pubs.acs.org/Langmuir © 2009 American Chemical Society
Evaporation Rate of Graphite Liquid Marbles: Comparison with Water Droplets Merve Dandan and H. Yildirim Erbil* Gebze Institute of Technology, Department of Chemical Engineering, Cayirova, Gebze, 41400, Kocaeli, Turkey Received March 1, 2009. Revised Manuscript Received May 4, 2009 Liquid marbles are liquid drops made completely nonwetting by encapsulating the drop with a hydrophobic powder. The absence of contact with the substrate avoids contamination problems and produces high marble displacement velocities. Liquid marbles behave as microreservoirs of liquids able to move without any leakage and are promising candidates to be applied in biomedical and genetic analysis where 2D microfluidics and lab-on-a-chip methods are used. The lifetime of a liquid marble depends on the chemical nature and particle size of the hydrophobic powder as well as the liquid used to form it. There is a need for chemically inert liquid marbles, which can be used over sufficiently long periods for industrial applications. In this work, we successfully synthesized graphite liquid marbles for the first time by encapsulating graphite micropowder on water droplets and determined their evaporation periods and useful lifetimes in constant relative humidity and temperature conditions in a closed chamber. The evaporation rates of graphite liquid marbles were compared with the rates of pure water droplets in the same conditions, and it was found that they had nearly twice the lifetime of pure water droplets. The use of chemically inert graphite particles having electrical conductivity and dry lubrication properties to form a liquid marble may be a starting point for their successful use in microfluidics, genetic analysis, antifouling, wear-free micromachine, electromechanical actuator, and valve applications.
1. Introduction Liquid marbles are formed when hydrophobic grains self-organize on the liquid-vapor interface of a hydrophilic liquid.1-24 Quere and Aussillous created so-called “liquid *Corresponding author. E-mail:
[email protected]. (1) Aussillous, P.; Quere, D. Nature 2001, 411, 924–927. (2) Mahadevan, L. Nature 2001, 411, 895–896. (3) Quere, D.; Aussillous, P. Chem. Eng. Technol. 2002, 25, 925–928. (4) Quere, D. Physica A 2002, 313, 32–46. (5) Pike, N.; Richard, D.; Foster, W.; Mahadevan, L. Proc. R. Soc. London, Ser. B 2002, 269, 1211–1215. (6) Aussillous, P.; Quere, D. J. Fluid Mech. 2004, 512, 133–151. (7) Dorvee, J. R.; Derfus, A. M.; Bhatia, S. N.; Sailor, N. J. Nat. Mater. 2004, 3, 896–899. (8) Rao, A. V.; Kulkarni, M. M.; Bhagat, S. D. J. Colloid Interface Sci. 2005, 285, 413–418. (9) Quere, D. Rep. Prog. Phys. 2005, 68, 2495–2532. (10) Aussillous, P.; Quere, D. Proc. R. Soc. London, Ser. A 2006, 462, 973–999. (11) Binks, B. P.; Murakami, R. Nat. Mater. 2006, 5, 865–869. (12) Zeng, C.; Bissig, H.; Dinsmore, A. D. Solid State Commun. 2006, 139, 547– 556. (13) McHale, G.; Herbertson, D. L.; Elliott, S. J.; Shirtcliffe, N. J.; Newton, M. I. Langmuir 2007, 23, 918–924. (14) Newton, M. I.; Herbertson, D. L.; Elliott, S. J.; Shirtcliffe, N. J.; McHale, G. J. Phys. D: Appl. Phys. 2007, 40, 20–24. (15) McHale, G.; Shirtcliffe, N. J.; Newton, M. I.; Pyatt, F. B. Hydrol. Process. 2007, 21, 2229–2238. (16) McHale, G.; Shirtcliffe, N. J.; Newton, M. I.; Pyatt, F. B.; Doerr, S. H. Appl. Phys. Lett. 2007, 90, 054110. (17) McHale, G.; Eliot, S. J.; Newton, M. I.; Herbertson, D. L.; Esmer, K. Langmuir 2009, 25(1), 529–533. (18) Gao, L.; McCarthy, T. J. Langmuir 2007, 23, 10445–10447. (19) Zhao, N.; Zhang, X.; Li, Y.; Lu, X.; Sheng, S.; Zhang, X.; Xu, J. Cell Biochem. Biophys. 2007, 49, 91–97. (20) Bormashenko, E.; Pogreb, R.; Bormashenko, Y.; Musin, A.; Stein, T. Langmuir 2008, 24(21), 12119–12122. (21) Bormashenko, E.; Bormashenko, Y.; Musin, A. J. Colloid Interface Sci. 2009, 333, 419-421. (22) Bormashenko, E.; Pogreb, R.; Whyman, G.; Musin, A.; Bormashenko, Y.; Barkay, Z. Langmuir 2009, 25(4), 1893–1896. (23) McEleney, P.; Walker, G. M.; Larmour, I. A.; Bell, S. E. J. Chem. Eng. 2009, 147, 373–382. (24) Bhosale, P. S.; Panchagnula, M. V.; Stretz, H. A. Appl. Phys. Lett. 2008, 93, 034109.
