The water absorptivity of the test paper is indicated by the time needed to detect a change in the intensity of the fluorescence. The method has been used for water sorption studies in the contact time range of IO-lOO s. A method for the optical measurement of water transport in paper was first described by Windle, Clark, Climpson and Beazley (51-53). The penetration depth of water in paper is calculated from the measured light reflectance data using the KubelkaMunk theory. The water transport can be studied under the influence of a high external pressure (PE = 6.9 MPa) as well as under the influence of capillary forces only. The contact times between paper and liquid can be as low as 3u-·50 ms. Anderson and Riggins (20) have interfaced a similar apparatus to a data acquisition system designed around a microcomputer. This has enabled water sorption studies over millisecond time intervals. The liquid uptake of a paper can be determined at

36

Studies of water tmnsport in paper during short contact times

different temperatures and humidities, and the computer controlled liquid delivery system is capable of handling a variety of liquids, including aqueous clay slurries. Hoyland (27) has placed several pairs of chrome/nickel electrodes into a thick laboratory sheet during its formation. A low voltage is applied to each pair of electrodes, and the current in each circuit is detected by a multi-channel recorder. When water is applied to one side of the sheet, the advancing water front successively causes a rapid rise'of current in each circuit. The determination of the depth of each elec. trode pair by a micrometer screw makes it possible to obtain a relationship between the depth of water penetration and the contact time. This apparatus can also be used to study the swelling of a paper.

4.1.2 Dynamic systems In the "nip spreading" apparatus described by Wink and Van den Akker (54), a given volume of liquid is applied in the nip between a rubber roll and a glass plate. A paper sample is transported through this pip under the influence of considerable hydrodynamic forces. The liquid volume taken up by the paper is determined by these hydrodynamic forces as well as by the liquid absorptivity of the sample. The apparatus of Sweerman (55) has been a model for many subsequent liquid sorption systems. In this method, the paper sample is mounted on a wheel rotating against a liquid applicator of known dimensions. The liquid flow through the applicator is determined by injecting a small air bubble into a capillary. According to Sweerman, the pressure drop due to liquid flow in this capillary is so high that it must be compensated by an external pressure. Determination of this external pressure is reported to be time consuming. The method of Hawkes and Bedford (56) is similar, but the paper sample is placed on a plane support, and the liquid applicator is drawn with a fixed velocity over this sample. Instead of measuring the liquid flow through the applicator, the length of the liquid track of a known volume is measured. In 1967 an apparatus was presented by Bristow (14), which has been used succesfully in several studies. A paper sample is fixed onto the circumference of an aluminium wheel and a known quantity of liquid is applied from a liquid applicator directly above the wheel. The length and the width of the liquid track and the liquid volume have to be known for the calculation of the liquid sorption. The contact time between the paper and the liquid is obtained from the relationship:

t

=

b u

(2.11 )

where t is the contact time, b is the width of the slit opening and u is the transport velocity of the paper.

37

Measurement of liquid sorption

The Bristow wheel can be driven at nine different velocities and the contact time varied from 0.01 s to 2 s. Later, Lyne and Aspler have developed the apparatus to enable water sorption studies at still lower contact times.

4.2 The new experimental method The design of the new apparatus for the liquid sorption measurement is based on the ideas of Sweerman (55), Hawkes and Bedford (56) and Bristow (14). The apparatus was designed with the aim measurements to be made at elevated external pressures and liquid temperatures as well as at atmospheric pressure and room temperature. In addition, the objective has been to enlarge the contact time range. The apparatus consists of a liquid applicator with a slit opening, a system for the measurement of liquid flow through the slit opening, a backing roll, a system for the measurement and adjustment of the web velocity, a conditioning unit and a rewinding system for the paper web. Fig. 4.1 illustrates the main characteristics in the liquid flow measurement system.

151 111 11.)

~

b

131 I

I

I

I

I

I

121

Fig. 4.1 System for measuring water sorption. (1) Backing roll, (2) Liquid applicator, (3) Burette, (4) Reservoir, (5) Reservoir for filling, (6) Three-way valve.

The liquid applicator (2) is made of Teflon and the mechanical pressure which it exerts on the paper can be varied by the means of weights. The standard mechanical pressure in the pressurized water sorption studies was 380 kPa. The length of the slit opening across the liquid applicator is 50.0 mm and the rim in contact with the paper is 2.1 mm wide. Three different liquid applicators have been manufactured and the width of the slit opening can thus be chosen to be 0.95, 1.85 or 3.80 mm.

38

Studies of water tmnsport in paper during short contact times

In order to obtain perfect contact between the liquid applicator and the paper, the final grinding of the Teflon surface is done in situ after each change of the liquid applicator and adjustment of the mechanical pressure. The test liquid is fed from a 2 L reservoir (4) to the applicator through a burette (3), a 1.2 m long plastic tube with 10 mm radius and a three-way valve (6). The liquid flow through the slit opening is determined by injecting a small air bubble into the burette. The decline of the water level in the water reservoir during one measurement is approximately 0.5 mm and can thus be neglected. The pressure drop in the system can be calculated with the formulas for laminar flow in a tube. Such calculations suggest that the pressure drop is usually below 30 Pa. Therefore, it can be approximated that the external pressure in the liquid applicator is determined by the water level in the reservoir. However, the pressure at the paper surface may also be influenced by the counter pressure of air. As discussed previously, liquid penetration into paper requires removal of air from the system. During a long measurement at zero pressure, at very high speed and under very high mechanical pressure, when the air transport is rendered more difficult, air can therefore be accumulated at the slit opening and the wetting of the paper surface may be incomplete. This counter pressure can be compensated by carefully raising the hydrostatic pressure in the reservoir and thus ensuring zero pressure at the paper surface. In order to study the effect of external pressure, the water level in the reservoir can be raised to a height of 1.0 m. For studies at higher external pressures, compressed air is used and pressure determined by a mercury manometer. Because of a leakage problem, the practical upper limit for the external pressure is determined by the sorption characteristics and surface roughness of the paper, as well as by the viscous properties of the liquid. External pressures in the range of 0.0 - 1.0 atm can be studied. The liquid applicator can be heated by a heating resistor element (400 W / 30 V) and the temperature controlled by a system consisting of a sensor (Pt-lOO) and a PID-regulator. In this situation a magnetic stirrer is also put into the applicator in order to ensure a uniform temperature. The effect of water temperature can be studied up to 90°C. The rubber coated backing roll (1) has a diameter of 0.5 m and is driven by a hydraulic motor. This makes it possible to study water sorption steplessly in the web velocity range of 0.008-95 m/min. The web velocity is measured and controlled by a microcomputer. After each measurement, the required amount of liquid is added to the system from the reservoir for filling (5) through the three-way valve (6). This is done in order to keep the air bubble in the burette and obtain a constant water level in the water

Measurement of liquid sorption

39

reservoir (4). Prior to all measurements, the test roll of paper was conditioned at 50 % R.H. and 23°C by way of slow overnight rewinding. Unless otherwise indicated, groundwood containing LWC base paper and distilled water was used in the sorption experiments. The measured variables are the web velocity, u, and the time, t G , needed for the penetration of a given liquid volume VG into the paper. The length, a, and the width, b, of the slit opening as well as the wall thickness of the liquid applicator, z, are also known. Because the width of the liquid stain on the paper is equal to the length of the slit opening, the liquid sorption per area unit, V/A, is given by the following formula:

V A

(4.1 )

=

The contact time between the liquid and paper surface has been obtained by dividing the sum of the slit opening and the wall thickness of the liquid applicator by the speed of the paper.

t

=

b+z u

(4.2)

It has been shown elsewhere (35) that for most papers the distance b+z, rather than the distance of the slit opening only, b, corresponds to the real wetting distance. In uncertain cases, however, this formula has been experimentally verified by the use of two different liquid applicators having different slit widths and by extrapolation to the true wetting distance. It can be pointed out that formula (4.2) presumably applies for most dynamic water sorption measurement systems. The experimental water sorption curves reported in the literature (14-19) should be recalculated with the suggested formula in order to obtain correct contact time values for comparative studies.

The influence of liquid characteristics on the transport rate

41

5. THE INFLUENCE OF LIQUID CHARACTERISTICS ON THE TRANSPORT RATE In this chapter, the influence of various characteristics of aqueous liquids on the transport rate is discussed. External pressure and liquid temperature are discussed first, because of their great importance for the fundamental understanding of the water transport process. This is followed by the influence of viscosity, which traditionally has been assumed to constitute the retarding forces in water penetration. The liquid variables which can be assumed to be the most important for the driving potentials of water transport are discussed at the end of this chapter.

