Surfactant solutions and porous substrates: spreading and imbibition

In Section 1, spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base, and (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations has been derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters, one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate, and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments were used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactory for the experimental data. According to theory predictions [1]: (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function, and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation. These conclusions again are in good agreement with experimental observations [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. In Section 2, experimental investigations are reviewed on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates (nitrocellulose membranes) in the case of partial wetting [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]. The time evolution was monitored of the radii of both the drop base and the wetted area inside the porous substrate. The total duration of the spreading process was subdivided into three stages-the first stage: the drop base expands until the maximum value of the drop base is reached; the contact angle rapidly decreases during this stage; the second stage: the radius of the drop base remains constant and the contact angle decreases linearly with time; the third stage: the drop base shrinks and the contact angle remains constant. The wetted area inside the porous substrate expends during the whole spreading process. Appropriate scales were used with a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate, and the dynamic contact angle on the dimensionless time. Experimental data showed [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]: the overall time of the spreading of drops of SDS solution over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamic reasons. It is shown using independent spreading experiments of the same drops on nonporous nitrocellulose substrate that the static receding contact angle is equal to zero, which supports the conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates. In Section 3, a theory is developed to describe a spontaneous imbibition of surfactant solutions into hydrophobic capillaries, which takes into account the micelle disintegration and the concentration decreasing close to the moving meniscus as a result of adsorption, as well as the surface diffusion of surfactant molecules [N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747]. The theory predictions are in good agreement with the experimental investigations on the spontaneous imbibition of the nonionic aqueous surfactant solution, Syntamide-5, into hydrophobized quartz capillaries. A theory of the spontaneous capillary rise of surfactant solutions in hydrophobic capillaries is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface [V.J. Starov, Colloid Interface Sci. 270 (2003)]. In Section 4, capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting [V. Straov, S. Zhdanov, M. Velarde, J. Colloid Interface Sci. 273 (2004) 589]. Cylindrical capillaries are used as a model of porous media for theoretical treatment of the problem. It is shown that if an averaged pore size of the porous medium is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants at any concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of the pure water. The critical radius is determined by the adsorption of the surfactant molecules on the inner surface of the pores. If an averaged pore size is bigger than the critical value, then the permeability increases with surfactant concentration. These theoretical conclusions are in agreement with experimental observations. In Section 5, the spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, M.G. Velarde, J. Colloid Interface Sci. 227 (2000) 185]. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilise the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by experimental observations. In Section 6, the process of the spontaneous spreading of a droplet of a polar liquid over solid substrate is analyzed in the case when amphiphilic molecules (or their amphiphilic fragments) of the substrate surface layer are capable of overturning, resulting in a partial hydrophilisation of the surface [V.M. Starov, V.M. Rudoy, V.I. Ivanov, Colloid J. (Russian Academy of Sciences English Transaction) 61 (3) (1999) 374]. Such a situation may take place, for example, during contact of an aqueous droplet with the surface of a polymer whose macromolecules have hydrophilic side groups capable of rotating around the backbone and during the wetting of polymers containing surface-active additives or Langmuir-Blodgett films composed of amphiphilic molecules. It was shown that droplet spreading is possible only if the lateral interaction between neighbouring amphiphilic molecules (or groups) takes place. This interaction results in the tangential transfer of "the overturning state" to some distance in front of the advancing three-phase contact line making it partially hydrophilic. The quantitative theory describing the kinetics of droplet spreading is developed with allowance for this mechanism of self-organization of the surface layer of a substrate in the contact with a droplet.     

Spontaneous rise of surfactant solutions into vertical hydrophobic capillaries

It has been found earlier (N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747) that aqueous surfactant solutions spontaneously rise in vertical hydrophobized quartz capillaries. A theory of this phenomenon is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface.     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

Viscosity of Milk: Influence of Cluster Formation

Recently, a new theory of viscosity of concentrated emulsions dependence on volume fraction of droplets (Starov, V. and Zhdanov, V., J. Colloid Interface Sci., 2003, vol. 258, p. 404) has been proposed that relates the viscosity of concentrated emulsions to the formation of clusters. Through experiments with milk at different fat concentrations, cluster formation has been validated using optical microscopy and their properties determined using the aforementioned theory. Viscometric studies have shown that, within the studied range of shear rates, both the packing density of fat droplets inside clusters and the relative viscosity of milk (viscosity over skim milk viscosity) are independent of shear rate but vary with volume fraction. Comparison of the experimental data with previous theories that assumed that the particles remained discrete shows wide variation. We attribute the discrepancy to cluster formation.     