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marbles” by coating water and glycerol droplets with micrometer-sized hydrophobic powders.1,3,4,6,9,10 They initially used hydrophobized lycopodium (spores of moss plant) as the coating powder. Hydrophobic particles encapsulate the droplet and prevent the liquid from contacting surfaces that it encounters. The size of the hydrophobic grain was usually between 5 and 30 μm and much smaller than the drop size. If the volume of the drop liquid is less than 10 μL on a hydrophobic substrate, then the radius of the droplet is usually less than the capillary length of the liquid, κ-1 = (γLV/gFL)1/2 (2.72 mm for water), and the liquid marble usually adopts a spherical shape since the gravity (flattening) effect is minimal. Liquid marbles are microreservoirs, which can move quickly without any leakage. The force needed to move these marbles on solid surfaces is extremely small because of the diminished area of liquid-solid contact. An inclination angle of only a few degrees makes the liquid marble roll on most surfaces. The velocity of the rolling marbles depends on the competition between the gravity effect due to the inclination angle and the internal fluid dissipation determined by the contact area. Larger marbles roll more slowly than smaller ones because of their larger contact area, which increases more rapidly than the volume as the size of the marble increases.1-3 The transport of a small amount of water or other liquids on a solid surface is not a simple process.1,7-10 It is difficult to push small amounts of liquids through tubes or across surfaces as microfluidics requires, because the liquids wet the surfaces and create high friction forces. Superhydrophobic coatings giving water contact angles larger than 150 may overcome this problem;25-27 however, liquid marbles seem to be an alternative, if chemically inert hydrophobic grains can be used. Quere et al. studied the manipulation of liquid marbles using (25) Erbil, H. Y.; Demirel, A. L.; Avci, Y.; Mert, O. Science 2003, 299, 1377– 1380. (26) Callies, M.; Quere, D. Soft Matter 2005, 1, 55–61. (27) Li, X. M.; Reinhoudt, D.; Calama, M. C. Chem. Soc. Rev. 2007, 36, 1350– 1368.
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gravitational, electrostatic, or magnetic fields.3,6,9,10 Dorvee et al. used magnetic grains to drive the marbles using a magnetic fluid.7 McHale et al. studied the electrowetting of liquid marbles recently.13-17 Gao and McCarthy studied with ionic liquids and formed ionic liquid marbles by using fluoride containing polymers.18 These liquid marbles were transferred at the surface of water and maintained their shape without coalescing for long durations depending on the type of powder used.18 Bormashenko et al. investigated ferrofluidic liquid marbles and provided motion of these marbles by magnetic field on superhydrophobic surfaces.20 Bormashenko and co-workers also studied floating and sliding of liquid marbles.21,22 McEleney synthesized liquid marbles by using Cu-based and poly(methy methacrylate) powders and proposed the future use of them in drug encapsulation.23 Bhosale et al. formed optically transparent and mechanically robust liquid marbles from water and glycerol drops embedded in surface-treated fumed silica nanoparticles.24 Liquid marbles are promising candidates to be applied in the biomedical and genetic analysis fields where very small amounts of materials must be analyzed in short durations so that 2D microfluidics and labon-a-chip methods are used.7,13-17 They can be used in powder encapsulation operations and in wear-free micromachines, such as electromechanical actuators and valves.2 However, there is a need for chemically inert liquid marbles, which can be used sufficiently long periods. Various hydrophobic particles were used for the formation of liquid marbles: Lycopodium powder (spores of moss plant) hydrophobized with fluorinated silanes,1,3,6,9 with