5.1 External pressure During capillary transport under no external pressure, the dynamic capillary pressure is the main driving potential. As discussed previously, the dynamic capillary pressure is strongly influenced by various molecular processes ahead of the liquid front, which makes the capillary pressure dependent on time and the transport velocity of the liquid front. In addition, it has been indicated that the capillary transport rate is affected by the expansion of the fibre matrix, fibre sorption, counter pressure of air, and diffusion controlled water transport. As a result, the capillary transport under no external pressure is not necessarily proportional to the square root of the contact time. On the contrary, the theoretical models suggest that the power of the rate function often is higher than 0.5, which makes the sorption curves parabolas on a square root time scale. The driving potential for capillary transport under the influence of external pressure is the sum of the external pressure and the dynamic capillary pressure. The external pressure is, of course, not affected by the liquid transport velocity, and the velocity and time dependence of the driving potential is therefore reduced during liquid transport under external pressure. Obviously, the role of fibre matrix expansion, water sorption into the fibres, and diffusion is also diminished during a rapid liquid transport under high external pressure. In this situation, therefore, the transport rate is primarily determined by a pressure balance between the relatively constant driving forces and the pressure drop due to liquid flow. This corresponds to a straight line on a square root time scale. Below, the expression zero pressure transport refers to liquid transport under the

Studies of water transport in paper during short contact times

42

-

50

E .2-

40

'"E

.-. ~

Co

1\1

30

Co

.s '0

~

i

20

~c

01 PE cl PE l;.: PE xl PE PE *'1 PE 0 1 PE

~

J

+1

/10

=

O.~ aim

•= O'i O. aim aim = O. aim = O. aim = 0.$ aim =

O.~

aim

0~4--4~~~~~~~---+~--~~~~~~

0.0

0.2

0.4

0.6

Contact time,

0.8

1.0

1.4

1.2

1.6

Vs

Fig. 5.1 The influence of external pressure on water transport in 52 g/m2 base paper for coating, quality A. 50

-

.-. ~ ..

'"E

Cl)

Co

40

30

&

I 0

20 0 PE IJ PE l;. PE X PE + PE PE 0 PE

c

~

10

Ji! :;, SE

*

....

0 0.0

0.2

0.4

0.6

Contact time,

0.8

1.0

1.2

= • • = • = •

0.0 0.1 0.2 0.3 0.4 0.5 0.6

aim aim aim aim aim aim aim

1.4

1.6

Vs

Fig. 5.2 The influence of external pressure on water transport in 52 g/m2 base paper for coating, quality B.

influence of no external pressure. Liquid transport under the influence of external pressure, on the other hand, is referred to as pressure penetration.

The influence of liquid characteristics on the transport rate

43

Fig. 5.1 and Fig. 5.2 illustrate the influence of external pressure on the water transport in two groundwood containing coating base papers. The results indicate that the curves for water sorption under low external pressure are parabolic in the beginning of the water transport, and that the relationship between water transport and contact time is rather linear. The rate of diffusion and fibre matrix expansion govern the water sorption at extended contact times as the pore system gradually becomes saturated. At high external pressures, however, the water sorption is a relatively linear function of the square root of the contact time. The decisive role of the external pressure on the water transport rate should be noted. In Fig. 5.1, the contact time required to obtain a sorption volume of 18 cm3 /m 2 during zero pressure transport is about 1.0 s, whereas the corresponding contact time for pressure penetration (0.6 atm) is approximately 10 ms, i.e. the water transport rate increases in this case about 100 times when the external pressure is increased to 0.6 atm. It can be concluded that external pressure is the key factor for control of water penetration into the paper in many industrial wetting processes.

40 ~

'"E 35

-

M

E 30

.!:!. ~

a. a.

25

III

.s

20

'C

~ 15

~c

~

10

:g

5

::I

g

0 0 l!. X

+

Paper Paper Paper Paper Paper

"'" "2" "3" "4" "5"

0 0

2

3

4

5

6

7

8

Contact time, s

Fig. 5.3 Zero pressure water transport (linear time scale) in five different papers.

Zero pressure water transport in five papers on a linear time scale is illustrated in Fig. 5.3. The results support the conclusion that the zero pressure water transport often is linearly dependent on contact time, rather than being proportional to the square root of time. Nevertheless, a square root time scale will be used for water transport presentation henceforth. This is motivated by the better accuracy of

44

Studies of water transport in paper during short contact times

reading at short contact times, the suggested square root relationship for pressure penetration, and the tradition of plotting water sorption values on a square root of contact time scale.

5.2 Temperature The temperature dependent factors which may have an influence on the water sorption are at least the viscosity of the liquid, the surface tension and the contact angle towards the paper, as well as the vapour pressure over the water surface. The viscosity and the surface tension of water affect mainly the liquid phase factors, whereas the vapour pressure determines the molecular interactions ahead of the liquid front. The influence of temperature on the viscosity of water is well known, and is illustrated in Fig. 5.4. The connection between surface tension and temperature is shown in Fig. 5.5, and the correlation between vapour pressure and temperature in Fig. 5.6. 1.5 ::: 1.0

c..

e

~. 0.5 VI

ou

VI

:>

00 20 40 TEMPERATURE, "c

60

80

Fig. 5.4 Viscosity of water at different temperatures (57).

~72 :z:

e

S'

68

Vi :z:

.... lt:

64

'""

"0:: :::> VI

60~~~~-L~~~~

o

20 40 TEMPERATURE:C

60

80

Fig. 5.5 Surface tension of water at different temperatures (57).

The influence of temperature on zero pressure water transport in a rather hydrophobic base paper is illustrated in Fig. 5.7. The influence of water temperature is of such a magnitude that changes in the viscosity and the surface tension of the liquid

The influence of liquid characteristics on the transport rate

en ::c 300

~

uj

~200 VI

~

co. a::

~

100

>

0 0-==2:1..0-l.--L40--'-'---J6"""0...J-....J ao TEMPERATURE.

·c

Fig. 5.6 Vapour pressure of water at different temperatures (57). 60

~ 50

E .......

£40 l

:t

30

S

o o A X

T=23'C T=3S'C T-54'C T-69'C

o o

0.5

1.0

1.5

2.0

Contact time,

2.5

3.0

3.5

4.0

4.5

Vs

Fig. 5.7 Influence of water temperature on zero pressure water transport in hydrophobic groundwood containing base paper.

phase are insufficient as an explanation. For example, according to the classical capillary transport model, the viscosity change caused by a temperature increase from 23°C to 69 °C suggests that the slope of the penetration curve should be increased only by 50 %, whereas the experimental results show that it has been multiplied. The results are thus best explained by the influence of the increased vapour pressure on the capillary pressure determining processes ahead of the liquid front, and on the rate of diffusion. The observation supports the conclusions made in chapter 3, and stresses the inadequacy of the Washburn equation to explain water transport in paper. Fig. 5.8 illustrates the zero pressure water transport in a comparatively hydrophilic base paper. The effect of liquid temperature is still partly explained by the temper-

Studics o} woder transport. in papcr during short contact times

46

-

36

N

E

'"E

25

~

....
20

Do Do

III

,g

15

't:I

~

~,c

10

:2

5

g :::I

o o

/j.

C"

:::i

X

T=23"C T=30'C T=5S"C T=80·C

0 0.0

0.2

0.4 Contact time,

VS

0.6

0.8

1.0

Fig. 5.8 Influence of water temperature on zero pressure water transport in hydrophilic groundwood containing base paper.

ature dependence of the vapour pressure, although the differences are reduced by the hydrophilic charadeI' of the paper. As discussed previously, the importance of the interadion between vapour phase and fibre mat.rix ahead of the liquid front is diminished with an increased hydrophilic charadeI' of the paper. During pressure penetration, Fig. 5.9 and Fig.5.l0, the external pressure increases the trans.port rate and the importance of molecular processes ahead of the liquid front is further reduced. At t.he same time,the role of the pressure drop due to liquid flow is accentuated. The temperature dependence of pressure penetration is probably related :"0 the connection between temperature and viscosity.

47

The influence of liquid chamcteristics on the tmnsport mte

-

'"E .,-.

E .2-

...

30 25 20

Q)

c.. ." c..

.s

15

"C

~

10 .! I/) s:

o

~ :s!

o

5

l!.

~

x

~

T=23" C T=30'C T=ss'll., T = 80" C.

0 0.0

0.2 Contact time,

0.4

Vs

0.6

0.8

Fig. 5.9 Effect of water temperature on pressure penetration (PE=O.l at m) in hydrophilic base sheet.

30 ~

'"E .,-.

25

E .2-

... Q)

20

c..

!i

.s

15

"C

~

.! I/)

10

s:

~ "C

"5

o

5

o l!. X

g

T = 23" C T=30'C T=5S'C T=80'C

0

0.00

0.05

0.10

Contact time,

Vs

0.15

0.20

Fig. 5.10 Effect of water temperature on pressure penetration (PE=0.5 atm) in hydrophilic base sheet.

48

Studies of water transport in paper during short contact times

5.3 Viscosity According to the previously suggested penetration theory, the capillary transport rate is dependent on the pressure balance between the dynamic capillary pressure and pressure drop due to liquid flow. It is well known that the pressure drop is directly proportional to the viscosity of the liquid. Recent studies (31,32) have established a relationship between dynamic contact angle and viscosity as well. Thus, the forces opposing capillary transport are increased and the driving forces reduced by the viscosity of the penetrating liquid. However, if the the capillary transport rate is determined primarily by molecular interaction between the water and the fibre wall ahead of the liquid front, the effect of the viscosity is diminished. In order to experimentally study the effect of viscosity, the penetration rate of aqueous 0.5 % carboxymethyl cellulose (Finnfix) solutions of different molecular chain lengths was determined. According to Table 5.1, the CMC grade does not affect the surface tension of the solutions. The effect of the CMC addition is therefore probably limited to the influence on the viscous properties of the different solutions.

