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How Do Emulsions Evaporate? Ibon Aranberri, Kate J. Beverley, Bernard P. Binks, John H. Clint, and Paul D. I. Fletcher* Surfactant & Colloid Group, Department of Chemistry, University of Hull, Hull HU6 7RX, United Kingdom Received October 25, 2001. In Final Form: January 21, 2002 Evaporation rates of water and oil from creamed oil-in-water emulsions have been measured under conditions of controlled gas flow. The continuous water phases of the emulsions evaporate at rates equal to that for pure water under the same conditions. The evaporation rates of dispersed oil drops are retarded, relative to nonemulsified oil, by factors ranging from 1 to 20. Rates for different emulsified oils are all consistent with a mechanism in which the oil drops remain separated from the vapor phase by a thin water film at the emulsion surface. Oil transport from the drops to the vapor occurs by diffusion of dissolved oil across this water film. Measured evaporation rates show good agreement with model calculations based on this proposed mechanism.
Introduction Evaporation rates are of interest from many viewpoints including assessment of hazards arising from the spillage of volatile chemicals, drying processes, and the release of volatile active species such as perfumes and flavors from commercial products. In many systems of practical interest, evaporation occurs from liquid mixtures which may be multiphase and possess microstructure. As part of a program to study evaporation rates in different types of nonstructured and structured liquid systems, we have previously investigated rates for pure liquids,1 water contained within porous solids,2 water-in-oil microemulsions,3 and different liquid mixtures including water/ surfactant systems showing a variety of microstructured phases.4 Evaporation from a range of related surfactant colloidal mixtures has also been studied by the group of Friberg.5-7 In this study, we discuss the rates of evaporation of both oil and water from creamed oil-in-water emulsions. The emulsions contain a dispersion of micron-sized oil drops within an aqueous continuous phase and are stabilized by a monolayer of adsorbed surfactant coating the droplets. The emulsions examined here were all nonflocculated and stable with respect to coalescence of the oil drops. The drops creamed fairly rapidly (typically within 10 min) to form a top cream layer rich in oil drops (typically 60 vol % or so) above a drop-free aqueous layer. The depth of the cream layer was dependent on the overall volume fraction of oil in the emulsion which was typically in the range of 5-30 vol %. For emulsions of the type considered here, the equilibrium vapor pressures of both the oil and water are virtually equal to the values of the * To whom correspondence should be addressed. E mail: P.
[email protected]. (1) Beverley, K. J.; Clint, J. H.; Fletcher, P. D. I. Phys. Chem. Chem. Phys. 1999, 1, 149. (2) Beverley, K. J.; Clint, J. H.; Fletcher, P. D. I.; Thubron, S. Phys. Chem. Chem. Phys. 1999, 1, 909. (3) Clint, J. H.; Fletcher, P. D. I.; Todorov, I. T. Phys. Chem. Chem. Phys. 1999, 1, 5005. (4) Beverley, K. J.; Clint, J. H.; Fletcher, P. D. I. Phys. Chem. Chem. Phys. 2000, 2, 4173. (5) Friberg, S. E.; Kayali, I. J. Pharm. Sci. 1989, 78, 639. (6) Friberg, S. E.; Langlois, B. J. Dispersion Sci. Technol. 1992, 13, 223. (7) Langlois, B. R. C.; Friberg, S. E. J. Soc. Cosmet. Chem. 1993, 44, 23.