trimethylsilyl chloride,13 and with hexamethyldisilizane;14 aphid wax;5 silica treated with dichlorodimethylsilane,10,11,24 hexamethyldisilizane,24 and with trimethylsilyl chloride;13 methyltrimethoxysilane based aerogel;8 phtholocyanine blue B and Hansa yellow dye;11 oligomeric and polymeric tetrafluoroethylene;11,18 hydrophobic copper powders, and poly(methyl methacrylate)23 were also used as hydrophobic powders. However, these compositions severely restrict the range of liquid marble applications, because hydrophobized silica and lycopodium contain Si-O bonds that are reactive under nucleophilic, basic, or acidic conditions. In addition, undesired rapid evaporation of the liquid marble usually occurs.10,16,24 Evaporation control is important in both genetic analysis and in special processes where the powder will be used after the liquid is completely evaporated at the target. The lifetime of a liquid marble depends on the size and type of hydrophobic powder and also the liquid used to form it. If the liquid is very volatile, it evaporates easily, and the liquid marble will deform very quickly as the liquid evaporates, and finally, it will collapse. Here, we show that the liquid marbles can be successfully synthesized from chemically inert graphite micropowder by encapsulating water droplets. Since graphite is composed of pure carbon; insensitive to chemical reactions and stable at room temperature; extremely resistant to acids, bases, and oxidation; biocompatible; nonstick; and having self-lubrication, antifouling, and superior electric and thermal conductivity properties; these liquid marbles may be used in many industrial applications. The evaporation rates of graphite liquid marbles were compared with the rates of pure water droplets in constant relative humidity and temperature conditions in a closed chamber. For this purpose, evaporation was monitored by a video camera in the chamber where the relative humidity is kept constant by using different hygrostat salt solutions. The useful lifetimes of liquid marbles were also determined. Evaporation rates were modeled from (28) Picknett, R. G.; Bexon, R. J. Colloid Interface Sci. 1977, 61, 336–350.
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drop profiles by using previously derived diffusion controlled evaporation equations,28-45 and the results were compared in terms of evaporation resistance equations.46-48 We hope that the use of chemically inert graphite particles having electrical conductivity and dry lubrication properties in the formation of liquid marbles may be a starting point for their use in microfluidics, genetic analysis, antifouling, wear-free micromachine, electromechanical actuator, and valve applications.
2. Theoretical Basis A spherical cap drop shape can be characterized by four parameters: height of the drop, h; liquid-solid contact radius, rb; equilibrium contact angle, θ; and radius of the spherical drop, R. The relationships between the two radii and the contact angle are given from the spherical geometry31-39,44 1=3 3V rb ¼ R sin θ and R ¼ πβ
ð1Þ
where V is volume of drop, β is geometric factor given as follows β ¼ ð1 -cos θÞ2 ð2 þ cos θÞ ¼ 2 -3 cos θ þ cos3 θ
ð2Þ
The volume of a spherical cap can be calculated by using threeparameter geometric volume model as follows V3 ¼
πrb 2 h ð2 þ cos θÞ 3 ð1 þ cos θÞ
ð3Þ
For a liquid drop having a spherical cap shape on a substrate, the rate of volume decrease by time for a diffusion-controlled evaporation is given as38 DV 4πD 3V 1=3 ¼ ðco -c¥ Þf ðθÞ ¼ K f ðθÞV 1=3 Dt FL πβ
ð4Þ