CMC grade

FF FF FF FF FF

5X 5 30 300 1500

'f/

I

mPas

m}l m

1.544 1.921 2.881 8.909 19.21

73.1 72.4 73.1 73.5 73.5

Table 5.1 Viscosity (Ostwald) and surface tension (du Noiiy) of various aqueous 0.5 % CMC solutions at 25°C. Fig. 5.11 indicates that the differences for zero pressure water transport are much smaller than the increase in pressure drop for liquid flow would suggest. Even if the previous reports (11,13) of viscosity having no influence on the capillary transport rate cannot be confirmed, the results show that the zero pressure transport of aqueous liquids is not determined by a simple pressure balance between the constant driving forces and the pressure drop due to liquid flow.

The influence of liquid characteristics on the transport rate

49

40~--------------------------------------~

...... «

.~ ..g.

30

.s

20

E 35

Q)

25

o

Tl;;: 1.54 mPas

D

T);;:

1.92 mPas

A

1) '"

2.88 mPas

X

11 '" 6.91 mPas

+

11;;; 19.2 mPas

Do

e ~

,g:

O~--~--~--~--~--~---L--~--~--~

0.0

0.5

1.0

1.5

2.0

Contact time,

2.5

Vs

3.0

3.5

4.0

__

4.5

~

5.0

Fig. 5.11 Influence of viscosity on zero pressure aqueous liquid transport. 40

......

-

'"E

35

'"E 30 .2-

.. Q)

Do Do

!'Cl

.s

25 20

"0

~ 15

o o

Q)

'Iii I::

,g:

~

.!2" ....I

10

l!.

11" .1.54 mPas ~.

x ,,=

5

+

1.92 mPas

~. 2.88 mPas

1')

8.91 mPas

= 19.2 mPas

0 0.0

0.1

0.2

0.4

0.3

Contact time,

0.5

0.6

0.7

Vs

Fig. 5.12 Influence of viscosity on pressure penetration (PE=O.5 atm).

External pressure, Fig. 5.12, decreases the velocity dependence of the capillary forces and the influence of the fibre matrix expansion. The pressure penetration curves are strongly influenced by the pressure drop of the liquid movement and the effect of viscosity can be clearly observed. The slope of the penetration curves, K,

Studies of water tmnsport in paper during short contact times

50

is approximately proportional to the square root of the inverse viscosity:

I


.l:>

10

"0

·s

0-

5

::.i

to

x.

0.1 %

x

x""

2.5 %

0 0.0

0.05

0.10

Contact time,

0.15

Vs

0.20

0.25

0.30

Fig. 5.14 The influence of sodium dodecyl sulphate addition on pressure penetration (PE=O.5 atm).

suggested transport theory. However, as suggested earlier by Aspler et al., high molecular surface active agents at low concentrations do not have an influence on the zero pressure transport, and the equilibrium surface tension does not necessarily

The influence of liquid characteristics on the transport rate

53

determine the transport of aqueous solutions in paper. As shown in 5.14, the external pressure further reduces the effect of surface active agents. The liquid characteristics of various aqueous isopropanol solutions are illustrated in Table 5.4. It can be observed that the isopropanol addition increases the viscosity of water, which affects the pressure drop due to liquid flow. The difference between equilibrium and dynamic surface tension (surface age 2.5 ms) is negligible, which suggests that surface age does not influence the surface tension of aqueous isopropanol solutions.

Volume isopropanol

1725 0

c

'{E

,{2.5m,

vol-%

mPas

mN

mN

m

m

0.0

0.890 0.964 1.09 1.35 1.78 2.02

72.6 57.9 49.0 40.5 33.0 21.7

72.8 56.9 48.0 41.4 32.2

-

') ~.:)

6.0 12.0 20.0 100

Table Cd Viscosity (Ostwald), equilibrium surface tension (du Noiiy c! t 25 oC) and dynamic surface tension (oscillating jet method at 23 °C) of aqueous isopropanol solutions.

Zero pressure water transport of the solutions is illustrated in Fig. 5.15. A distinct relationship between the transport rate, and the measured surface tension of the solutions can be observed. More interesting, however, is to note the great difference in the saturation volume for pure water and the isopropanol solutions. This is probably a result of the higher fibre sorption and the higher expansion of the fibre network obtained with the more aqueous solutions. The pressure penetration curves, Fig. 5.16, show a more rapid transport of solutions containing isopropanol. This indicates that the influence of surface tension differences still dominate over "he influence of viscosity differences, even if the role of capillary forces has been strongly reduced by the external pressure.

Studies of water transport in paper during short contact times

54 65 60 ~

'"E '"E

~

...

55 50 45

~ 40 ca Q.

.s

35

-a 30 ~ 25 c 20

'*

ca .l::

15 -a ·5 .2" 10 ....I 5 0 0.0

0.5

1.0 Contact time,

2.0

1.5

Vs

2.5

3.0

Fig. 5.15 Zero pressure transport of aqueous isopropanol solutions.

40 ~

'"E '"E

~

35 30

!is 25 Q.

o

ca

Q.

.s ~ ...

20

-a

'~* c

-a ·5

0-

15

o x o X

10

5

::::i

= 0.0 % =

6.0 %

/:,.

X ~ 20%

x

x

= 100 %

0

0.0

0.05

0.10 Contact time,

0.15

Vs

0.20

0.25

0.30

Fig. 5.16 Pressure penetration (PE=O.5 atm) of aqueous isopropanol solutions.

The influence of liquid characteristics on the transport rate

55

5.5 Salt concentration Salt concentration has an influence on many of the fundamental liquid characteristics affecting the transport rate. The values in Table 5.5, however, indicate that the salt concentration has only a minor influence on the viscosity, and surface tension of the water; i.e. a difference in water transport cannot be related to differences in viscosity and surface tension in this case. The relationship between salt concentration and vapour pressure may be more important, but can hardly explain major differences in the liquid transport rate.

CNaCI

1]20 0 C

IE,20°C

Pvap,18°C

moles -1-

mPas

mN m

Pa

1.00 1.00 1.06

72.8 72.9 74.4

2063 2055 1991

0.0 0.1 1.0

Table 56 Interpolated viscosity (59), equilibrium surface tension (60) and vapour pressure (61) values of aqueous NaCl solutions.

The mam effect of salt addition is probably a decrease of the osmotic pressure differential between the interior and exterior of the fibres. As discussed in chapter 3.4, the osmotic pressure differential is one of the major driving potentials for water transport into the fibres. The salt addition should therefore strongly affect the osmotic pressure induced transport rate into the fibres, and the water transport within the fibres. The effect of salt concentration on the zero pressure transport rate is illustrated in Fig. 5.17. The relationship between salt concentration and reduced transport rate suggests that the osmotic pressure dependent water transport within the fibres is the rate determining transport mechanism in this severely self-sized paper. The water transport within the fibres is in this case probably a process preceeding capillary transport in the pores (see chapter 3.1.2), although it can also be an important transport mechanism as such.

Studies of water transport in paper during short contact times

56

40

o o

..

35

..,

30

~

-i

. X

E

...

25

0m 0-

20

Cl)

C

= 0.0 M

C = 0.1 M C = 1.0 M

S

l

15

~c

10

~

r' ,f

5

~ ~

0 1.0

0.0

1.5

Contact time,

2.0

2.5

3.0

3.5

4.0

Vs

Fig. 5.17 Zero pressure transport of aqueous NaCl solutions.

The sorption curves in Fig. 5.18 show that the effect of salt is almost completely eliminated in pressure penetration. As expected, water is primarily transported in the pores, and the influence of osmotic pressure dependent diffusion transport is strongly diminished. 40

.

-i

35

I

25

l i.G

15

"0

5

~

E

..,

S

5-

30

20

10 0

0 X

C=D.OM C = 0.1 M C=l.OM

::J

0 0.0

0.1

0.3

0.2

Contact time,

0.4

Vs

Fig. 5.18 Effect of NaCl-concentration on pressure transport (PE=0.5 atm).

0.5

The influence of liquid chamcteristics on the transport mte

57

5.6 pH of the liquid A few studies of the effect of pH on the liquid transport rate have been reported in literature. Price, Osborn and Davies observed (62) that 0.3 % hydrochloric acid penetrates about three times as fast as pure water in rosin-sized paper. It was suggested that hydrochloric acid lowers the hydrophobicity of paper by reacting with the rosin-aluminium complex, which is .the actual sizing agent. The work of Bristow (63) showed that adding alkali increases the transport rate above pH value of approximately 10. The results indicated that alkali influences the chemical interactions between the aqueous liquid phase and the fibre matrix. Similarily, Lelah and Marmur (64) explained the connection between pH and spreading rate of aqueous drops on glass by pH dependent chemical interactions between the solid and the solution. The influence of pH on the swelling of individual fibres may also affect the transport rate. As indicated by Scallan (46), this effect is probably best explained by the ionic effects which determine the osmotic pressure differential between the interior and exterior of the fibres. However, if precautions are not taken, the amounts of chemical required to adjust pH will also change the ionic strength of the solutions, and influence the liquid transport in a way discussed previously in chapter 5.5. The effect of the ionic strength could then easily be misinterpreted as a pH-effect. In the present study, the pH was adjusted with HCI and NaOH to 3.0, 6.2 and 10.5. In order to minimize the influence of ionic strength variations, NaClwas added to keep the total number of added ions constant. The ionic strength' of the' solutions studied was 0.1 M. Fig. 5.19 illustrates the. effect of pH on the zero pressure transport rate in groundwood containing, self-sized paper. It can be seen that the pH does not have a major influence on the water transport within the pH range studied. The slightly faster penetration of the acidic solution could perhaps be explained by pH dependent chemical interactions between the solution and the hydrophobic compounds in the fibre matrix. The effect of pH on the swelling of the fibres does not seem to be of such magnitude that the total water transport rate in the system studied would be influenced. As expected, external pressure reduces further the effect of chemical interactions and pH dependent water transport into the fibres. The pressure penetration rate, Fig. 5.20, is independent of the pH of the penetrating aqueous solution.