Thermodynamic quantities of surface formation of aqueous electrolyte solutions. V. Aqueous solutions of aliphatic amino acids

The surface tension of aqueous solutions of glycine, L-alanine, L-valine, and L-leucine has been observed using the drop volume method as a function of temperature and concentration. The L-leucine molecules form an adsorbed film, while glycine affects the water surface in accordance with simple salts which dissociate into cations and anions completely. The surface tension data have been analyzed in view of K. Motomura's thermodynamic treatment (J. Colloid Interface Sci.64, 348 (1978)), and the thermodynamic quantities relevant to the surface have been shown systematically.     

From homogeneous dispersion to micelles-a molecular dynamics simulation on the compromise of the hydrophilic and hydrophobic effects of sodium dodecyl sulfate in aqueous solution

The structural and functional diversity of surfactant systems has attracted simulation works in atomistic, coarse grain, and mesoscopic models (Bandyopadhyay, S.; et al. Langmuir 2000, 16, 942; Senapati, S.; et al. J. Phys. Chem. B 2003, 107, 12906; Maiti, P. K.; et al. Langmuir 2002, 18, 1908; Srinivas, G.; et al. J. Phys. Chem. B 2004, 108, 8153; Groot, R. D.; et al. J. Chem. Phys. 1999, 110, 9739; Rekvig, L.; et al. Langmuir 2003, 19, 8195). However, atomistic models have suffered from their tremendous computational cost and are, so far, not able to simulate the structural behaviors in sufficient spatio-temporal scales (Shelley, J. C.; Shelley, M. Y. Curr. Opin. Colloid Interface Sci. 2000, 5, 101). The other two approaches are not microscopic enough to describe the configurations of the surfactants that determine their behaviors (Shelley and Shelley). In this study, we propose to simplify atomistic models based on the observation that the compromise of the hydrophilic and hydrophobic effects (Li, J.; Kwauk, M. Chem. Eng. Sci. 2003, 58, 521-535) and molecular structures of surfactants are the dominant factors shaping their structures in the systems. With this simplification, we are able to simulate with moderate computing cost the whole process of micelle formation from an initially uniform dispersion of sodium dodecyl sulfate (SDS) in aqueous solution. The resulting micelle structures are different from those predicted by atomistic simulations that started with a predefined micelle configuration at the same surfactant concentrations. However, if we use their initial micelle configuration, micelle structures the same as theirs are obtained. Analyses show that our results are more realistic and that the results of the atomistic simulations suffer from artificial initial conditions. Therefore, our model may serve as a reasonable simplification of atomistic models in terms of the general structure of micelles.     

Three-phase capillary entry conditions in pores of noncircular cross-section

In this work we challenge the assumption that the capillary entry pressures for displacements in three-phase flow are the same as those in two-phase flow. Using an energy balance, as derived by R.P. Mayer and R.A. Stowe (J. Colloid Interface Sci. 20 (1965) 893-911) and H.M. Princen (J. Colloid Interface Sci. 30 (1969) 69-75; 30 (1969) 359-371; 34 (1970) 171-184) for two-phase flow, we derive a general formula for determination of the capillary entry pressures for piston-like displacement of two bulk phases in a pore where a third phase may also be present. The method applies to capillaries of angular cross-section and uniform but arbitrary wettability. To use this method we have determined all possible underlying phase occupancies in cross-sections on either side of the main terminal meniscus, in particular the presence of corner arc menisci (AMs). Indeed, the capillary entry pressures for piston-like displacements depend on the pressure in the remaining third phase if the cross-sectional fluid configurations contain this phase. This dependence only vanishes when layers of the intermediate-wetting phase completely separate the wetting and the non-wetting phases. The complexity of the corresponding equations and the quantitative effects are studied using two different geometries, the equilateral triangle and the rhombus. The main difference is that the latter geometry has unequal corners, which may carry different AMs. We have carried out a limited sensitivity study with respect to the effect of wettability, the spreading coefficient of the intermediate-wetting phase, and the aspect ratio of the principal radii of the rhombus.     