where t time, D diffusion coefficient, FL density, co is vapor concentration at surface and c¥ at infinite distance, and θ equilibrium contact angle, which is assumed constant during this process. f(θ) parameter shows the retardation of evaporation in (29) Birdi, K. S.; Vu, D. T. J. Phys. Chem. 1989, 93, 3702–3703. (30) Bourges- Monnier, C.; Shanahan, M. E. R. Langmuir 1995, 11, 2820–2829. (31) Rowan, S. M.; Newton, M. I.; McHale, G. J. Phys. Chem. 1995, 99, 13268– 13271. (32) Erbil, H. Y.; Meric- , R. A. J. Phys. Chem. B 1997, 101, 6867–6873. (33) Meric, R. A.; Erbil, H. Y. Langmuir 1998, 14, 1915–1920. (34) McHale, G.; Rowan, S. M.; Newton, M. I.; Banerjee, M. K. J. Phys. Chem. B 1998, 102, 1964–1967. (35) Erbil, H. Y. J. Phys. Chem. B 1998, 102, 9234–9238. (36) Erbil, H. Y. J. Adhes. Sci. Technol. 1999, 13, 1405–1413. (37) Erbil, H. Y.; Dogan, M. Langmuir 2000, 16, 9267–9273. (38) Erbil, H. Y.; McHale, G.; Newton, M. I. Langmuir 2002, 18, 2636–2641. (39) Erbil, H. Y.; Avci, Y. Langmuir 2002, 18, 5113–5119. (40) Panvar, A. K.; Barthwal, S. K.; Ray, S. J. Adhes. Sci. Technol. 2003, 17(10), 1321–1329. (41) Fang, X.; Li, B.; Petersen, E.; Ji, Y.; Sokolov, J. C.; Rafailovich, M. H. J. Phys. Chem. B 2005, 109, 20554–20557. (42) McHale, G.; Aqil, S.; Shirtcliffe, N. J.; Newton, M. I.; Erbil, H. Y. Langmuir 2005, 21, 11053–11060. (43) Kim, J.-H.; Ahn, S. I.; Kim, J. H.; Zin, W.-C. Langmuir 2007, 23, 6163– 6169. (44) Erbil, H. Y. Surface Chemistry of Solid and Liquid Interfaces; Blackwell Publishing: Oxford, U.K., 2006. (45) Liu, C.; Bonaccurso, E.; Butt, H.-J. Phys. Chem. Chem. Phys. 2008, 10, 7150–7157. (46) La Mer, V. K.; Aylmore, L. A. G.; Healy, T. W. J. Phys. Chem. 1963, 67, 2793–2795. (47) La Mer, V. K.; Healy, T. W. Science 1964, 148, 36–42. (48) Tosun, A.; Erbil, H. Y. 2009, submitted to Applied Surface Science.
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the downward direction due to the presence of a horizontal surface given by28,38,42,44 f ðθÞ ¼ ð4:4785 10 -5 Þ þ 0:31665θrad þ ð5:8 10 -2 Þθ2rad -ð4:439 10 -2 Þθ3rad þ ð5:165 10 -3 Þθ4rad ð5Þ After integration of eq 4 one obtains 2=3
V 2=3 ¼ Vi
2 - K f ðθÞt 3
ð6Þ
Thus, V 2=3 versus time plot should give a straight line. This approach was reported to be experimentally correct in several previous publications.31-39,42 The constant, K, is independent of drop volume and can be calculated from the slope of eq 6 as given in eq 4 K ¼
4Dπ2=3 31=3 ðco -c¥ Þ FL β1=3
ð7Þ
The vapor concentration difference can be calculated as ðco -c¥ Þ ¼
Mw PVS ð1 -RHÞ RT
ð8Þ
where RH is the relative humidity of water vapor in the closed chamber, Mw is the molecular weight of water, and PVS is the saturation water vapor pressure, R is the gas constant, and T is the temperature in Kelvin. After determination of the K value from the V2/3 versus time plot, D of water vapor can be calculate from eq 7. La Mer et al. derived a specific evaporation resistance parameter, φ, to investigate the rate of evaporation when the surface of a liquid is covered with a monolayer by the following expression46,47 dt dt φ ¼ Aðco -c¥ Þ dmM dmL
ð9Þ
where mM is the mass of the coated material (liquid marble), mL is the mass of the uncoated material (pure liquid drop), and A is the initial surface area of the evaporating materials, which can be calculated for objects having spherical cap shapes as A ¼ πðrb 2 þ h2 Þ and also A ¼ 2πR2 ð1 -cos θÞ
ð10Þ
and the reciprocal of the mass lost during evaporation can be calculated as dt 1 1 ¼ dm ðdV=dtÞ FL
ð11Þ
3. Experimental Section Materials. Graphite micropowder was purchased from Sigma-Aldrich. Teflon plate was purchased from Gul-Birfaz Polymer and Chemical Ltd., Turkey. Merck ultrapure grade water was used. All the solvents and salts were analytical grade and were purchased from Merck. Graphite Liquid Marble Formation. A Plexiglass cell having dimensions 20 7 3 cm3 was used in the experiments. A rubber 8364 DOI: 10.1021/la900729d
