Jul 15, 1998 - To better understand the reasons for this finding, sea surfactant adsorption and desorption time .... wave apparatus, this frequency range is 0 to 4 Hz. A separate .... Transverse. Motion Table ' ... Trak Photonics Model OT-300 electronic system which ..... that had been offshore in Cape Cod Bay shortly before.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103,NO. C8, PAGES 15,695-15,715,JULY 15, 1998
Dynamic behavior of natural sea surfactant films JohnT. Mass1 and JeromeH. Milgram Departmentof OceanEngineeringMassachusetts Institute of Technology, Cambridge
Abstract. The dynamic behavior of sea surfactantsis studied at timescalesfrom 0.04 to 2 secondsby generatingwaveson the water containingits natural surfactants in the laboratory and comparingdynamical measurementswith theoretical predictionsfor prescribedsurfactantproperties. The propertiesconsideredare film pressure,elasticity and surfaceviscosity. For longitudinalMarangoni waves in the frequencyrange of 0.5 to 4.0 Hz, time-varying film pressuresare measured. For transverse waves in the frequency range of 3 to 25 Hz, spatial decay rates are measured. Prior to conductingexperimentswith sea water containing soluble natural surfactants,the proceduresand methodsof analysisare validated by experiments with clean fresh water and with an insolubleoleyl alcohol film. A notable findingis that the static film elasticityaccuratelypredictsthe dynamicbehaviorof both the insolubleoleyl alcohol film and the solublenatural sea surfactant films. To better understand the reasonsfor this finding, sea surfactant adsorption and
desorptiontime historiesweremeasured.The adsorption/desorption time scales rangedfrom 46 to 196 min. One reasonfor the accuratepredictionof surfactant dynamicbehaviorby the static elasticityis that the timescalesof the wavesare muchshorterthan the adsorption/desorption timescales.The conclusion is that the static elasticity controlsthe interactionsof surfactantswith most hydrodynamic disturbanceshaving timescalesup to several min.
1.
The influences of surfactants on the flows are due to
Introduction
Much of the ocean surface contains organic surfactant moleculeswhich can have sufficientsurfacedensity to form surfacefilms over regionswith a wide range of sizes. Most natural
sea surfactants
have sufficient
sol-
ubility for there to be exchangesof them between the surfaceand the underlying bulk fluid. It is well known that the viscoelasticproperties of surface films have a major influenceon the viscousdamp-
the surfacestressesand their gradients.On cleanwater, for which there is no surfactant, the only surfacestress is the constant surface tension of the air-water
inter-
face. Surfactants can, in general, have dilational and shear elasticities and surface viscositieswhich depend on both the concentration and molecular arrangement
of the surfactant. Huhnerfusset al. [1985a]conclude that for wavesof small steepnessthe effectsof the shear coefficientsare negligiblein comparisonto thoseof the
ing of shortgravity and gravity-capillaryseawaves[cf. dilationalcoefficients, and Hansenand Ahmad[1971] Hansen and Ahmad, 1971; Cini and Lombardini,1978; show that for two-dimensional waves the surface visor Tangand Wu, 1992]andon the interactions between couseffectsare due to a singlesurfaceviscouscoefficient vorticesand a free surface[cf. Hirsa and Willmarth, which is the sum of the surface shear and dilational vis1994;or Tsai and Yue,1995]. The literatureon these cosities. To our knowledge,no studieshave been done surfactant
interactions
is extensive
so that
the
refer-
which show significantinfluencesdue to surfaceshear elasticity and viscosity. For these reasons,our studies here are directed toward the dilational elasticity E and the total surface viscosity of deadorganisms[Zutic et al., 1981; Bock and Frew, Severalinvestigatorshaveconsideredor proposedthat encesabove are only a few of the many existing examples. In the open sea the largest sourcesof surfactants are phytoplankton exudate and the chemicalbreakdown
ss31.
the interactionof surfactantswith vortices[cf. Tsai and Yue,1995]and with seawaves[cf. Huhnerfuss et al., 1985a,b] may be morecomplexthan singlevalues
Now at The Exeter Group, Cambridge, Massachusetts. Copyright1998by theAmericanGeophysical Union. Papernumber98JC01190. 0148-0227/98/98JC-01190509.00
of surfaceelasticity and surfaceviscosityimply due to changesin surfaceconcentrationor form of the molecular arrangementduring the timescaleof the wave or vortex interactions. Even if the surface elasticity and nonzero surfaceviscosity are constants,their influence
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MASS AND MILGRAM' DYNAMIC BEHAVIOR OF NATURAL SEA SURFACTANT FILMS
on wave and vortex dynamics obviously depends on their magnitudes. Although severalinvestigatorshave measuredthe elasticity of ocean surfactant films, little is known about their surface viscosities.