Studies of water transport in paper during short contact times

58

40

........

35

..,

30

-

o o X

E

E .2.

...

25

Q.

20

!. III

PH = 3.0 PH = 6.2 PH = 10.5

S 'C

15

~

~c 10

g

5

~

:3"

0 0.0

0.5

1.0

1.5

Contact time,

2.0

2.5

3.0

3.5

4.0

Vs

Fig. 5.19 Effect of pH on the zero pressure liquid transport in groundwood containing base paper for coating. 40

........E

-

..,

!

8.

:t S

!

tg ~ 0'

35 30 25 20 c

/

15 10

0 0

5

X

PH = 3.0 PH a 6.2 PH • 10.5

:::J

0 0.0

0.1

0.2

Contact time,

0.3

0.4

0.5

Vs

Fig. 5.20 Effect of pH on the pressure penetration (PE =0.5 atm) of aqueous solutions.

The influence of paper characteristics on the water transport

59

6. THE INFLUENCE OF PAPER CHARACTERISTICS ON THE WATER TRANSPORT Water transport in paper can be influenced by structural as well as by surface chemical modifications of the fibre matrix. Below, the various characteristics which primarily affect the paper structure are discussed. This is followed by the effect of hydrophobic sizing and self-sizing, as well as variables which influence structural as well as surface chemical aspects of water transport. Finally, at the end of this chapter, situations where diffusion is the main transport mechanism are discussed.

6.1 The mechanical pressure exerted on the paper The mechanical pressure, PD, which the liquid applicator exerts on the paper primarily influences the pore structure of the paper, and its effect on the water transport is therefore discussed in this chapter. The mechanical pressure can affect the form of the water transport curve in at least three different ways: 1. An increasing mechanical pressure decreases the surface roughness, and the water uptake at the extrapolated time tA=O.O s is lowered. 2. Compression of the paper diminishes the apparent pore radius. As a result, the pressure drop due to liquid flow is increased and the cross section of the penetrating water front is decreased. In addition, the air transport from the system is rendered more difficult and the counter pressure of air is therefore increased. The water transport rate, i.e. the slope of the water sorption curve, is thus diminished. 3. The total pore volume of the paper is decreased. Consequently, the water sorption at long contact times is diminished because the liquid volume needed to saturate the pore system is lower. It can be seen from Figs. 6.1 and 6.2 that the mechanical pressure has the expected influence on the water transport. At short contact times, when the liquid sorption is determined by the surface roughness, the sorption values are reduced by the mechanical pressure. During penetration in the pore system of the paper, the reduction of the apparent pore radius caused by increasing mechanical pressure further diminishes the penetration rate. Finally, the amount of water taken up at long contact times under increasing mechanical pressure is reduced by the reduction of the total pore volume.

Studies of water transport in paper during short contact times

60 70

0 ~

'"E ..,

-

PO= 7.6 kPa Po= 52 kPa Po = 101 kPa Po = 160 kPa

A

60

X

+

E 50 .!:!.

... Q)

Q.

ca

40

Q.

S 30

'tI

~

oS! 20 III C

~ 10

:2 ::s

~

0 0.0

0.25

0.50

0.75

Contact time,

1.0

1.25

1.50

1.75

2.0

Vs

Fig. 6.1 Influence of mechanical pressure exerted by the liquid applicator on the zero pressure water transport in 38 g/m2 coating base paper.

65 60

o o

Po= 52 kPa

55

X

Po = 160 kPa

~

'"E ..,

E

.!:!.

...

40 35

S

30

'tI

25

oS! III c

20 15 10 5

~

~

:2 ::s

~

kPa

50 45

!aQ.

Q)

po=101

0 0.0

0.25

0.50

0.75 Contact time,

1.0

Vs

1.25

1.50

1.75

Fig. 6.2 Influence of mechanical pressure on zero pressure water transport in 52 g/m2 coating base paper.

2.0

The influence of paper characteristics on the water transport

61

6.2 Grammage Classical water transport models suggest that capillary transport of a liquid in an open pore system with a constant pore radius is not dependent on the thickness of the pore system ahead of the liquid front as long as saturation does not occur. Consequently, the grammage of paper should not have any effect on the liquid sorption curve before the saturation .of the pores. In practise, however, the grammage may influence the water transport in paper before the complete saturation in at least two ways: 1. The counter pressure of air ahead of the liquid front and the response of the pore structure to mechanical pressure may be affected by the grammage of paper.

2. It is known that the transport veloci~y of a liquid front, especially during pressure penetration, depends on' the pore radius. This results in a distribution of the saturation times for the different pore size fractions in a heterogeneous pore system. Consequently, in a low grammage paper, the large pores will be saturated by a small quantity of liquid and a slower penetration into the smaller pores becom~s predominant even at short contact times. In high grammage paper, the volume of the large pore size fraction is larger and the corresponding saturation time longer. As a result, the water transport rate may be affected by the grammage of the paper even before the complete saturation of the pore network. This effect is greatly accentuated by external pressure, because the pore radius dependence of the transport velocity of a liquid front is increased with external pressure. In order to study the influence of grammage, three groundwood containing papers with different grammage were manufactured from the same pulp with a laboratory paper machine. Mercury porosimetry (65) indicated that porosity was somewhat increased by grammage. As shown in Table 6.1, also the Parker Print Surf surface rougness increased slightly with grammage. Figure 6.3 illustrates the zero pressure water transport in these papers. It can be seen that the zero pressure transport rate is independent of the grammage until pore saturation occurs (t~O.2 s). The water movement of a seemingly uniform liquid front is not dependent on the thickness of the pore system ahead of the front. The total water sorption for the saturated and expanded fibre matrix is, not surprisingly, proportional to the grammage of the paper.

62

Studies of water transport in paper during short contact times

45

-

'"E

...

E .2"CD Q. III Q.

oS 'C

~

40 35 30 25 20

.! U)

15

~

10

c

:2 ::J

:3"

o o

5

t.

30 glm 2 40 91m2 559/m2

0 0.0

0.5

1.0

Contact time,

1.5

Vs

2.0

Fig. 6.3 Effect of grammage on zero pressure transport.

Grammage g/m 2 30 40 55

Roughness

Roughness

Porosity

PPS lO

PPS 20

PPS 20

4.5 5.1 5:5

3.4 3.9 4.3

260 210 150

Table 6.1 Influence of grammage on the surface roughness and porosity of a coating base paper (Parker Print Surf).

External pressure, Fig. 6.4 and Fig. 6.5, causes some variations in the transport rate even at short contact times. The water transport rate appears to decrease with decreasing grammage, especially for the 30 g/m2 paper. One explanation for this is the increased influence of counter pressure of air during the rapid pressure penetration in the low graJ;llmage paper. The penetration rate differences into pores of different size and shape may also be the cause of transport rate variations before the complete saturation of the pore network. The main reason for the lower pressure penetration rate, however, is probably the somewhat denser pore structure of the low grammage paper.

The influence

0/ paper characteristics

on the water transport

63

45 ~

..-

'"E

40

35 E .2- 30

...

!la

c..

25

.si 20

~

~c

15

~

10

I

5

0 0 l!.

30 gJm 2 40 gJm 2 55 gJm 2

...I

0 0.0

0.25

0.75

0.5

Contact time,

1.0

Vs

Fig. 6.4 Influence of grammage on pressure penetration (PE=O.l atm) of water.

45 ~

.-.

'"E

i...

40 35 30

Cl)

c.. 25 la c..

.si 20 "Cl

I

15

c

~ 10

~CT

0 0 l!.

5

30 gim2 40 g/m 2 55 g/m 2

:::i

0 0.0

0.1

0.2 Contact time,

0.3

0.4

0.5

0.6

Vs

Fig. 6.5 Influence of grammage on pressure penetration (PE=O.5 atm) of water.

Studies of water transport in paper during short contact times

64

6.3 Beating A study of the relationship between the degree of beating and the zero pressure water sorption of a paper has been reported in literature (27). The results showed that the penetration depth is significantly decreased when the degree of beating is increased from 25 oSR to 69 °SR. In practice, however, the degree of beating is seldom varied over this large a range. The experiments in the present study were limited to two papers, both of which contained 50 % groundwood pulp. This groundwood was made at two degrees of freeness, CSF 29 and CSF 41. Parker Print Surf porosimetry and surface roughness measurements showed only slightly lower values for the paper made from the lower freeness pulp, Table 6.2.

Beating degree

Roughness

Roughness

Porosity

6.7 6.8

5.4 5.4

130 150

CSF 29

41

Table 6.2 Influence of beating degree on the surface roughness and porosity of a coating base paper (Parker Print Surf).