Evaluation of the precision of drop-size determination in oil/water emulsions by low-resolution NMR spectroscopy

The accuracy of the recently reported low-resolution NMR method (Goudappel, G. J. W.; et al. J. Colloid Interface Sci. 2001, 239, 535) for the determination of drop-size distribution in oil-in-water emulsions is evaluated by comparing the NMR results with precise data from video-enhanced optical microscopy. A series of 27 soybean-oil-in-water emulsions, differing in their mean drop size, polydispersity, oil volume fraction, and emulsifier, is studied. Soybean oil is selected as a typical component of food emulsions. The experimental error of our optical procedure for drop-size determination is estimated to be around 0.3 microm, which allows us to use the microscopy data as a reference for the mean drop-size and distribution width of the studied emulsions, with known experimental error. The main acquisition parameters in the NMR experiment are varied to find their optimal values and to check how the experimental conditions affect the NMR results. Comparison of the results obtained by the two methods shows that the low-resolution NMR method underestimates the mean drop size, d33, by approximately 20%. For most of the samples, NMR measures relatively precisely the distribution width (+/-0.1 to 0.2 dimensionless units), but for approximately 20% of the samples, larger systematic deviation was registered (underestimate by 0.3-0.4 units). No correlation is found between the emulsion properties and the relative difference between the microscopy and NMR data. Possible reasons for the observed discrepancy between NMR and optical microscopy are discussed, and some advantages and limitations of the low-resolution NMR method are considered.     

Effect of capillary element aspect ratio on the dynamic imbibition within porous networks

The Washburn equation is widely accepted for describing capillary imbibition. It has, however, been shown to be insufficient at very short times due partly to the lack of inertial terms. Bosanquet (C. H. Bosanquet, Philos. Mag. ser. 645, 525 (1923)) applied an inertial term via momentum, Szekely et al. (J. Szekely, A. W. Neumann, and Y. K. Chang, J. Colloid Interface Sci.35, 273 (1971)) examined single capillaries based on a revised boundary-condition model, and Sorbie et al. (K. S. Sorbie, Y. Z. Wu, and S. R. McDougall, J. Colloid Interface Sci. 289 (1995)) reviewed and applied Szekely's work to examine the effects of comparative imbibition into a parallel pore doublet. The study here extends the work of Sorbie et al. by applying the equation of Bosanquet to a three-dimensional network model, Pore-Cor. All authors agree that, with the inclusion of inertial terms at short times, smaller radius capillaries will initially fill faster than larger radius capillaries which disagrees with the Washburn equation. It is shown that the aspect ratio of a capillary, defined as its length divided by its radius, plays an important role, in combination with the capillary radii themselves, in determining the filling rate of individual elements. The distribution of this ratio associated with the capillary throat elements within a network structure is investigated. The result is that a preferred pathway of permeation is observed under supersource imbibition conditions in the case where a broad size distribution of capillary elements occurs within a network structure.     

Gas-solid coexistence in highly charged colloidal suspensions

Aqueous suspensions of highly charged polystyrene particles with different volume fractions have been investigated for structural ordering and phase behavior using static light scattering (SLS) and confocal laser scanning microscope (CLSM). Under deionized conditions, suspensions of high-charge-density colloidal particles remained disordered whereas suspensions of relatively low charge density showed crystallization by exhibiting iridescence for the visible light. Though for the unaided eye crystallized suspensions appeared homogeneous, SLS measurements and CLSM observations have revealed their inhomogeneous nature in the form of the coexistence of voids with dense ordered regions. CLSM investigations on disordered suspensions showed their inhomogeneous nature in the form coexistence of voids with dense disordered (amorphous) regions. Our studies on highly charged colloids confirm the occurrence of gas-solid transition and are in accordance with predictions of Monte Carlo simulations using a pair-potential having a long-range attractive term [Mohanty, P. S.; Tata, B. V. R. J. Colloid Interface Sci. 2003, 264, 101]. On the basis of our experimental and simulation results, we argue that the reported reentrant disordered state [Yamanaka et al. Phys. Rev. Lett. 1998, 80, 5806 and Toyotama et al. Langmuir 2003, 19, 3236] in charged colloids observed at high charge densities is a gas-solid coexistence state.     