The
central
issue which
we address here is the ex-
tent to which the static elasticity of ocean surfactants predicts their dynamic behavior over timescalesin the range of 0.04 to 2.0 s. In addition, to better understand our findings at these timescales, we have measured adsorption and desorption kinetics over much longer timescales. These measurements, and the ad-
Here kT is the wavenumber of the transverse wave which is the familiar gravity, capillary-gravity,or capillary wave;kL is the wavenumberof a waveknownas the longitudinal, or Marangoni, wave which has very little transversemotion. Its longitudinal motion is suchthat the dynamic viscousshear stressin the bulk fluid at the
interfaceis balancedby the gradient of the longitudinal stress in the surface film.
We have made facilities to generate each of these kinds of waves,longitudinal and transverse,and to measuretheir propertiesover rangesof frequencies.By comsorptiondata providedby BockandFrew[1993],figure paring the measurementswith similar quantities pre7, lead to tentative conclusionsfor timescalesup to sev- dicted by the theory, also given by Hansen and Ahmad eral min.
[1971],valuesor rangesof surfacefilm elasticityand surfaceviscosityunder dynamic conditionscan be estimated.
2. Basis for the Primary Wave Measurements and Their Analysis
Ting et al. [1984]showed that longitudinal wavesare
more sensitiveto small variations in surfacefilm properThe approachtaken here is to generatewaveson sur- ties than are transversewaves. This makeslongitudinal faces with and without surfactants and to infer the waves preferable for the study of film properties over surfactant properties from measurementsof the time- the range of frequenciesfor which almost purely lonvarying surfacetension and the spatially varying sur- gitudinal wavescan be generated. In our longitudinal faceelevation.Hansenand Ahmad[1971]haveshown wave apparatus,this frequencyrange is 0 to 4 Hz. A that the dispersion relation for small-amplitude sinu- separatetransversewave apparatuswas made and used soidal waveson an air-liquid interface, with the stresses to determine film properties at higher frequencies. due to the air neglected,is Longitudinal waves, with the longitudinal surface
fluid displacement denotedby •(x,t), weregenerated
(pw2 - Tk3 - pgk)(pw • - mk•e)- ek3(Tk • + pgk)
+4ipt•wak • + 4t•2w2ka(m - k) - 0 (1) where;
on a surfaceof length d with a wave maker at x - 0 with boundary conditionsas follows:
•(0, t)- Aexp[i(• - wt)]
•(d, t)- 0 (4)
p is the densityof the water;v•is the circularfrequency where t is the time and physical quantities are the of the waves; T is the mean surface tension on the in-
real parts of all equations with a time dependenceof
terface;k is the complexwave numberin the longitudinal direction;g is the acceleration due to gravity; e - E- iw/•s equal to complexsurfacestiffness;and /• is the absoluteviscosityof the bulk fluid, m is the
exp(-iwt). The boundaryconditionat x - 0 matches the surfacefluid motion to that of the horizontallymoving longitudinal wave maker, whereas at the opposite
endof the apparatus(x - d), no longitudinalfluidmo-
tion can occur. Sinusoidalwavessatisfying theseboundstreamfunctionwhich describesthe rotationalcompo- ary conditionsare given by complex wavenumber in the vertical direction for the
nent of the flow, givenby the solutionto the following equation with a positive real part:
m - v/k• -iwp/l•
(2)
The complexwavenumberis k - k• + iki, where k• =
2•/A, andA is the wavelength.ki is the spatialdecay rate of the waves.