Fig. 6.6 illustrates the influence of the freeness of the groundwood part on the zero pressure transport of water. It can be seen that the effect is almost negligible. At short contact times, when the surface roughness is the sorption determining variable, the sorption values are probably slightly lower for the paper made from the lower freeness pulp. At long contact times, on the other hand, the water sorption is slightly increased with decreasing freeness. This is in accordance with the previous studies (66) showing that beating increases the swelling tendency of a fibre. The pressure penetration curves, Fig. 6.7, indicate that the structural differences between the two papers are not sufficient to cause changes in the pressure sorption volumes. This supports the conclusion that minor adjustments of the beating degree do not necessarily have a significant influence on the sorption characteristics of a paper.

The influence of paper characteristics on the water transport

65

35 ~

N

E

30

..,.....

E 25 .!:!. ~

Cl.

[

$a

20 15

'0

~

~c 10 ~

'0

·5

0 0

5

CSF 29 CSF 41

g 0 0.0

0.5

1.0

Contact time,

1.5

rs

2.0

Fig. 6.6 Influence of the freeness of the groundwood fraction on capillary transport.

35 ~

N

.....E

30

CO>

E 25 .!:!.

...

8. lIS

20

Cl.

$a '0

15

~

~c 10 ~

'0

·5

0

0

5

CSF 29 CSF41

g 0

0.0

0.1

0.2 Contact time,

rs

0.3

0.4

Fig. 6.7 Influence of the freeness of the groundwood fraction on pressure penetration (PE=O.5 atm).

0.5

66

Studies of water transport in paper during short contact times

6.4 Calendering Calendering can decrease the apparent pore radius, surface roughness and total pore volume, and thereby influence the water transport in paper. However, during the penetration of an aqueous solution, the fibre matrix also has a tendency to expand. This expansion may have a diminishing effect on the original differences in the pore structure, i.e. the fibre matrix expansion tends to relieve the stresses built in during calendering. It has been indicated previously that the pressure drop due to liquid flow, and the cross section of the penetrating water front are determined by the pore structure of the expanded fibre matrix behind the water front, not by the pore structure ahead of the water front. The significance of this counter effect (fibre matrix expansion) is probably reduced during rapid pressure penetration.

35

'"E '"E

-

30

.2-

25

ca:! c-

20

....Q)

S "0

~Q) Vi r::

a:!

15 10

.l:; "0

':; C" :::i

o o

5

UNCAL. 830 ml/min

CAl.

580 mlfmin

II

CAl.

430 mllmln

X

CAl.

320 ml/mln

0 0.0

0.25 Contact time,

0.50

Vs

0.75

1.0

Fig. 6.8 Influence of calendering and surface roughness values (Bendtsen) on capillary transport. Fig. 6.8 illustrates the effect of calendering on the zero pressure water transport in a ground wood containing paper. It can be seen that significant differences are obtained only at short contact times (t :::;0.1 s), when the liquid uptake is strongly dependent on the surface roughness. At longer contact times, the expansion of the fibre matrix levels out the original differences in the dry pore system. Consequently, it can be argued that calendering is not an effective method of regulating zero pressure transport of aqueous solutions in paper.

j *

CURVEFIT

~ l-,_~~~ s-t '3J, 'i?)7:> *

,J( ..

1'; ,+2·/2:. - 7-,..2D 7"

CURVE FITTING

CURVE

"*

a

bX a+bX

1) 2) 3)

bX+cX~2

4)

a+bX+cX-2 l/(a+bX X/(aX+b) a+b/X a+bX+c/X a+b/X+c/X"2

) 6) 7) 8) 9)

CURVE 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

aX-b ab~(X)

ab" Cl/x) aX" (bX) aX-(b/X) aX/b-X abAX*XAc ab A(l/X)*X"c 1/[a(X+b)~2 + c] a+b*lnX l/(a+b*lnX) aeA(bX) ae~(b/X)

22) ;.. r

I' ~ ..



...............

""i

J

No. of data rows 9 RR(adj'd) b c n/a 26.69317

9.863635 19.96929 62.72541 46.76494 062 -0.05236 0.067579 0.000356 22.36964 -0.07551 11.32155 19.00824 27.79549 -0.46292 MAX RR CURVES

a

"*

30.70076 9.675361 17.98850 14.07957 17.19797 260.8118 21.22779 33.68448 0.065811 33.13505 0.033720 9.675361 17.98850

j(]

0.8630518 0.5453473 0.3624807 0.0846411 -0.02130 0.8586432 0.001400 0.2737816 1 to 9 = 0.9950556

b c RR(adj'd) 0.332298 0.8793274 2.463929 0.7274721 0.995455 0.2082202 0.623209 0.1799903 0.000734 0.1502859 4.072162 n/a 1.421555 0.238517 0.9187300 1.003519 0.448000 0.9584395 -1.44574 -0.01115 0.8778034 0.7360002 6.346859 -0.02250 0.9566223 0.7274721 0.901757 0.2082202 -0.00455

24.) ae lLlb-lnX) LJ/C) 25) a[(X/b)~c]e~(X/b)

b.70Q../Ci/

-:.J."f."f.l.w'+

..I.O'.v777;

.,

0..

,g '0 Cl>

x*

15

j

Cl>

Ui 10 C

g

'5

*

!Pt-

20

I::

'0

x

"

,£.

0..

+

0

30

;-

5

,.

19.4.1986 28.4.1986 19.5.1986 23.6.1986 27.7.1986 24.9.1986

0

~

0

t:.

'"

X

+

*

C'

::i

0 0.0

0.25

0.50

0.75

Contact time,

1.0

1.25

1.50

1.75

2.0

Vs

Fig. 6.13 Effect of storage time on zero pressure water transport in base paper for coating, quality A. 40

'"E 35

-

M

.... X

E

30

...

25 ..

8

"

,£. Cl> 0..

., 0.. ,g '0 Cl>

I::

.!! U) c

g !!

::I C'

+ x

*

20

0

"

t

15 10

l

+

4,.,

0 0

t:. X

+

5

*

::i

=

19.4.1986 28.4.1986 19.5.1986 23.6.1986 27.7.1986 24.9.1986

0 0.0

0.05

0.10 Contact time,

0.15

0.20

0.25

0.30

Vs

Fig. 6.14 Effect of storage time on the pressure penetration (PE=O.5 at m) in base paper for coating, quality A.

structure has expanded during storage. Because the degree of self-sizing was rather low during the first five months of storage, the self-sizing was accelerated by heating the paper in the dryer of a laboratory

Studies of water transport in paper during short contact times

72

coater. The dwell time in the dryer was about 50 s at a temperature of 180°C. The treatment caused a significant reduction in the zero pressure transport rate, Fig. 6.15. However, the extension of the storage time to one and a half year resulted in a yet lower capillary sorption rate. It can hence be deduced that the self-sizing of this quality of groundwood containing paper, when stored as rolls, is an extremely slow process. 40 ~

N

-

35

E

...

E 30

.

~ Q)

Co la Co

oS 1:1

25 20

~

15

c

10

~

5

J!! (/)

~

o

As received

t::.

After heat treatment After 1.5 years

X

:3" 0 0.0

0.5

1.0

1.5

Contact time,

2.0

2.5

3.0

3.5

4.0

Vs

Fig. 6.15 Self-sizing of coating base paper, quality A.

The first testing of another test paper, which contained practically no alum, was done only five hours after manufacture. Fig. 6.16 shows that only minor changes in the zero pressure transport rate can be observed during the first days of storage. The pressure sorption curve, Fig. 6.17, indicates that no major structural changes have occured during the first days of storage. Further storage of this quality (up to four months) caused only slight self-sizing effects. It has been shown that the self-sizing of the papers studied is, when stored in rolls, a rather slow process, also during the first weeks of storage. However, sheet storage substantially accelerates the self-sizing rate and has a strong influence on the sorption characteristics of the paper. It has been found that overnight storage of a paper sheet exposed to indoor light may reduce the zero pressure sorption volume to one third of that for paper stored in a roll. This indicates that light probably is an important factor in the self-sizing mechanism. Reactions between the fibre matrix and air may also account for the difference between sheet and roll storage, although this explanation suffers from the fact that even a paper roll has a void fraction

The influence of paper characteristics on the water transport

73

40

-

35 I-

..,

30

-

N

0

+ "

E

E .2-

...

'il"

Cl

25

~ a.

x

"b

"x

"

x"

20

Q,

.$I

x"

l.;

15

iaJ!

.

10

~

~

,~

+

o

A

5

:g

=

[]

X

j...J

0

0.0

0.2

0.4

,

,

0.6

0.8

17.12.1986 18.12.1986 19.12.1986 22.12.1986 29.12.1986

1.0

1.2

Vs

Contact time,

Fig. 6.16 Influence of storage time on capillary transport of water in coating base paper, quality B. 40

..,

-

N

0

35

\!'

E

E .2-

25

!.

20

8-

S

I 'Iii c

g

g~

~

30

...

AB

0

i"

>R

a ~

15 10

o = [] =

l;. •

5

X =

18.12.1986 19.12.1986 22.12.1986 29.12.1986

-,

0 0.0

0.1

0.2

Contact time,

Vs

0.3

0.4

Fig. 6.17 Influence of storage time on pressure penetration (p=0.5 atm) in coating base paper, quality B.

around 0.5. Whatever the cause, and it is not the aim of this study to elucidate the cause, the sheet storage of a paper may affect all the paper characteristics which are dependent on the water transport rate.