bulk, pure liquids. In principle, for the continuous water phase, one might expect a slight vapor pressure lowering from the presence of the dissolved surfactant. However, this effect is negligible for the low surfactant concentrations used here. For the dispersed oil drops, one might expect a slight raising of the oil vapor pressure due to the Kelvin effect. However, for the oil drop sizes and oilwater tensions in these emulsions, this effect is also negligible. It is therefore expected that both the continuous water and dispersed oil components of an emulsion evaporate simultaneously, but at different rates.5-7 The key question addressed in this study is, how does the oil get from the dispersed drops to the vapor phase during the dynamic evaporation process? Three possible mechanisms of oil transport across the emulsion surface can be envisaged. As shown schematically in Figure 1, the emulsion surface initially contains buoyant oil drops situated below the surfactant monolayer adsorbed at the water-vapor surface and separated from the vapor phase by a thin water film of nanometer thickness. Depending on the relative magnitudes of the oil-water, water-vapor, and oil-vapor interfacial tensions and the colloidal forces between the oil drops and the water-vapor surface, entry of the oil drops through the water film to the emulsion surface may or may not be thermodynamically feasible.8 Although the prediction of drop entry under dynamic evaporation conditions is uncertain, if oil drop entry forms the rate-limiting step to oil transport to the vapor phase (mechanism 1), one might expect that the oil evaporation rates should correlate with the relative magnitudes of the three relevant interfacial tensions and the strength of repulsive colloidal forces across the water film. If entry does not occur, the drops remain separated from the vapor phase by the thin water film. In this situation, either the oil must diffuse across the thin water film to reach the vapor phase (mechanism 2) or oil drop evaporation can only occur following evaporation of the upper water film acting to “uncover” the oil drops (mechanism 3). For mechanism 2, the oil evaporation rate is predicted to depend on the solubility of the oil in water, its diffusion coefficient in water, and the water film thickness (dependent on the colloidal forces). For mechanism 3, the evaporation rate should depend on (8) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; Peck, T. G.; Rutherford, C. E. Adv. Colloid Interface Sci. 1994, 48, 93.
10.1021/la0115942 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/28/2002
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Figure 2. Mass loss curve for a 20 vol % squalane-in-water emulsion stabilized by SDS (20 mM). The theoretical curve corresponding to the evaporation of pure water overlies the experimental data. thickness of the stagnant vapor layer above the liquid surface (h) has been demonstrated to be equal to the distance between the liquid surface and the mouth of the sample tube.1 The knowledge of h from the experimental configuration is important since it enables full quantitative analysis of the measured evaporation rates. All measurements were made at 25.0 °C.
Results and Discussion Figure 1. Schematic diagram of the gravimetric apparatus used to determine evaporation rates. The lower diagrams show expanded views of a creamed emulsion sample and the thin water film separating the oil drops from the vapor.
the relative volatilities of the oil and water. To discriminate between the different mechanisms, we have determined evaporation rates for a series of emulsion systems stabilized by different surfactants (charged and uncharged) and containing oils whose solubility in water varies over many orders of magnitude. Experimental Section Water was purified by reverse osmosis followed by treatment with a Milli-Q Reagent water system. The oils squalane (Aldrich, 99%), benzene (Fisons, 99.8%), cyclopentane (Lancaster, 99%), heptane (Fischer, 99%), hexamethyl disiloxane (HMDS, Lancaster 99.7%), methylcyclohexane (Aldrich, 99%), octane (Fluka, 99+%), toluene (Fischer, 99.9%), hexane (Beecroft & Partners, GLC grade), and o-xylene (Avocado, 99%) were used as received. The surfactants hexadecyl trimethylammonium bromide (HTAB, BDH, 98%), sodium dodecyl sulfate (SDS, BDH, specially pure grade), and n-decyl-β-D-glucopyranoside (DBG, Sigma, 98%) were used without further purification. Sodium bromide (99%) was from BDH. Oil-in-water emulsions were prepared using an UltraTurrax rotor-stator homogenizer fitted with a T25 shaft operating at 11 000 rpm for 1 min. Average volume-weighted oil drop radii, measured using a Malvern Mastersizer MS 20, were in the range of 2-5 µm. The polydispersities of the drop distributions, expressed as the 10-90% size distribution width divided by the median, were typically around 1. Some samples (those containing relatively water-soluble oils) showed some growth in drop size over the experimental time scale, whereas samples containing oils which have very low water solubility showed no growth. The correlation between drop growth and oil solubility suggests that the growth is due to Ostwald ripening. No separation of free oil, indicative of drop coalescence, was observed on leaving the samples for periods of up to 1 week. Evaporation rates were determined gravimetrically using the apparatus fully described in ref 1 and shown schematically in Figure 1. Briefly, a sample of creamed emulsion was placed in a cylindrical, open-topped tube suspended from a balance. The sample was mounted within a thermostated chamber, and nitrogen gas was flowed vertically around the sample tube. For this experimental geometry and gas flow configuration, the