Aexp[i(•
exp(ikLd) exp(-ikLx)
exp(ikLd)- exp(-ikLd) exp(-ikLd)
(5) -exp(ikLd) - exp(-ikLd) exp(ikLx)
The time varying surfacetension due to distortionsof HansenandAhmad[1971]haveshownthat onlytwo of the six solutions(roots)for k in (1) are physically the surfacein a longitudinalwaveis T'(x,t) - ed•/dx realistic.They are calledkL and kT and are givenap- which is given explicitly as
proximately by
k• • Pl/q•3/q•l/qei•/8 (3) and thesolution to •P (k•)• • gk•-• - 0
-ieAkL exp[i(•
exp(ikLd) - exp(-ikLd) exp(-ikLx) exp(ikLd) +exp(ikLd) - exp(-ikLd) exp(-ikLd) exp(ikLx)] (6)
Thesevaluesfor k• and k• can be usedas initial apIn our longitudinalwave experiments,the wavemaker proximationsto obtain refinedestimatesby applying motionand T • at a fixed valueof x weresimultaneously Newton'smethodto (1).
MASS AND MILGRAM:
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measuredas functions of time and stored as computer files. From thesemeasurements,the followingtwo quan-
tities weredetermined:ITaliA whichis the ratio of the amplitude of the surface tension oscillation to the amplitude of the wave maker motion and the phase lag, which we call 0, of the surface tension oscillation with
5O
SEA SURFACTANT ,
FILMS
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.
• 40 •
30
respectto the wavemaker motion. ITalIA and 0 are comparedwith their predictions by (6) for variousprescribed valuesof E and/•8 to infer these values. Equa-
• 20
tion (6) is influencedby thesefilm properties,not only by e appearingas a multiplicativefactor in the equation but also by its influenceon kL. When transverse waves were generated, the spatial decay rate was measuredand comparedwith the imag-
i
0
inary part of k•, in the solutionto (1).
I
2
•
i
i
4
i
i
6
8
10
FILM PRESSURE, I1, (mN/m)
3. Apparatus and Measurement Methods
Figure 2. Elasticity versusfilm pressurefunction generated by differentiation of polynomial fit to a compression isotherm.
Two deviceswere built for measuringwavesand surfacefilm properties: a trough and instrument systemfor generatinglongitudinalwavesand measuringthe timevarying surfacetension at a fixed location, and a wave decay tank with instrumentation for generating transverse waves and measuring their spatial decay rates. Both devices were equipped for measuring the static surface tension
3.1.
versus surface
Measurement
area.
of Static
Surface
measurestatic surfacetensions. Film pressureII versus
surfacearea ,4 (or ln,4) isothermswere measuredby the repeated processof changingthe surfacearea, waiting for the disturbanceassociatedwith the area change to subsideand measuringthe surfacetension. The film pressureis defined as
Tension
II = Tclea n- T
and Elasticity Static surfacetensionswere usually measuredwith a
whereTclea n is the surfacetensionof the bulk fluid
conventional Wilhelmyplate [cf. Adamson,1976]hung
without
from a computer-interfaced electronic balance. The Wilhelmy plate was a platinum rectangle 0.1 mm thick and 2.5 cm long, toughenedby sandblastingor chemical etching. The transversewave laser phase meter, which is described in section 3.2, was implemented for measurement of dynamic surface tensions, but could also
tension for the film-covered
15
,
(7)
a surfactant
film and T is the measured surface fluid.
The static elasticity E8 is defined by dII
E•= -d(lnA)
(8)
To determine Es, the film pressure versus ln A function was first fitted with a fifth-order polynomial having minimum mean squared error. This polynomial function was then differentiated analytically to obtain Figure 1 showsan example of a polynomial fit to mea-
Polynomial fit ed Data
sureddata usingan oleyl alcohol[Z-9-octadecen-l-ol, CH3(CH2)7CH:CH(CH2)aOH] surfacefilm on distilled
water. The resulting Es versusIi function is shown in Figure 2. 3.2.
Longitudinal
Wave Trough
The longitudinal wave trough and someof its instrumentation are shown in Figures 3 and 4. It is 80 cm long, 16.5 cm wide, and 2.5 cm deep and was precision t• t• t• • t•...O a
i
i
i
6.2
Log(Area [cm2]) Figure
1.