74

Studies of water transport in paper during short contact times

6.7 Moisture content The two primary transport mechanisms for zero pressure water transport are capillary transport and diffusion via the vapour phase. It is obvious that adsorbed water molecules on the fibre surfaces increase the attraction forces between water and the fibre matrix (see chapter 3.1.2). Therefore, a decrease in the moisture content of a paper should reduce the dynamic capillary pressure and the capillary transport rate. On the other hand, the moisture concentration gradient and the osmotic pressure gradient increase when the moisture concentration decreases. The effect of adsorbed moisture on these gradients probably overcomes the increase in diffusion coefficient caused by absorbed moisture. For diffusion controlled water sorption, as with very hydrophobic or extremely dense papers, the zero pressure water transport rate is probably increased when the moisture content is diminished. Moisture content may also have an influence on the pore structure of the paper. Lyne (68) showed that absorbed moisture increases the capillary transport rate in a rather hydrophilic paper made with slush pulp, whereas the absorptivity of a more hydrophobic paper made with bale pulp was lowered by moisture. These effects were explained by the role of drying history in determining whether the pore structure will expand or contract with absorbed moisture. However, as discussed previously in chapter 6.4, the importance of moisture-related structural effects should be reduced by the expansion of the fibre matrix during the penetration process. The influence of moisture content on the zero pressure water transport in a comparatively hydrophilic paper is illustrated in Fig. 6.18. It can be seen that the transport rate is slightly increased by the adsorbed moisture, indicating that the capillary pressure is increased with absorbed moisture. The importance of capillary forces is diminished during pressure penetration, Fig. 6.19, and the influence of the moisture content on the pore structure should be clearly observed. Nevertheless, it can be seen that the pressure penetration rate is independent of the moisture content. The obvious explanation for this is that the fibre matrix expansion in this case is so rapid that the moisture content dependent differences in the pore structures are eliminated by expansion even during the rapid pressure penetration. Therefore, it can be argued that the relationship between the moisture content and the increasing zero pressure water sorption, Fig. 6.18, is not a result of the different pore structures, but can be ascribed to the increased dynamic capillary pressure (compare ref. (68) ). In hydrophobic paper, on the other hand, the effect of moisture content has previously been suggested to be different, because the moisture concentration gradient

75

The influence of paper characteristics on the water transport 50.---------~--------------------------~

i

45

-

"'E 40

£. 35

lis

g. c.. .s

30 25

~

~ 20

J!!

la g

15 M.C. - 16 %

10

0.0

0.1

0.2

0.3

Contact time,

0.4

o

R.H. = 50 %

M.C. = 7 %

/j.

R:H. = 30 %

M.C•• 5 %

0.5

0.6

0.7

0.8

Vs

Fig. 6.18 Influence of relative humidity and moisture content on the zero pressure water transport in hydrophilic paper.

40r---------------------------______

~

o

-

'" ~ 30

8. 25 (Q

c..

.s

20

1

15

c

g

o o

10

:g

.~ 5

/j.

R.H. = 80 %

M.C•• 16 %

R.H.· 50 %

M.C•• 7 %

R.H.· 30 %

M.C. = 5 %

..J

o 0.0

0.05

0.10 Contact time,

0.15

Vs

0.20

0.25

0.30

Fig. 6.19 Influence of relative humidity and moisture content on the pressure penetration (PE=O.5 atm) into hydrophilic paper

and the osmotic pressure gradient are probably the main driving potentials. The inverse relationship between moisture content and zero pressure water transport, Fig.

Studies of water transport in paper during short contact times

76

60r---------------------------------------~

'"

~ 50

'"E

o

R.H.· 80 %

M.C.· 16 %

(;

R.H .• 50 %

M.C. = 7 %

X R.H.

= 30 %

M.C. = 5 %

.!:!. '- 40 ~

'"0-

.El 30 "tJ

~

~ 20 c:

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0.0

1.0

0.5

1.5

Contact time,

2.0

2.5

___ L_ _~

3.0

3.5

4.0

Vs

Fig. 6.20 Effect of relative humidity and moisture content on zero pressure transport in hydrophobic paper.

40

NE 35

--

'".Q.

30

...

~ 25

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0-

.El 20 "tJ

~ 15

Q)

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10

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5

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6.

R.H.· 50 %

M.C. = 7 %

X

R.H. '" 30 %

M.C. '" 5 %

M.C. '" 16 %

-I

o 0.0

0.05

0.10 Contact time,

0.15

Vs

0.20

0.25

0.30

Fig. 6.21 Effect of relative humidity and moisture content on the pressure penetration (PE=0.5 atm) into a hydrophobic paper.

6.20, indicates that diffusion is probably the rate controlling transport mechanism in this severely self-sized paper.

The influence of paper characteristics on the water transport

77

The pressure penetration rate in the hydrophobic paper is increased by the adsorbed moisture, Fig. 6.21. In this case, the expansion of the fibre matrix is not fast enough to eliminate pore structure differences caused by the moisture.

6.8 Filler addition The addition of filler to the paper causes surface chemical, as well as structural changes in the fibre matrix. The most common filler pigments have surface energies higher than that of dry cellulose. In general, their influence on the dynamic capillary pressure is therefore positive. On the other hand, the filler particles are often relatively small, which may result in a more compact pore structure. In addition, the filler addition may reduce the expansion of the fibre matrix. In order to experimentally study the effect of filler addition, four different papers were manufactured. The reference contained no filler, while the remaining contained 6 % talc, 6 % clay and 15 % clay respectively. Clay addition reduced the porosity (Parker Print Surf) of the paper, while the coarse talc particles gave an open pore structure, Table 6.5.

Filler addition

No filler 6 % Talc 6 % Clay 15 % Clay

Roughness

Roughness

Porosity

PPS lO

PPS 20

PPS 20

5.1 4.7 4.9 4.6

3.9 3.4 3;6 3.4

210 260 170 150

Table 6.5 Effect of filler addition on the surface roughness and the porosity of a coating base paper. The zero pressure water transport in the papers is illustrated in Fig. 6.22. It can be seen that 6 % talc and 15 % clay cause an increase in the transport rate. This is probably a result of the increased capillary forces between water and the fibre matrix, although the open pore structure of the talc containing paper is also conducive to the increased transport rate. The lower water sorption of the paper containing 6 % clay may be attributed to the decreased porosity, which counteracts the small increase in the capillary pressure. Recalling the importance of the fibre matrix expansion, it is easy to understand the different water sorption volumes at

Studies of water tmnsport in paper during short contact times

78

35

-

N

E

30

x-

M

+------+

E 25

£.

...

~ 20

III

Co

.s

-

15

'0

~ .!!! 10 tI) c:::

g

ORe! b. Talc 6% X SPS 6% + SPS 15%

5

:2

:::I .rz ..J

0 0.0

0.5

1.0

Contact time,

1.5

Vs

2.0

Fig 6.22 Influence of filler addition on zero pressure water transport in coating base paper. 35

'"E 30

-

-

M

E 25 £.

lii Co

20

III

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.s

-

15

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~ 10

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-

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0 b. X

5

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+

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Re! Talc 6% SPS 6% SPS 15%

0 0.0

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0.2 Contact time,

0~3

Vs

0.4

0.5

0.6

Fig. 6.23 Influence of filler addition on pressure penetration (PE=O.5 at m) in coating base paper.

long contact times. The filler addition reduces the degree of expansion, and the saturation volumes are therefore proportional to the filler content. During pressure penetration, Fig. 6.23, the importance of the surface chemistry

The influence of paper characteristics on the water transport

79

related forces is diminished and the role of the pore structure accentuated. Thus, the highest transport rates are measured for the porous paper containing 6 % talc and the paper without filler. The lowest transport rate is obtained for the paper containing 15 % clay, which also has the most dense pore structure.

6.9 Surface chemistry and paper structure enhancing water transport through vapour phase In most zero pressure sorption experiments described above, the dynamic capillary pressure has been an important driving potential. In certain situations, however, the capillary transport is prevented, and the zero pressure water transport must occur through vapour phase. Diffusion prevails presumably in the following situations: 1. Capillary pressure opposes the liquid movement. 2. The pores are too small to allow capillary transport of liquid phase.

6.9.1 Capillary pressure opposes liquid movement According to the Young-Laplace capillary theory, the capillary pressure is negative when the dynamic contact angle between the liquid and solid phases is higher than 90 degrees. In this case, the capillary pressure opposes the movement of the liquid phase in the pore system. Previously, it has been suggested that various time dependent molecular mechanisms ahead of the liquid front may lower the contact angle, allowing for capillary transport. However, the fibre surface may also be treated in such a way that these molecular processes are not capable of increasing the capillary pressure from a negative value to a positive. In this case, diffusion is the main transport mechanism for zero pressure water transport. Extremely hydrophobic fibre matrixes were manufactured by impregnating two kraft pulp containing papers with 3 % aqueous solution of a fluorochemical chrome complex (3M FC-3175) in a size press. The two paper samples were made with the same pulp, but were wet-pressed to different porosity levels, Table 6.6. The hydrophobic treatment was so effective that the contact angle between the paper and water remained well over 90 degrees after a contact time of several minutes. Fig. 6.24 illustrates the zero pressure water transport in the untreated papers. It can be seen that water penetration is extremely rapid in these woodfree, unsized papers. The results indicate also that the difference in the dry pore structures is not eliminated during the penetration process, but the transport rate is lower for the denser quality (B).