Stable drop shapes under disjoining pressure. II. Multiplicity and stability

The stability of the contact line region as affected by the disjoining pressure has been analyzed by solving the augmented Young-Laplace equation. Because of the results in Part I (Zhang, X., Neogi, P., and Ybarra, R. M., J. Colloid Interface Sci.), we have concentrated on obtaining multiple solutions for the same set of conditions. As many as five solutions were obtained: drops that end in a thin film with uniform thickness and where the film shape oscillates, drops that end with microscopic contact angles, as well as uniform thin films of two different thicknesses. The results of linear stability analysis were used to show that most cases were unstable to infinitesimal disturbances. Only two stable drop shapes for the particular disjoining pressure investigated are stable, a thin film of constant thickness and a thin drop that ends in a film of same thickness. Both multiplicity and stability have been discussed here for the first time and shed considerable light on the role of the attractive and repulsive forces.     

Molecular orbital theory study on surface complex structures of phosphates to iron hydroxides: calculation of vibrational frequencies and adsorption energies

Quantum mechanical calculations were applied to resolve controversies about phosphate surface complexes on iron hydroxides. Six possible surface complexes were modeled: deprotonated, monoprotonated, and diprotonated versions of bridging bidentate and monodentate complexes. The calculated frequencies were compared to experimental IR frequency data (Persson et al. J. Colloid Interface Sci. 1996, 177, 263-275; Arai and Sparks J. Colloid Interface Sci. 2001, 241, 317-326.). This study suggests that the surface complexes change depending on pH. Four possible species are a diprotonated bidentate complex at pH 4-6, either a deprotonated bidentate or a monoprotonated monodentate complex at pH 7.5-7.9, and a deprotonated monodentate complex at pH 12.8. In addition, reaction energies were calculated for adsorption from aqueous solution to determine relative stability to form a monoprotonated monodentate complex and a deprotonated bidentate complex. According to these results, the monoprotonated monodentate complex should be favored. Vibrational frequencies of the monoprotonated monodentate and deprotonated bidentate complexes were analyzed with electronic effects on the Fe-OP and H-OP bonds.     

Response to the comment on [J. Colloid Interface Sci. 253 (2002) 196] by J. Eggers and R. Evans

We examine the comment on our paper [J. Colloid Interface Sci. 253 (2002) 196] by Eggers and Evans and show that the assertions made there have no foundation in fact nor in scientific substance.     

Forces between a rigid probe particle and a liquid interface. II. The general case

The semianalytic theory developed previously (Chan, D. Y. C., Dagastine, R. R., and White, L. R., J. Colloid Interface Sci. 236, 141 (2001)) to predict the force curve of an AFM measurement at a liquid interface using a colloidal probe has been expanded to incorporate a general force law with both attractive and repulsive forces. Expressions for the gradient of the force curve are developed to calculate the point at which the probe particle on the cantilever will spontaneously jump in toward the liquid interface. The calculation of the jump instability is reduced to a straightforward embroidery of the simple algorithms presented in Chan et al. In a variety of sample calculations using force laws including van der Waals, electrostatic, and hydrophobic forces for both oil/water and bubble/water interfaces, we have duplicated the general behaviors observed in several AFM investigations at liquid interfaces. The behavior of the drop as a Hookean spring and the numerical difficulties of a full numerical calculation of F(deltaX) are also discussed.     

Diffuse Double-Layer Interaction between Two Identical Spherical Colloidal Particles

A simple method is given for calculating the potential energy of the diffuse double-layer interaction between two identical spherical colloidal particles in a symmetrical electrolyte solution with the help of Derjaguin's approximation. This method uses accurate analytic expressions for the corresponding interaction energy between two parallel similar plates obtained previously (Colloids Surf. A Physicochem. Eng. Asp. 146, 213 (1999); J. Colloid Interface Sci. 212, 130 (1999)). Agreement with numerical data provided by Honig and Mul (J. Colloid Interface Sci. 36, 258 (1971)) is excellent particularly for small particle separations. Copyright 2000 Academic Press.     