For a single pure liquid evaporating under conditions of high gas flow rate, the evaporation rate E, expressed as rate of mass loss, is independent of the gas flow rate and is given by1
E)-
dm MADVPz ) dt hRT
(1)
where m is the sample mass at time t, M is the molecular weight of the evaporating species, A is the surface area of the sample, DV is the diffusion coefficient of the evaporating species in the stagnant vapor space of thickness h, P is the equilibrium vapor pressure, R is the gas constant, and T is the absolute temperature. The parameter z is a factor which allows for the countercurrent flow of the second gas component (nitrogen) within the stagnant layer and is given by
z)
[
(
)]
Patm 1 ln P 1 - (P/Patm)
(2)
where Patm is atmospheric pressure. For this study, the flow rate of nitrogen was kept constant at 1710 mL min-1, sufficiently high that eq 1 is valid within 2% or so. The same sized sample tube was used for all measurements, and thus the area A was constant (258.4 mm2). The initial value of h was varied from run to run but was typically around 22 mm, and the initial liquid depth was around 15 mm. The depth of the cream layer in the emulsion samples was varied by control of the overall oil volume fraction but was typically a few millimeters. Using emulsions containing the involatile oil squalane, it was established that the evaporation rate of the water continuous phase in an emulsion is identical to that of pure water under the same conditions, that is, gas flow rate and stagnant layer thickness h. Figure 2 shows a comparison of the measured mass loss versus time curve for a squalane-in-water emulsion with a theoretical curve calculated according to eq 1 using the known sample masses, tube dimensions, and parameters listed for water in Table 1. The measured curve agrees very closely with the curve calculated using no adjustable parameters, thereby providing strong evidence that the evaporation
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Figure 3. Mass loss curves for 8, 18, and 26 vol % toluenein-water emulsions stabilized by SDS (20 mM). The experimental data and fitted curves (corresponding to a best-fit value of f ) 0.85 ( 0.08) are overlaid. Table 1. Values of Vapor Phase Diffusion Coefficient DV, Vapor Pressure P, and Solubility in Water S for Water and the Oils Used in This Study liquid
DV/10-6 m2 s-1
P/Pa
S/M
water benzene cyclopentane heptane HMDS methylcyclohexane octane toluene hexane o-xylene
24.0 8.16 7.90 6.81 6.51 6.58 6.50 8.10 8.27 6.83
3167 12614 42296 6113 4887 6151 1864 3786 19812 891
2.28 × 10-2 2.23 × 10-3 2.93 × 10-5 5.70 × 10-6 1.43 × 10-4 5.70 × 10-6 5.85 × 10-3 1.10 × 10-4 1.65 × 10-3
rate of the continuous water phase is identical to that of pure water. For creamed emulsions containing a volatile oil, the mass loss curves show a two-stage decay. In the first stage, both water and oil evaporate simultaneously giving a steep initial mass loss rate. In the second stage, when all the oil has evaporated, the reduced slope corresponds to evaporation of water alone. For emulsions containing volatile oils, the mass loss curves were accurately fitted using an integrated form of eq 3,
E ) Ewater + fEoil E ) Ewater
when oil is present
when all oil has evaporated
(3)
where E is the total, measured mass loss rate and Ewater and Eoil correspond to the mass loss rates for water and oil, respectively. The factor f, with values between 0 and 1, represents the factor by which the rate of evaporation of oil emulsion drops is reduced below that for pure oil. Figure 3 shows illustrative examples of a series of mass loss curves for emulsions containing different volume fractions of oil (toluene). As expected, the point at which the slopes change (corresponding to the point at which all the oil is lost) shifts to longer times for increased volume factions. The mass loss curves were fitted using eq 3 with f as the only adjustable parameter, and as shown in Figure 3, agreement with measurement is excellent. For the calculations of the fits, values of the densities and vapor pressures were taken from the literature.9-13 Diffusion (9) Selected Values of Properties of Hydrocarbons and related Compounds; Thermodynamics Research Center, AP144, Texas A&M University: College Station, TX, 1978. (10) McAuliffe, C. Nature 1963, 200, 1092. (11) Varaprath, S.; Fryf, C. L.; Hamelink, J. Environ. Toxicol. Chem. 1996, 15, 1264. (12) Hunter, M. J.; Warrick, E. L.; Hyde, J. F.; Currie, C. C. J. Am. Chem. Soc. 1946, 68, 2284.