sheet gasket was used under the lid to prevent air and water vapor transfer to the cell. A thick, white, clean Teflon plate was used as the substrate and placed on the floor of the cell. The surface of the Teflon plate was cleaned in advance by washing with distilled water, acetone, and ethyl alcohol and finally again with distilled water. Then, it was dried at 50 C overnight and kept in a desiccator prior to use. Different hygrostat solutions in a small container were kept in the evaporation cell during the experiments. Saturated solutions of MgCl2 3 6H2O (40% RH); Ca(NO3)2 3 4H2O (52-56% RH); NH4NO3 (67-68% RH); NaNO3 (77-79% RH); and KCl (84-87% RH) salts were used as hygrostat solutions to maintain constant relative humidity within the cell between 20 and 26 C; and silica gel was used to maintain 5% RH after drying at 110 C overnight. The relative humidity and temperature in the cell was measured with a small TFA thermohygrometer located inside the cell during experiments. There was a septum on the lid of the cell for the insertion of the needle. After reaching temperature and RH equilibrium, pure water drops of volumes 5 μL and 10 μL were placed on the Teflon plate with a Hamilton syringe, and their evaporation rates were monitored. Graphite particle size distribution was measured by using Malvern Mastersizer 2000, and it was determined that the powder contains particles between 2 and 30 μm in size, where 60% of the particles are between 10 and 20 μm in size. Graphite liquid marbles were formed by rolling the water drop on the graphite powder layer previously located on the Teflon plate with the back and forth movement of the cell. Graphite grains self-assemble on the water-air interface in the cell to form the graphite liquid marble as seen in Figure 1.
Pure Water Drop and Liquid Marble Evaporation Experiments. CAM 200 contact angle meter of KSV Instruments Ltd. was used to monitor the horizontal profiles of both pure liquid drops and graphite liquid marbles, and another digital camera (Imaging Source-DMK 21F04) was also used to monitor the plan views. Drop profiles were recorded in 1 min intervals up to 360 min depending on the RH of cell. The real dimensions of the water drops were determined by using both KSV software and UTHSCSA Image Analysis program after calibration. Three parameters, base radius, rb, height, h, and the contact angle, θ, of the droplets were determined. The accurate determination of the contact angles of graphite liquid marbles was difficult due to the “fluffy” profile created by the powder skin; however, the inaccuracy was no more than 3. rb and h were measured with good accuracy when the vertical baseline was located correctly. Indicative images of the plan views of a graphite liquid marble during the evaporation process are shown in Figure 1 and their corresponding horizontal profiles are shown in Figure 2. The evaporation of the pure water droplets having 5 and 10 μL volume on the PTFE substrate was also monitored within the same cell for comparison.
4. Results and Discussion In the first part of this work, the evaporation of pure water droplets having the same volumes of the graphite liquid marbles (5 and 10 μL) were monitored in a closed cell at constant RH of 5%, 40%, 52-56%, 67-68%, 77-79%, and 84-87% between 20 and 26 C as described in the Experimental Section. All the experimental h, rb, and θ values of 5 μL pure water drops are given in the Supporting Information Table 1 for 87%, 77%, and 68% RH and in Supporting Information Table 2 for 56%, 40%, and 5% RH in the Supporting Information. The same drop profile data for 10 μL pure water drops are given in Supporting Information Table 3 for 84%, 78%, and 68% RH and in Supporting Information Table 4 for 55%, 40%, and 5% RH in the Supporting Information. Volumes of the drops were calculated using eq 3 from the three-parameter spherical cap geometry model and were also reported in these tables. V2/3-time plots of water droplets for all constant RH conditions are given in Figure 3 Langmuir 2009, 25(14), 8362–8367
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for 5 μL water drops and in Figure 4 for 10 μL water drops. Droplet evaporation obeys eqs 4 and 6 in all cases, showing a linear plot in these figures; hence, it can be said that the volumes of
Figure 1. Plan view of the graphite liquid marble during evaporation.