Polynomial fit to film pressure versus In
(area) measureddata.
machined from a solid block of aluminum
and hard coat
anodized. It was coated with a thin layer of paraffin applied by heating the trough enoughto melt paraffin on its surfaceswhich were then polished after the trough cooled. For use, the trough was filled with fluid to the extent that the fluid surface just barely bulged above the top of the trough. The nonwetting wax-coated sur-
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facesprevented the fluid from spilling out of the overfilled trough. The long edgesof the trough were machined with 5 mm wide rails along the highest point. Film barriers, made of paraffin-coated Lucite bars with a 6 mm x 6 mm cross section were placed acrossthe trough and in contact with the fluid surface. The troughwassupportedby three legs,with leveling screwsin their bases,whichelevatedthe trough abovea computer-interfaced motor-drivenlead screwtraversing system.A U-shapedbracketon the movingpart of the traversing system surrounded the bottom and sides of the trough crossection. A film barrier in contact with the liquid surfaceand the trough rails fitted into notches
lary waves by using "electrocapillarity" following the
methodsof $ohl et al. [1978],whereaswe generated
the capillary waves mechanically. Also, Miyano et al. determinedlongitudinal wave properties by measuring time-varying surfacetensionsat two locationsalongthe direction of propagation, whereas we determined the properties from measurementsat a single location and knowledgeof the amplitude and phase of the longitudinal waves imposed by the wave maker at x = 0. Operation of the TWLPM is based on the dispersion relation of transversecapillary waveswhich were generated by a barely immersedteflon bar having a wedgeshaped crossectionand 8 cm long, located along one in the sides of the bracket. Rubber bands were used of the long sidesof the trough. An electricallydriven betweenthe film barrier and the bracketto apply slight shaker oscillated the bar vertically at 200 Hz with an compressive force (0.1 to 0.2 N) on eachsidebetween amplitude of about 0.1 mm. The capillary wavespropthe barrier and the top of a trough rail. This kept the agated acrossthe tank parallel to its short walls and barrier hard againstthe rails which preventedleakage therefore perpendicular to the direction of propagation of the surfacefilm past the barrier at the rails. of the longitudinal waves. The barrier movementcomputerwasprogrammedto The time-varying slope of the transverse waves was move the barrier back and forth in sinusoidal motion to
measured at a position between 6.0and7.1cmfromthe
act as a wavemaker for longitudinalwavesor to slowly
transverse wavemakerand7 cm (x) frommeanposition
movethe barrierin smallsteps(typically0.5 or 1.0cm)
of the longitudinal wave maker by a laser slope gauge between which the surface tension was measured with as sketchedin Figures 3 and 4. A vertical laser beam the systemquiescentto obtain film pressure,II, versus generatedby 19 mW Lasermax laser having a wavearea A (or In A) data. When longitudinalwaveswere length of 670 nm passedthrough a half-silveredmirror generated,the mean positionof the longitudinalwave and part of it was reflected by the water surface. The maker was 40 cm from one end of the trough, and the transverse slope of the reflected beam deviated from experimentwas conductedin this 40 cm long space. the vertical direction by twice the transverse wave anIn the presenceof longitudinal waves,dynamic sur- gle. The small slope of the longitudinal wavesresulted facetensionswere measuredby their influenceon trans- in a small longitudinal beam deflection. The reflected versecapillary waves. The method is implementedin beam intersected the half silvered mirror and half of it a transversewave laserphasemeter (TWLPM), also was reflected nearly horizontally and illuminated a Sicalled a capillary wave probe and is similar to that Tek Model IL-10SP (p-n semiconductor) light sensitive of Miyano et al. [1983]. They generatedthe capil- position detector. The slope of the transverse waves
c
FilmBarrier
/
•
Motion Table'
Position Detector_ N•
Transverse
Wave Maker ?%f Laser • $ I I
(• •_Mirror
Laser Position Detector • . •_•
Transverse
Wave Maker
NI
I
•
rl• • II
(•
Figure 3. The longitudinal wave trough. The transversesurface-touchingbar used for surface film compressionand dilation and for generatinglongitudinal wavesis shown. Also shown are the transversecapillary wave generator and the laser slope gauge. For clarity, the lens between the mirror and the position detector is not shown.