coefficients in the vapor phase DV were determined separately from measurements of the evaporation rate of the pure liquid component and are listed in Table 1. Values of the rate reduction factor f were determined for emulsions stabilized by either nonionic (DBG), cationic (HTAB), or anionic (SDS) surfactants. Emulsions with a range of volatile oils (toluene, benzene, hexane, heptane, cyclopentane, methylcyclohexane, o-xylene, hexamethyl disiloxane), for which the aqueous solubility ranges from 2.28 × 10-2 M (benzene) to 5.7 × 10-6 M (hexamethyl disiloxane, HMDS), were studied. Measurements were made only for emulsion systems for which the volatilities of the oils were significant compared with that of water, thereby giving a significant change in mass loss rates with and without oil. This is necessary to ensure that f is determined accurately. For the different emulsion systems, the key findings are as follows: 1. For the same oil component, f is higher for nonionic surfactants than for ionic surfactants. 2. For the same surfactant, the values of f correlate with the aqueous solubility of the oil, that is, f is low when the solubility is low. 3. Variation of the overall volume fraction of oil in the emulsion produces no change in f (shown in Figure 3). The observed correlation between f and the oil solubility in water suggests that the oil evaporation involves mass transport of dissolved oil through the water film present at the emulsion surface, that is, evaporation occurs by mechanism 2. For this mechanism, Figure 1 shows the local concentrations of oil expected during steady-state evaporation of the oil. At the mouth of the sample tube, the partial pressure of oil vapor is virtually zero for the high gas flow rate used in this work.1 Since the oil evaporation rate is f times less than that for pure oil, the oil vapor pressure on the vapor side of the emulsion surface must be fP. The corresponding molar concentration (mol dm-3) is fP/RT. Assuming that the distribution of oil between vapor and the thin water film corresponds to local pseudoequilibria across both the water-vapor and the oil-water interfaces, the concentration of oil on the water side of the emulsion surface is fS, where S is the equilibrium aqueous solubility of the oil, and that at the oil drop surface is S. This also assumes that Henry’s law applies over the range of P from fP to P and aqueous oil concentration from fS to S. This latter assumption is reasonable in view of the low solubilities of the oils in water. Fick’s first law of diffusion relates the oil flux J to the linear concentration gradients across both the stagnant vapor phase and the thin water film. Mass conservation requires that these fluxes be equal, and hence
(fP/RT - 0) (S - fS) ) DW J ) DV h d
(4)
where DW is the diffusion coefficient of oil in the water film. Solving the second equality for f gives
f)
1 1 ) DVdP 1/X + 1 +1 DWhRTS
(
)
(5)
where X is the product of the ratios of the diffusion coefficients, saturated concentrations, and thicknesses corresponding to the stagnant vapor phase and water film, that is, X ) (DW/DV)(RTS/P)(h/d). Thus, if mechanism 2 operates, it is predicted that for X , 1 virtually all (13) Stull, D. R. Ind. Eng. Chem. 1947, 517.