80

Studies of water transport in paper during short contact times

Paper

Roughness

Roughness

Porosity

PPS lO

PPS 20

PPS 20

6.4 7.8 7.6 8.0

5.2 6.6 6.3 7.0

690 400 1260 490

Untreated A Untreated B Hydrophobic treated A Hydrophobic treated B

Table 6.5 Surface roughness and porosity data of untreated and hydrophobic treated paper samples.

120

E

-

..,

o

Paper A

X

Paper B

100

E

..

.2- 80 CD

CL CL

ca

S

i"1:

60 40

c

"

!

20

o 0.0

0.1

0.2

!l.3

0.4

Contact time,

0.5

Vs

0.6

0.7

0.8

0.9

1.0

Fig. 6.24 Zero pressure water transport in two hydrophilic papers.

The effect of the hydrophobic treatment on the water transport is illustrated in Fig. 6.25. The water sorption rate has now been reduced dramatically. More interesting, however, is to notice that the curves extrapolate to the origin of the coordinate system. This indicates that in this case the attraction forces between the . paper surface and water are smaller than the cohesive forces of water at the liquid application zone, and that no water film is transferred to the paper surface. On the other hand, the water penetration volumes obtained at the measured contact times show that water is in contact with the paper during the time it passes the applicator

The influence of paper characteristics on the water transport

81

8;0

-

'"E

o

...-K ... Bm Cl.

.e 'U

~

4.0 3.0

'U

1.0

...I

/ x/

5.0

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Paper A Paper B

6.0

~c

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X

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/

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. I

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1.0

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3.0

4.0

5.0

6.0

Vs

Fig. 6.25 Zero pressure water transport in hydrophobic treated papers.

zone. It can also be noticed that the porosity does not appear to have an influence on the diffusion rate; the water penetration rate is constant in these papers. This can hardly be explained by an expansion of the fibre matrix as discussed earlier, because the capillary transport in the untreated papers was clearly affected by the porosity. Therefore, in this case, it can be suggested that water diffusion in the pores has a negligible effect on the water transport rate. The main transport mechanisms are probably surface diffusion on the fibres and diffusion within the fibres. This is in accordance with previous studies (41) suggesting that diffusion within the pores is of minor importance, and that surface diffusion probably plays a key role in the diffusion process.

6.9.2 The pore structure is not of capillary dimensions It is generally accepted that the pore dimensions of conventional papers allow capillary penetration, but the water transport into the fibres is primarily diffusion controlled. Regenerated cellulvoe films, on the other hand, have probably a pore structure which prevents capillary transport, but allows diffusion.

The water sorption into an unlacquered 35 g/m2 Cellophane in different pressure situations is illustrated in Fig. 6.26. It can be seen that the external pressure, as expected, does not have any influence on the water transport rate. This indicates

Studies of water transport in paper during short contact times

82

40 ~

N

-

0

35

0

E

..,

E .&

... Cl)

0

30

0

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25

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Cl.

.s "C

~

...

20 15

~c 10

0 PE = 0.0 aim 0 PE = 0.1 aim 6 PE = 0.5 aim

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"C

'5

:3"

5 0 0.0

0.5

1.0

1.5

Contact time,

2.0

2.5

3.0

3.5

4.0

Vs

Fig. 6.26 Water transport in cellophane film.

that water is not transported as a liquid phase, but rather through a diffusion mechanism, which is independent of the external pressure. It is interesting to note that the rate function of water transport III Cellophane follows rather well the one-dimensional solution of the Fick,s diffusion model. The power of the rate function is thus quite close to the 0.5 predicted by this model. The slight curvature upwards is probably best explained by the increase in the film volume accessible for water transport, i.e. the swelling of the Cellophane film.

Concluding

r~marks

on. wetting of a paper surface

83

7. CONCLUDING REMARKS ON WETTING OF A PAPER SURFACE In this chapter, some further aspects of the water sorption process at extremely short contact times, i.e. during initial wetting, are discussed.

7.1 Extrapolation of contact time to zero It has been experimentally shown that the rough surface of the paper is wetted quickly, and that the sorption values usually seem to extrapolate to a volume which is dependent on the surface roughness of the paper. Fig. 7.1 and Fig. 7.2 illustrate the connection between the extrapolated water sorption and the surface roughness (Parker Print Surf) values of a variety of different papers. It can be seen that the relationship between these quantities is rather linear, and that the earlier reports (14) of the zero time sorption volume being surface roughness dependent seem to be correct. 8

-

-

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.!:!. c

i 0

...

7

x

6

5 4

1/1 G)

1;j ~

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x )0(

E

1
el6c

2

x lIC

o

o

2

3

4

Surface roughness

5

6

7

8

( PPS20 )

Fig. 7.2 Relationship between Parker Print Surf roughness values (head pressure 20 kg/m2 ) and zero contact time extrapolated sorption volumes of different papers.

On the other hand, it has been found that the extrapolated volume is slightly increased by the viscosity of the liquid and by the external pressure. This indicates that the sorption determining surface roughness volume can be considered to be a dynamic quantity, and that the dynamic character is determined by the equilibrium between the compressibility of the paper, the mechanical forces, the external pressure of the liquid, and hydrodynamic forces. It is self-evident that the filling of the surface roughness requires flow from the liquid applicator to pape~. Therefore, according to the classical physics, the transferred liquid volume at zero contact time should be zero, since no flow occurs in zero time. The apparent contradiction between the experimental extrapolation and the classical physics is explained by the extreme rapidity of the surface wetting process. In practice, the wetting of the rough paper surface is completed in a time period which is considerably shorter than the experimentally measurable contact times (beginning from one millisecond). The appearence of the liquid sorption curve between zero and the experimentally measurable contact times is therefore unknown. It is probable that this part of the sorption cl,lIve is determined by a complicated balance between external pressure, spreading and capillary pressures, pressure drop due to liquid flow, hydrodynamic forces, and counter pressure of air.

However, the extrapolated volume of the water transfer to zero contact time is, as discussed previously, primarily determined by the surface roughness volume of the

Concluding remarks on wetting of a paper surface

85

paper. During the experimentally measured contact times, the surface volume of the paper has been filled, and the water penetration into. the fibre system has started. The water sorption volume is then the sum of the surface roughness volume and the contact time dependent bulk penetration. The physical significance of the zero time extrapolation is therefore to eliminate the influence of penetration into bulk system, and thus approximate the surface volume. At this point, it can be noted that the distinction between the surface and the bulk system of the paper is rather artificial, and that no sharp boundary can be drawn between these two systems. This may also be conducive to the dynamic character of the extrapolated surface roughness volumes.

7.2 The concept of wetting delay By now, it should be obvious that the concept of wetting delay introduced in the literature (14,16,23) is misleading. Theoretical considerations (chapters 2 and 3) and experimental results indicate that the wetting of a paper surface is faster than the experimentally measurable contact times. Nevertheless, the wetting delay is a widely used concept, and evidence for its existence has been reported from time to time. Therefore, it is interesting to discuss the possible explanations for such reports, The m.ost obvious reason for the water not penetrating into the paper is, of course, the situation wh'Te no actual contact between the two phases has been obtained. This situation is l)robably best explained by the air which has to be removed before wetting of the surface is accomplished (see chapter 3.2). In addition, during dynamic conditions, the position of the contact line between the solid and the liquid may be influenced by the transport velocity of the solid (69,70,71). Therefore, the contact time and the thickness of the wetting zone between the liquid and the solid could be affected by the dynamic spreading behaviour in the paper plane. However, the water sorption experiments made in the present study have shown that the spreading kinetics in the paper plane do not appreciably influence the results for the experimental method used. It can be concluded that the counter pressure of air and the rate of wetting in the paper plane could influence the wetting process at extremely high speeds. These factors are, however, primarily characteristic to the liquid application process, not to the surface chemistry of the paper. They are only indirectly associated with the fundamental paper variables, and they cannot be related to the wetting delay described in the literature. It has also been proposed that the wetting delay corresponds to the time required to bring down the contact angle from a non-wetting value to below 90 degrees. According to this suggestion, different molecular processes on the paper surface

86

Studies of water transport in paper during short contact times

precede the capillary penetration into the pore system. On the other hand, a similar contact angle lowering mechanism has to precede the capillary transport within the paper as well. As discussed in chapter 3, the square root relationship between the contact time and the penetration depth in the Washburn equation is in this case not valid, and the levelling off of the sorption curve at short contact times on a square root scale does therefore not represent any physical quantity of the paper surface. In order to demonstrate the existence of the wetting delay in a graphical representation, the true power of the rate function has to be known, and the sorption values have to be plotted on the corresponding time scale. However, the water sorption experiments in the present work do not give any support to the wetting delay theory. It has been found that the water starts to penetrate into the paper immediately. Since no theoretical and experimental evidence for the wetting delay theory has been obtained, it has to be concluded that the wetting delay illustrations reported in literature represent only a misinterpretation of the water penetration theory. The water transport under no external pressure does not follow the classical Washburn theory, and the experimental sorption curves on a square time scale are often similar to parabolas. Hence, dividing of these continuous sorption curves into a horizontal part and a linear inclined slope does not correspond to physical reality.