Figure 2. Horizontal profiles of the same graphite liquid marble during evaporation.
the drops fit the spherical cap geometry and the experiments were done with high precision. Evaporations on a Teflon surface proceeded with the constant contact area mode initially, and then constant θ mode dominated. Initial θ was between 110 and 123 due to the somewhat rough structure of the Teflon plate and θ becomes constant around 71-88, and these values were used to calculate β from eq 2 and later K from the slope of the plots. The vapor concentration difference, ΔC = (c0 - c¥) was calculated from eq 8 by using experimental RH values, and D of water vapor was found from eq 7 so that the mean experimental D was found to be 0.23 ( 0.02 cm2/s, very close to the theoretical value of D = 0.25 for this temperature range. When the f(θ) parameter was taken into account, the experimental values were much closer to the theoretical values. These results show that the evaporation was purely diffusion controlled in the chamber and the f(θ) parameter must be considered in the calculations. Evaporation durations increased as the RH% of the medium increased from 50 min for 40% RH to 230 min for 87% RH for 5 μL droplets and from 90 min for 40% RH to 360 min for 84% RH for 10 μL droplets as given in Figures 3 and 4. Droplet size affects the lifetime of the pure water droplet as expected: the larger the droplet, the longer the droplet lifetime. We also checked the deviation of experimental drop evaporation rate from the theory by using the theoretical value of D = 0.25 cm2/s as a constant for this temperature range. The deviation of the experimental (dV2/3/dt) values from theory according to the RH of the evaporation medium for a 5 μL water droplet is given in Table 1 and for 10 μL water droplet in Table 2. As seen in these tables, when the RH of the medium increases, the deviation of the experiment from the theory decreases. We calculated a deviation of 20.5% for 5% RH medium, and this decreases down to 11.3% for 87% RH medium for 5 μL droplet as seen in Table 1 and a deviation of 19.1% for 5% RH medium, and this decreases down to 6.6% for 84% RH medium for 10 μL droplet as seen in Table 2. There is an inverse relationship with the size of the droplet and the deviation from the theory. All these findings are related with the cooling on the drop surface during evaporation. The higher rate of evaporation in the low RH medium resulted in larger surface cooling, and this increases the deviation from theory. Thus, we obtained very low deviation for water drop evaporations in 84% and 87% RH mediums with small drop cooling. Later, evaporation of graphite liquid marbles was monitored in the same conditions. Plan view and horizontal profiles of graphite liquid marble during evaporation are shown in Figures 1 and 2.
Table 1. Deviation of the Experimental (dV2/3/dt) Values from Theory According to the Relative Humidity of the Evaporation Medium for 5 μL Water Droplet Evaporation relative humidity (%)
temperature (Kelvin)
constant θ (deg)
(dV2/3/dt) experimental (cm2/s)
(dV2/3/dt) theoretical (cm2/s)
deviation (%)
5 40 56 68 77 87
296 299 297 295 297 296
85 73 83 77 86 76
12.90 10-6 10.10 10-6 6.53 10-6 4.28 10-6 3.51 10-6 1.98 10-6
16.22 10-6 12.48 10-6 8.01 10-6 5.15 10-6 4.18 10-6 2.23 10-6
20.5 19.1 18.5 16.9 16.1 11.3
Table 2. Deviation of the Experimental (dV2/3/dt) Values from Theory According to the Relative Humidity of the Evaporation Medium for 10 μL Water Droplet Evaporation relative humidity (%) 5 40 55 68 78 84
temperature (Kelvin) 295 297 294 298 298 294
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constant θ (deg) 71 77 77 75 80 80
(dV2/3/dt) experimental (cm2/s) -6
12.70 10 9.22 10-6 5.90 10-6 5.37 10-6 3.82 10-6 2.25 10-6
(dV2/3/dt) theoretical (cm2/s) -6
15.68 10 10.97 10-6 6.92 10-6 6.24 10-6 4.27 10-6 2.41 10-6
deviation (%) 19.1 16.0 14.8 14.0 10.6 6.6
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Table 3. Buckling Time and Evaporation Resistance, O of 5 μL Graphite Liquid Marbles, According to the Variation of Relative Humidity of the Mediuma RH (%)
buckling time (s)
(dV/dt) (graphite marble) (cm3/s) -7
(dV/dt) (water) (cm3/s) -7
31.3 10 5 300 20.7 10 20.3 10-7 40 780 12.1 10-7 14.0 10-7 52 1020 8.07 10-7 12.2 10-7 68 1320 6.01 10-7 10.0 10-7 77 1380 4.10 10-7 3.9 10-7 87 3000 1.83 10-7 a A is the initial surface area of the graphite liquid marble, and (dV/dt) is the evaporation rate.