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Figure 4. Variation of oil evaporation rate reduction factor f with X for all the emulsion systems studied. The solid line is calculated according to eq 5. The dashed boundary lines correspond to a factor 2 uncertainty in X.
resistance to oil transport is located within the water film and f ≈ X. For X . 1, the resistance is located within the stagnant vapor phase and f ) 1. To compare experimental f values for all the different emulsions with the predictions of eq 5, the values of DV, P, h (averaged over the run duration), and S required to estimate X were either known or taken from the literature.9-13 DW values were estimated using a literature value of 1.06 × 10-9 m2 s-1 for pentane14 and assuming that DW for different oils scales as (molar volume)-0.4, where the scaling exponent was taken to be intermediate between -1/3 (spherical molecules) and -1/2 (random coil chains). The uncertainty in DW estimated in this way is (30%. Thicknesses of equilibrium water films at emulsion surfaces are known to be of the order of tens of nanometers but are dependent on the balance between the capillary pressures and colloidal forces across the thin film.15,16 Films are expected to be thicker for ionic surfactant films where electrostatic repulsions thicken the films relative to those stabilized by nonionic surfactants. However, water film thicknesses during the dynamic evaporation process are likely to differ somewhat from equilibrium values. To proceed, we have taken d to be 147 nm for all emulsions stabilized by SDS (anionic), 89 nm for HTAB (cationic) emulsions, and 39 nm for DBG (nonionic) emulsions, where the values have been adjusted to obtain the best correlation between the experimental f values and the predictions of eq 5. The uncertainty in X for each system mainly arises from the crude approximation made here that d is constant for a particular surfactant but independent of the nature of the oil. In fact, d may depend on the magnitude of the capillary pressure exerted by the buoyant oil drops and hence might be expected to depend on the oil drop sizes and the oil-water and vapor-water interfacial tensions. Neglecting these complicating factors probably gives rise to an uncertainty in d (and hence X) of the order of a factor of 2-3. Although large, this uncertainty is tolerable because the total variation in X for the different systems (dominated by the variation of oil solubility in water) covers 4 orders of magnitude. Figure 4 shows the measured variation of f with X for all the emulsion systems. The data all cluster around the theoretical line with almost all data falling within the boundary curves estimated assuming a factor 2 uncertainty in the absolute values of (14) Price, W. S.; Soderman, O. J. Phys. Chem. 2000, 104, 5892. (15) Lobo, L.; Wasan, D. T. Langmuir 1993, 9, 1668. (16) Bergeron, V.; Fagan, M. E.; Radke, C. J. Langmuir 1993, 9, 1704.
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Figure 5. Variation of f with h (averaged over the run duration) for 20 vol % heptane-in-water emulsions stabilized by SDS (20 mM). Vertical error bars indicate 10% uncertainty in f, and the horizontal error bars represent the variation in h during the evaporation runs. The solid line shows the calculated variation with d ) 147 nm.
Figure 6. Variation of f with aqueous phase electrolyte concentration (HTAB + NaBr) for 20 vol % heptane-in-water emulsions stabilized by HTAB (2 mM). The solid line is a guide for the eye.
X. It is concluded that evaporation of emulsified oil drops proceeds by diffusion of dissolved oil through a thin water film at the emulsion surface. The thicknesses of the water films during evaporation are estimated to be significantly larger than those of equilibrium oil-water-vapor films reported in the literature.15,16 For the same emulsion system, eq 5 predicts that f should increase with the stagnant vapor phase thickness h. This prediction was tested by measurement of f for a series of samples in which the initial total depth of emulsion in the sample tube was varied. Although h is necessarily changing during the evaporation process, a constant, average value was assumed in the fitting of the mass loss curves. The variation in h during the runs is represented on the graph as the horizontal error bars. As shown in Figure 5, the results are in reasonable agreement with the predictions of eq 5 with the assumption that the water film thickness d remains independent of h and equal to 147 nm (equal to the value taken for all SDS emulsions in Figure 4). Under conditions when X, and hence f, is