MASS AND MILGRAM: DYNAMIC BEHAVIOR OF NATURAL SEA SURFACTANT FILMS
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Position Sensitive
Laser
Detector Light Beam Lens
Half-Silvered Mirror
Water
Surface
Figure 4. Diagram of optical components of the transversewavelaserphasemeter. influenced the transverse location where the beam inWe usedthe approximate transversewave dispersion tersectedthe detectorand the small slopeof the longi- relationfor k• givenin (4) to determineexperimental tudinal
waves led to vertical
The detector
variations
in this location.
is not sensitive to small vertical
variations
in position of the beam, but is sensitive to transverse position which is proportional to the transversewave slope. The detector signal was processedby an OnTrak Photonics Model OT-300 electronic system which produceda +10 V signal that was proportional to transversebeam position. This systemmeasuresthe slopeof transversewavesextremely well in the presenceof longitudinal waveshaving a very small surfaceslope. However, at longitudinal wave frequenciesabove 3.0 Hz the longitudinalwave maker made small transversewavesas well. The slopesof theselow frequencytransversewaves deflectedthe light beam vertically on the detectorwith sufficientmagnitude to introduce noise and observable scatter
in the measured
data.
The value of the surface tension To before the lon-
gitudinal waves were started was measured with the Wilhelmy plate. Then, after the longitudinal waves were started, the surfacetension was measured40 times
values of the surface tension. Numerical experiments showedthat for the conditions of our experiments, the
error in computedsurfacetensiondue to useof the approximatedispersionrelation rather than the implicit
exact dispersion equation(1) for the transversewaves is lessthan 3% of the surface tension oscillation amplitude. The time-varying surfacetensionby this method
is [Mass,1996]
T(t)-To Lk•l+c)(t)
(9)
where d, was the distance between the wave maker and the slope measurement position.
During the 0.6 ms that the phase was determined, the longitudinalwavemaker positionwasalsomeasured electronically.The resultswere simultaneousrecordsof wave maker positionand surfacetension,sampledat 40
Hz, from whichthe relativeamplitudeIT'l/A and the
phase,0, of the surfacetensionwere calculated. For the 200 Hz transversewavesusedby the TWLPM per second.Eachof thesemeasurements consisted of a the relationship between wavelength and surface tencomputer-baseddata acquisitionof 1300 samplesof the sion is quite insensitiveto elasticity E and surfacevistransversewave maker driver signal and the transverse cosity b,, which is what accountsfor the validity of wave slope, with a data rate of 65,000 Hz per chan(9). Therefore, the TWLPM measures the time-varying nel. For eachof thesesetsof measurements, the change surface tension, but does not directly measure E or in phase •b between the transverse wave maker driver These quantities will be inferred by comparing the measignal and the transversewave slope signal was detersured time-varying surface tensions with predictions of mined from the time r betweenzero upcrossings of the the theory described by (1) and (6). signalsas •b = 27trip- C)o,where P is the periodof 3.2.1. Static surface tension measurement valthe 200 Hz. transversewavesand •bois the phasedifferidation. Initial experiments were conducted in disence between the slope transducer and the transverse tilled water with an oleyl alcohol film. A film pressure wave maker driver signal before the longitudinalwaves were turned on. If the surface tension variation
due to
versus surface area isotherm was measured in our stan-
dard way. This was to repeatedlymovethe film barrier 1 cm, wait for a prescribedtime which in this casewas 15 s, and then measure the surface tension with the +2nTr(n is an integer)to eachphasemeasurement such Wilhelmy plate hung from the electronicbalance. As that the phasechangefrom the measurement1/40 s was the casewith all of our experiments,the entire proearlier was less than 2•r. cesswas under computer control with computer-based the longitudinalwaveswas large enoughto changethe transversewave phaseby more than 2•r, the calculation can be erroneous.This difficultywasavoidedby adding
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MASS AND MILGRAM: DYNAMIC BEHAVIOR OF NATURAL SEA SURFACTANT FILMS
data acquisition. During this experiment the surface tension history was also measured with the TWLPM and the resulting surface tensionsfor the same times as the Wilhelmy plate measurementswere recorded. A comparisonof resultsfrom the two methodsis shownin Figure 5. The rms differencebetween results from the
two measurement methodsis about0.1 mN/m. 3.2.2. Correction for phase error in laser slope gauge response. An important experiment for dynamic instrument calibration is a comparisonof results of the measurementsmade by the TWLPM in the presence of longitudinal waveswith theoretical predictions based on the static elasticity and zero surface viscosity. The surface tension was measured in the absence of waves with the Wilhelmy plate and the associated film pressurewas usedin an elasticity versusfilm pressure function of the type shown in Figure 2 to obtain the elasticity for use in the theoretical equations. Using raw data
measured
with
the TWLPM
resulted
in the
comparisonshown in Figure 6. The scatter in the data at longitudinal wave frequencies above 3 Hz is common in this and similar experiments
due to "noise"
related
to the aforementioned
transversewavesgeneratedin addition to the longitudinal wavesby the longitudinalwave maker. Apart from this scatter, it is important to note the very good comparison between the measured and predicted values of
The time delay was partially due to the electronic systemthat processedthe light positiondetectorsignal and partially due to the transversewave hydrodynamics.The dispersion relationequations(1) and (3) strictly apply to a surfacewhosevariationsin surface tensionare due only to one set of waves. Our application of theseequationsto the high-frequencytransverse waveswas done in the presenceof time variations in sur-
facetensiondueto the longitudinal waves.Whenthe surfacetensionchangesdue to the longitudinalwaves, there is a small time delay before the high-frequency wave phase changesat the optical detection position to the dispersionrelation value associatedwith the new surface tension.