Ainitial (cm2) 0.125 0.128 0.128 0.135 0.125 0.126
Δc (g/cm3) -6
19.5 10 14.6 10-6 10.5 10-6 6.6 10-6 5.0 10-6 2.7 10-6
φ (s/cm) 0.401 0.629 0.700 0.754 0.902 0.981
Table 4. Buckling Time and Evaporation Resistance, O of 10 μL Graphite Liquid Marbles, According to the Variation of RH of the Mediuma RH (%)
buckling time (s)
(dV/dt) (graphite marble) (cm3/s) -7
(dV/dt) (water) (cm3/s) -7
42.9 10 5 450 10.1 10 26.7 10-7 40 1020 15.7 10-7 20.1 10-7 55 1200 9.18 10-7 15.4 10-7 66 2640 7.93 10-7 11.7 10-7 79 3000 3.05 10-7 5.81 10-7 84 4200 1.80 10-7 a A is the initial surface area of the graphite liquid marble, and (dV/dt) is the evaporation rate.
Figure 3. V2/3-time plot of 5 μL pure water droplets during evaporation in the closed chamber at constant relative humidity (RH = 5%, 40%, 56%, 68%, 77%, 87%) conditions.
Figure 4. V2/3-time plot of 10 μL pure water droplets during evaporation in the closed chamber at constant relative humidity (RH = 5%, 40%, 56%, 68%, 78%, 84%) conditions.
The initial θ values of liquid marbles were between 145 and 160 and much higher than that of pure water drop. These high contact angles were obtained as a result of the size of the graphite microparticles on the marble surface, which are approximately 15 μm in diameter. Evaporation time for a liquid marble is much longer (more than twice), when compared with that of the pure water droplets. However, the exact evaporation times of liquid marbles could not be determined with the usual video 8366 DOI: 10.1021/la900729d
Ainitial (cm2) 0.189 0.189 0.191 0.187 0.188 0.178
Δc (g/cm3) -6
21.9 10 13.1 10-6 7.78 10-6 7.60 10-6 3.63 10-6 2.75 10-6
φ (s/cm) 0.175 0.651 0.882 0.942 1.658 1.890
experiments, because buckling of the liquid marble dome started after a while as shown in Figures 1 and 2. The skin containing the graphite grains begins to close as the water within the marble evaporates and the micropowder becomes more dense on the liquid surface, and later, the marble buckles because the powder has reached its maximum packing density. The buckling times of liquid marbles varied between 300 and 3000 s for 5 μL liquid marbles and between 450 and 4200 s for 10 μL liquid marbles as given in Tables 3 and 4, respectively. When the relative humidity of the evaporation medium was changed, then the buckling times of marbles also changed as seen in these tables. The constant contact angle assumption could not be used for liquid marbles, because contact angles of liquid marbles were not constant but decreased with time, and the determination of the precise contact angles was also difficult due to the “fluffy” profile, so that the analysis applied to pure water droplets by using eqs 1-8 could not be applied to the liquid marbles. Instead, the volumes of liquid marbles were calculated from their profile dimensions, and evaporation rate calculations were done until buckling begins and the volume decrease of 5 μL graphite liquid marble with time during evaporation in the closed chamber at constant relative humidity (RH = 5%, 40%, 52%, 68%, 77%, 87%) conditions is given in Figure 5 and for 10 μL graphite liquid marble for (RH = 5%, 40%, 55%, 67%, 79%, 86%) conditions in Figure 6. It was realized that the liquid marble profiles retained their spherical shape in the first 5 to 70 min of the evaporation before the buckling began depending on the RH of the medium. The evaporation resistance parameter, φ was calculated by using eq 9, by considering the mass loss until buckling starts by comparing the results between the pure water drop and graphite liquid marbles. Equation 10 was used to calculate the initial surface area of marbles. φ parameter may not be constant due to the change of the powder density on the liquid surface during evaporation; however, the difference in mass loss rates of the pure liquid and liquid marble includes the variation in total area of the liquid and marble surfaces, which will affect the powder density on the liquid surface. Since we do not know the extent of deviation of the evaporation resistance from a mean value, and also, we need a single parameter to compare the powder size or chemistry effects on the evaporation rates of liquid marbles, the φ parameter is useful in practice. The results of buckling time and evaporation resistance, φ, according to the variation of RH of the medium for 5 μL graphite Langmuir 2009, 25(14), 8362–8367
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Figure 5. Volume variation of 5 μL graphite liquid marble with time during evaporation in the closed chamber at constant relative humidity (RH = 5%, 40%, 52%, 68%, 77%, 87%) conditions.