Summary

87

8. SUMMARY A study has been made of the transport mechanisms and rate determining variables for water penetration in paper. In order to do this, a new measurement system has been designed and constructed. This system enables water sorption measurements in the contact time range of 0.0015-60 s as a function of external pressure (0.0-1.0 atm) and liquid temperature (23-90 oC). It has been found that the capillary transport rate of water is determined by a complicated interaction between different transport mechanisms. Thus, the capillary transport is strongly influenced by the interactions between water molecules and the fibre matrix at the wetting zone and ahead of the liquid front. As a result, the dynamic capillary pressure is affected by the transport velocity of the liquid front and other factors controlling this molecular interaction. Therefore, the classical pressure balance between constant capillary pressure and the pressure drop due to liquid flow does not adequately describe the capillary transport rate. A significant influence of fibre matrix expansion and fibre sorption on the transport rate has been established as well. The water transport rate is primarily determined by the pore structure of the expanded fibre matrix behind the liquid front, not by the pore system of a dry paper. It has also been shown that the penetration rate may be influenced by the counter pressure of the air which is replaced by water during the transport process. The mathematical models presented suggest that this effect can be significant when the air transport in the paper plane is restricted. Diffusion is the primary penetration mechanism for zero pressure water transport in hydrophobic paper, where the balance between the surface tension forces prevents capillary transport. The concentration gradient of water and osmotic pressure between the interior and exterior of the fibres are probably the main driving potentials for water transport via diffusion. Surface diffusion and water transport within the fibres probably dominate over water diffusion in the pores. The driving potential for water transport under external pressure is the sum of the external pressure and the :apillary and diffusion potentials. As the external pressure increases, the importance of the latter potentials is diminished. Water transport under very high external pressure is therefore primarily determined by the balance between external pressure and pressure drop due to liquid flow, and the importance of fibre sorption and expansion of the fibre matrix is reduced. The experimental results show that the external pressure is a decisive factor for water

88

Studies of water transport in paper during short contact times

transport rate in many wetting processes. It has been found that the e'fect of other liquid and paper variables is dependent on the pressure conditions during the water penetration. The effect of the characteristics of the liquid can often be related to molecular interactions between water molecules and the fibre matrix ahead of the liquid front. Thus, the strong influence of water temperature on the zero pressure transport rate is explained by the effect the temperature dependent vapour pressure has on diffusion rate and on the capillary pressure-determining processes ahead of the liquid front. The pressure penetration rate, however, is less influenced by the liquid temperature. This temperature dependence probably corresponds to the relationship between temperature and viscosity of water. The influence of the viscosity on zero pressure water transport is smaller than the increase in pressure drop due to liquid flow would suggest. This result supports the earlier conclusion that the capillary transport is not determined by the simple pressure balance between constant capillary pressure and pressure drop due to liquid flow. Pressure penetration, on the other hand, is directly dependent on the increase in the pressure drop. A decrease in the dynamic surface tension of the liquid lowers the dynamic contact angle between the liquid and the fibre surface, and accelerates the water transport under no external pressure. However, the equilibrium surface tension of an aqueous solution does not necessarily characterize the penetration rate, because the migration time of high molecular surface active agents to a newly formed surface is often longer than the surface age in a sorption process. The pressure penetration rate is not significantly influenced by the surface tension of the water phase. The water transport rate in paper can be affected by surface chemical as well as structural modifications of the fibre matrix. Sizing and self-sizing primarily influence the surface chemistry of the fibre matrix. Their effect on the capillary transport of water is therefore especially important. However, the capillary transport rate is affected only when the dynamic contact angle is below 90°, because the main transport mechanism above this value, diffusion, is independent of the surface chemical forces between the liquid phase and the fibre matrix. The pressure penetration is less dependent on the surface chemical forces, although the external pressures reached in this study have not eliminated the effect of sizing. The rate of self-sizing is greatly accelerated by sheet storage of the paper sample. This indicates that light is probably an important factor in the self-sizing mechanism. Calendering influences the pore structure of the dry paper. However, the expansion of the fibre matrix during the penetration of an aqueous solution may cancel the original differences in the pore systems. Therefore, calendering is an inefficient

Summary

89

method of regulating the water sorption during slow capillary transport. The pressure penetration rate, however, is more depend~nt on the pore structure of the dry paper. The fibre matrix has insufficient time to expand during a rapid pressure penetration, and a connection between calendering and pressure transport has thus been observed. Moisture content influences surface chemical as well as structural properties of the paper. The zero pressure capillary transport in hydrophilic paper has been found to increase with adsorbed moisture. This effect is primarily dependent on the increased capillary forces. On the other hand, water transport rate in hydrophobic papers, where diffusion is the primary penetration mechanism, is reduced by increased moisture content. The structural variations caused by adsorbed moisture influence mainly the pressure penetration. However, the importance of the moisture content dependent pore structure is, as discussed earlier, diminished by the expansion of the fibre matrix during the penetration process. The experimental results indicate that the wetting of the paper surface is completed in a time period which is shorter than the experimentally measurable contact times in the method used. Therefore, the experimental sorption volumes seem to extrapolate to a value which corresponds to the surface roughness of the paper. The experimental results also indicate that water starts to penetrate into the paper as soon as it comes into contact with the fibre matrix. During zero pressure water transport, the experimental sorption curves are often similar to parabolas on the square root scale of the contact time, i.e. the power of the rate function is higher than 0.5. The pressure penetration rate, however, usually is a comparatively linear function of the square root of the contact time.

References

91

REFERENCES 1. Eklund, D.E., Salminen, P.J., Tappi Journal 69(9):116-119 (1986).

2. Salminen, P.J., STFI-meddelande Serie D 264:60-71 (1986). 3. Eklund, D.E., Salminen, P.J., Appita 40(5):340-346 (1987). 4. Sandas, P.E., Salminen, P.J., 1987 Tappi Coating Conference, Houston, Conference Proceedings. 5. Salminen, P.J., 1988 Tappi Coating Conference, New Orleans, Conference Proceedings. 6. Salminen, P.J., a paper presented at the 1988 STFI Bestrykningskonferens, Stockholm. 7. Lucas, R., Kolloid Zeitschrift 23:15-22 (1918). 8. Washburn, E.W., Physics Review 17(3):273-283 (1921). 9. Haishi, T., Mokuzai Gakkaishi, 27(11):767-774 (1981). 10. Nissan, A.H., Proc. Tech. Sect. P.M.A., XXX (1), 96-. Ref. Hoyland, R.W., Field, R., Paper Technology and Industry 17(8):304-306 (1976). 11. Verhoeff, J., Hart, J.A., Gallay, W., Pulp and Paper of Canada 64(12):T509T516 (1967). 12. Reaville, E.T., Hine, W.R., Tappi 50(6):262-269 (1967). 13. Van den Akker, J.A., Windle, W.A., Tappi 52(12):2406-2419 (1969). 14. Bristow, J.A., Svensk papperstidning 70(19):623-629 (1967). 15. Aspler, J.S., Davis, S., Lyne, M.B., J. Pulp Paper Sci. 13(2):55-60 (1987). 16. Lyne, M.B., Aspler, J.S., Tappi 65(12):98-101 (1982). 17. Aspler, J.S., Davis, S., Lyne, M.B., Tappi 67(9):128-131 (1984). 18. Aspler, J.S., Lyne, M.B., Tappi 67(10):96-99 (1984).

92

Studies of water transport in paper d'uring short contact times

19. Daub, E., Sindel, H., Gottsching, L., Das Papier 40(6):250-258 (1986). 20. Anderson, B.L., Higgins, B.G., 1986 Tappi Coating Conference, Conference Proceedings. 21. Zisman, W.A., Contact angle, wettability and adhesion, American Chemical Society Advances in Chemistry Series 43:1- (1964) 22. Lepoutre, P., Svensk Papperstidning 89(1 ):20-29 (1986). 23. Lepoutre, P., Ioue, M., Aspler, J.S., Tappi 68(12):86-87 (1985). 24. Kaelble, D.H., Paper Physics Seminar, STFI, Stockholm, June 1984. 25. Bristow, J.A., Svensk Papperstidning 74(20):645-652 (1971). 26. Bristow, J.A., Svensk Papperstidning 75(21):847-852 (1972). 27. Hoyland, R.W., Fibre-Water Interactions in Paper-Making, Tech. Div. BPBIF, London, 557-577 (1978). 28. Schubert, H., Fibre-Water Interactions in Paper-Making, Tech. Div. BPBIF, London, 537-553 (1978). 29. Rose, W., Heins, R.W., J. Colloid Sci. 17:39-48 (1962). 30. Cherry, B.W., Holmes, C.M., J. Colloid and Interface Sci. (1969).

29(1):174-176

31. Hoffman, R.L., J. Colloid and Interface Sci. 94(2):470-486 (1983). 32. Strom, G., to be published in J. Colloid and Interface Sci. 33. Luner, P., Sandell, M., J. Polymer Sci. 28:115-142 (1969). 34. Baird, P.K., Irubesky, C.E., Tech. Assoc. Papers 13:274-277 (1930). Ref. Casey, J.P., Pulp and Paper, John Wiley & Sons, Vol. 3:1751 (1981). 35. Salminen, P.J., M.Sc. Thesis, Abo Akademi (1985). 36. Skowronski, J., Lepoutre, P., Tappi 68(11):98-102 (1985). 37. Skowronski, J., Lepoutre, P., 72nd Annual Meeting of CPPAjTS, Montreal (1986), Conference Proceedings. 38. Lepoutre, P., Bichard, W., Skowronski, J., Tappi 69(12):66-70 (1986).

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