In order to quantify the time delay we conducteda set of experimentson the oleyl alcoholfilm for three longitudinal wave frequencies,2.0, 2.5, and 3.0 Hz. and three laserphasemeter transversewavefrequencies,100, 200, and 300 Hz, with nine combinationsin all. In all cases, there was excellent agreementbetween theory and ex-
perimentfor ITtl/A. The time delaycorrection required to bring the measuredphaseinto correspondence with theory was calculated,and the resultsare shownin Figure 7. The straight line in Figure 7 is given by P
r - 0.305d, w-•
+0.0013 s (10)
ITtl/A. This indicatesaccuracyin measuringthe variwhere wt is the transverse wave frequency. ationsin ITtl with the capillarywaveprobetechnique. It also indicatesthat the film stiffnessin the presence of the longitudinal wavesis very nearly the same as the static elasticity for this oleyl alcohol film. However, an apparent error appears in the measured phase of the longitudinal wave at the measurementpoint. Sincethis error is nearly proportional to longitudinal wave frequency, it has the form of a constant time delay rd in the capillary wave slope measurementsystem.
Scaling thevariable timebythequantity d,[p/(wtT)]•/3
was motived by its being proportional to the propagation time from the transverse
wave maker
to the laser
phasemeter. Equation (10) was usedto correctthe phase in all measurementswith the laser phase meter. For the conditionsof Figure 6 the time delay is 0.051 s. The phasedata with this correctionare shownin Figure 6.
3.3. Wave Decay Tank The wave decay tank, as shown in Figure 8, is 2.4 m long, 0.42 m wide, and 0.15 m high and was filled with water to a depth of 0.1 m. One end was fitted with a paddle-type wave maker which spanned the tank to generatetransversewaveswith frequenciesfrom 4 to 30 Hz. The wave maker is hinged at the top of the tank and was driven at a point 0.15 m higher by a rod from the driver unit of an acoustic speaker. Power to the speakerwas provided by a two-transistorpush-pull DC amplifier whoseinput signal came from a low-frequency
¸ 66 z
to 62
Laser Pha
o Wilhelmy Plate
sine wave generator. Experiments were conducted with several plunger-
58 950
900
850
800
750
FILMAREA[cm 2] Figure 5. Comparison of a film pressureversus area isothermusingWilhelmy plate and capillary waveprobe methods for an oleyl alcohol surface film.
type and paddle-type wave makers. All of them made wavesthat had somedeviation from pure two-dimensional waves.
The
wave
maker
whose waves were most
chosen for use was the one uniform
across the tank.
To
minimize error in measuring spatial decay rates, four laser slopegaugeswere fabricated and mounted at dif-
ferent transversepositionson a manually movedcar-
MASS AND MILGRAM: DYNAMIC BEHAVIOR OF NATURAL SEA SURFACTANT FILMS
T'I/A
Lines are Theoretical Results
15,701
++i•']
+
• q' ß
ß
q. + q. +
+
PhaseLag,0 From Instrument Output Correctedfor 0.051 s Lag From Instrument Output 3
4
FREQUENCY (Hz) Figure 6. Comparisonsof measuredand theoretically predictedoscillationsin the surfacetensions in longitudinal waves on an oleyl alcohol film. Lines in this and similar figures show theoretical predictions.