Figure 6. Volume variation of 10 μL graphite liquid marble with time during evaporation in the closed chamber at constant relative humidity (RH = 5%, 40%, 55%, 67%, 79%, 86%) conditions.
marbles are given in Table 3 and for 10 μL graphite marbles in Table 4. The presence of graphite micropowder on the marble reduced the evaporation rate of pure water, φ values increased from 0.401 to 0.981, and the liquid marble dome buckling time also increased from 5 to 50 min for 5 μL graphite marbles with the increase of RH as seen in Table 3. φ values increased from 0.175 to 1.890, and the liquid marble dome buckling time also increased from 7.5 to 70 min for 10 μL graphite marbles with the increase of RH as seen in Table 4. The variation of evaporation resistance, φ, of both 5 μL and 10 μL graphite liquid marble with RH of the medium is given in Figure 7. As seen in this figure, the increase in the % RH of the medium increases the evaporation resistance, φ. Since the graphite particles prevent the water molecules from evaporating while they are passing through the water/air interface, the screening effect of these particles is lower when the RH is low, because the tendency of water molecules to escape is high in this condition due to the high driving energy forcing the water molecules to evaporate from the liquid marble. We also compared our results with those given in two recent publications: Bhosale et al. studied the evaporation rate of liquid marbles made of μPTFE, nHMDS, nDMDCS micropowders in 20% RH medium.24 They described a parameter, η, to explain the evaporation resistance. They plotted normalized surface area of the liquid versus nondimensional time. They calculated the η parameter by taking the ratio of the measured average rate of evaporation of liquid marble and that of the plain drop under the same conditions. We extracted (V-t) data from the results of Bhosale et al. from their Figure 3 and compared with our results by using the evaporation rates (dV/dt) of graphite and μPTFE Langmuir 2009, 25(14), 8362–8367
Article
Figure 7. Variation of evaporation resistance, φ, of both 5 μL and 10 μL graphite liquid marble with RH of the medium.
marbles for 20% RH medium. The slopes of the plots are 1.80 10-3 mm3/s for the μPTFE marble in the paper of Bhosale et al. and 1.67 10-3 mm3/s for graphite liquid marble in this work. This indicates that the graphite liquid marble evaporation rate was 7% lower than that of the PTFE liquid marble. According to the equation of Bhosale et al.,24 the evaporation resistance was not influenced by the RH of the medium. However, in reality RH of the medium affects the evaporation resistance values as seen in our Figure 7. In addition, we compared the evaporation rate results of graphite liquid marble of this work with the results of PTFE liquid marble formed by using PTFE powder of 5-7 μm in diameter in varying RH mediums.48 The slopes of the plots were 1.78 10-3 mm3/s for the PTFE liquid marble in Tosun and Erbil’s paper48 and 1.67 10-3 mm3/s for graphite liquid marble in this work, indicating the slow evaporation rate of graphite liquid marble again.
5. Conclusion Liquid marbles using graphite micropowder and 5 and 10 μL water drops on PTFE surfaces were successfully synthesized for the first time. Their evaporation rates and evaporation resistance parameters, φ, were determined and compared with the evaporation rates of pure water droplets having the same volume by varying the % RH of the medium using hygrostat solutions. Pure water droplets evaporate in the diffusion-controlled evaporation mode similar to the cases given in previous publications. f(θ) factor, which physically represents the restriction of evaporation space by the presence of the substrate surface, is shown to be an important parameter for the theoretical calculation water droplet evaporation and should be taken into account. Graphite liquid marbles have longer lifetimes than the pure water droplets. The comparison between graphite liquid marble and pure water droplets has been done by using the evaporation resistance, φ, parameter. The presence of chemically inert graphite micropowder retards the evaporation of water within the liquid marble so that these marbles have enough lifetime to retain their spherical shape under normal atmospheric conditions for many industrial applications such as microfluidics, genetic analysis, antifouling, wear-free micromachines, electromechanical actuators, and valves. Supporting Information Available: The variation of contact angle, θ; contact radius, rb, and height, h, of pure water droplets having 5 and 10 μL volumes with time at constant relative humidity (RH = 5%, 40%, 55-56%, 68%, 7778%, 84-87%) conditions. This material is available free of charge via the Internet at http://pubs.acs.org. DOI: 10.1021/la900729d
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