riage which rode on a rail above the tank. The decay rates measuredby the four gaugeswere averaged together. Carriage position was measuredwith a 10-turn potentiometerwith a cogwheel on its shaft. A cogbelt from the carriage passedover the wheel, and the belt was kept taut by a weight hanging on its end. Figure 9 shows a laser slope gauge. The beam was generatedby a 19 mW Lasermax laser equippedwith a 5ø line generator so the beam has the shape of a narrow fan. The line of intersection
of this beam with
the
surfacewas oriented acrossthe tank so that it was par-
allel to wave crests and troughs. The reflected beam
passedinto the openend of a shieldedcan througha band pass optical filter, which passedthe laser light and blocked much of the ambient light, and then onto a SiTek model IL-30SP semiconductorposition detector. Its output was convertedto a +10 V signal by an On-Trak Photonics model OT-300 signal conditioner. In wave decayexperimentsthe four wave slopesignals, low-passfiltered with a two-poleButterworth filter having a cutoff frequencyof 50 Hz, and the carriage position signalwere eachsampledat a rate of 200 Hz by a computer-interfacedanalog-to-digitalconverter. Static surface tensions were measured with the Wil-
0.07 LONGITUDINAL
WAVE
helmy plate hung from the computer-interfacedelecFREQUENCIES tronic balance as was done with the longitudinal wave trough. However,for use in the wave decaytank the apparatuswas supportedby a bracket hung from the 0.06 o 2.5 Hz overheadrail as shownin Figure 8. Film pressureversus area isothermswere measuredby the Wilhelmy plate for areasset by manual positioninga barrier which slightly piercedthe surfaceand which was tightly sealedto the 0.05 walls. This processwas managed by a computer program which prompts the user to type in the barrier positionafter which the surfacetensionfrom the electronic balance was automatically recorded. Computa0.04 ' tion of elasticity and generation of the elasticity versus 0.14 film pressurefunction was done in the same way as for experimentsin the longitudinal wave trough. ds[p/(co t T)] When conductinga wave decayexperiment, the slope gaugecarriagewas moveda distanceof about 1.6 m in Figure 7. Time delayin laserphasemeterfor an oleyl a time span of about 20 s. The wave amplitude for alcohol film on distilled water. The measured surface each cycle was determinedcomputationallyfrom half tensionwas 65 mN/m, the measuredstatic elasticity was30 mN/m, the distanceds betweenthe transverse the peak to trough height difference. The amplitude wave maker and the phase meter was 7.1 cm, and the a(x) for a spatialdecayrate c• takesthe form distancex betweenthe longitudinal wavemaker and the phase meter was 7 cm. a(x) =aoe -'•: (11)
v 3.0 Hz o 2.0 Hz•/
/o
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SlidingCarriage l•alance
•cal•
FILMS
PositionEncoder
-
[
I
Carriage Stop •> ;tic Wave
•
•
u
• •
•sers
; •ilhel•y Plate
Figure 8. The wave decay tank.
This is equivalent to
shorefrom San Diego, California; and Hampton Harbor, New Hampshire. Experiments were conductedwith adIn a(x) - In ao- o•x (12) sorbed surfactant films on these samples. Samples were taken at Cohasset several times and In eachexperimentalmeasurementthe decayrate c•was analyzed. These were all taken during the flood tide, taken as the negative of the slope of the straight-line severalhours after the flood began. The sampleswere fit to the experimentaldata of ln a(x) versusx with taken near the narrow entrance cut, through which the minimum mean squarederror. flow is swift, so the sample was predominantly water that had been offshorein Cape Cod Bay shortly before collection. In all cases, the analysis included surface 4. Samples Tested and Experimental compression isotherms, measurementof time-varying Procedures surfacetensionsin the presenceof longitudinal waves, and measurement of decay rates of transverse waves. 4.1. Surfactant Samples Someof the Cohassetsampleswere unaltered, and some Natural slicks are mixtures of very many organic had their biologicalactivity poisonedat collectiontime compoundswhich can occur in both equilibrium and by addition of sodium azide at a concentrationof 5 nonequilibrium conditions of surface adsorption. It is ppm by weight. No difference was observed between essentiallyimpossibleto reproducein the laboratory the measurementsof poisonedand unpoisonedsamplesconexact physicaland chemicalconditionsof any particular ducted within 2 days of collection. slickin the openocean. In orderto makethe laboratory A sampleof the salt pond water was collectedwithin experimentsas closeto oceanicconditionsas possible, the cut to Vineyard Sounda few hoursafter the start of samplestaken were mixtures of both surface and subthe ebb tide. Thus this collectedwater was previously surface water. within the pond for a considerableperiod of time. Samples of seawater were obtained from four locaThe San Diego sample was taken to include water tions: Little Harbor entrance at Cohasset,Massachusetts; from a more offshorelocation. Since a few days were the Vineyard Sound exit of a tidal salt pond at Woods requiredfor its shipment to the laboratory, it was poiHole, Massachusetts;the Pacific Ocean a few miles offsonedwith sodium azide at collectiontime. Experiments with the San Diego water occurred before the wave decay tank was constructedso they were limited Laser
•
tomeasurement ofstatic concentration isotherms and
Mounting Rod.•••• surface tension variations inlongitudinal waves. We Line Generator • 3 •l '• have not included these results here because they were Window • ,..limited and obtained before our procedures were refined p-n Detector _ r• and standardized. However, weareable toreport that Optical riller/•_.• •• the results were entirely consistent with those from the SNeld • • other samples. Incident
Beam •
The Hampton water, taken late on the incomingtide
Reflected
Beam
in a currentto obtainwaterthat hadrecentlybeen
in the ocean,was obtainedprincipallyfor experiments otherthan thosereportedhere. However,we will report informationabout surfactantadsorptionand desorption Figure 9. Front and sideviewsof a laserslopegauge. to and from the surfacefor the Hamptonsampleto show Fourof thesewereconstructed and usedsimultaneously. their similarity to resultsfrom a Cohassetsample.
MASS AND MILGRAM: DYNAMIC BEHAVIOR OF NATURAL SEA SURFACTANT FILMS
15,702t
In addition to the experimentswith adsorbedfilms,
experiments wereconduced withcleanwaterandwith
40
two spreadfilms. One was Woods Hole salt pond surfactant that was isolated by solid phaseextraction and
30
dissolved in methanol[FrewandNelson,1992]andprovided to us by R. Nelson of the Woods Hole OceanographicInstitution. The other was oleyl alcoholsinceit
providesan exampleof a pure substance.No spreading to 20 solventwasusedwith the oleylalcohol.A smalldroplet of the pure material was allowed to spread, and subsequently, the film pressurewas reducedto a desiredvalue by trapping someof the film behind a secondarybarrier near the end of the apparatusoutsidethe regionof the
• lO
experiment wasmoved whilein contact ß Thisbarrier
i
00
i
desired film pressure.
Experimental
i
2
with the fluid surface and the tank rails to achieve the
4.2.
i
i
i
4
i
i
6
i
8
FILM PRESSURE
i
i
l0
i
12
(mN/m)
Figure 11. Elastic properties of a Cohasset seawater
Procedures
surfactant
film.
Dynamic experiments with waves in either the lon-
gitudinal wave trough or in the wave decay tank were precededand followedby measurements of film pressure versussurfacearea and calculationof elasticityversus film pressurefunctionsby the methodsexplainedin section 3.1. The natural sea films becomestiffer upon repeated compressions that are each followedby surface expansion. This phenomenonwas named "work hard-
componentsfrom the surfaceuponsurfacecompression, or to modificationsin surfactantmoleculearrangements whenthe surfaceis compressed requiresa chemicalanal-
ysis capable of detecting differencesin constituentsbefore and after work hardening. As far as we know, such an analysis has not been done, and the mechanism of ening"by BackandFrew[1993],whomeasured it in sevwork hardening is not known with certainty. Back and eral samplesof adsorbedseawaterfilms and in spread Frew [1993]providea comprehensive discussion about films of surfactants they extracted from seawater. In the experiments done by Bock and Frew, and in those selectivedesorptionbeing its most likely cause. No matter what mechanism is responsiblefor work we have done, most of the work hardeningoccursin hardening,we needto be sureit doesnot occurto a sigthe first few area compressions and expansionswith little changein film pressureversusarea isothermsupon nificant extent betweenthe times when static film propertieswere measuredfor usein the theoreticalequations subsequentmeasurements. It seemsthat determiningwhether work hardening and when dynamic experiments were carried out. To is due to selectivedesorption of the least surface-active achieve this, we carried out repeated static compres-
sionsand expansions (with a minimumof threetimes) until the measured elasticity versus film pressure be-
4O
3O
Z
C• 20
•'
20