Drop penetration into porous powder beds

The kinetics of drop penetration were studied by filming single drops of several different fluids (water, PEG200, PEG600, and HPC solutions) as they penetrated into loosely packed beds of glass ballotini, lactose, zinc oxide, and titanium dioxide powders. Measured times ranged from 0.45 to 126 s and depended on the powder particle size, viscosity, surface tensions, and contact angle. The experimental drop penetration times were compared to existing theoretical predictions by M. Denesuk et al. (J. Colloid Interface Sci.158, 114, 1993) and S. Middleman ("Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops," Academic Press, San Diego, 1995) but did not agree. Loosely packed powder beds tend to have a heterogeneous bed structure containing large macrovoids which do not participate in liquid flow but are included implicitly in the existing approach to estimating powder pore size. A new two-phase model was proposed where the total volume of the macrovoids was assumed to be the difference between the bed porosity and the tap porosity. A new parameter, the effective porosity epsilon(eff), was defined as the tap porosity multiplied by the fraction of pores that terminate at a macrovoid and are effectively blocked pores. The improved drop penetration model was much more successful at estimating the drop penetration time on all powders and the predicted times were generally within an order of magnitude of the experimental results.     

Characterization of silica-coated hematite and application to the formation of composite particles including egg yolk PC liposomes

According to the method of Ohmori et al. (J. Colloid Interface Sci. 150 (1992) 594), a procedure is examined for the buildup of uniform silica layers on monodispersed hematite particles. It appears that the silica layer resulting is homogeneous and the layer thickness is controlled by the concentration of tetraethylorthosilicate (TEOS) in the medium. Further, egg PC liposomes, a typical biocolloid, are introduced onto the silica-coated hematite particle. The formation was proceeded by two types of processes: (1) heterocoagulation between the silica-coated hematite and egg PC liposomes by controlling the concentration of LaCl(3) in the medium, or (2) buildup using two proteins (lysozyme or cytochrome C) as binder molecules. These results were analyzed by zeta-potential measurements and a contact-type X-ray microscope, which is a unique technique for obtaining X-ray images of biological specimens in water with high resolution.     

Shape analysis based critical Eotvos numbers for buoyancy induced partial detachment of oil drops from hydrophilic surfaces

Removal of oil drops from solid surfaces immersed in an aqueous medium is of interest in many applications. It has been shown that drop shape analysis can be used to predict conditions at which the stability limit of a lighter than water oil drop on a solid surface immersed in an aqueous bath is reached (Adv. Colloid Interface Sci. 98 (2002) 265). However the above analysis is restricted to cases where the contact angle made by the drop is below 90degrees and when the surface conditions result in a 'pinned' contact line. In this paper, it is shown that drop shape analysis can be used to predict the critical conditions at which drop stability limit is reached for drop contact angles of 90degrees and above, which is encountered with 'hydrophilic' surfaces. This critical condition can predict the occurrence of partial oil drop detachment, before complete removal due to 'roll-up', which occurs when the hydrophilic surface is adequately smooth which prevents 'pinning' of the contact line. The critical conditions at which partial drop detachment occurs can also be approximately predicted from simple force balances. It has been shown (Adv. Colloid Interface Sci. 98 (2002) 265) that for contact angles less than 90degrees, the critical limit based on shape analysis appears to resolve the differences that arise due to alternate expressions for capillary retention force. This paper shows that even for contact angles above 90degrees, the critical conditions predicted from the shape analysis resolves the differences in the predictions from the alternate force balances. Drop shape analysis used in this paper is based on the 'Arc-length' form of Young-Laplace or 'drop shape' equation, which is different from the 'Y vs X' form of the above equation that is used in Adv. Colloid Interface Sci. 98 (2002) 265. The above drop shape equation is solved by a fourth order Runge-Kutta technique and it is shown that for angles less than 90degrees, the two forms of the drop shape equation, predict almost identical values of the critical Eotvos number. This paper highlights the competing effects of interfacial tension lowering induced drop instability and 'roll-up', a term that is used to describe the retraction of the contact line of an oil drop on a surface, in being the primary c ause for drop detachment.     

Experimental study of vapor bubbles in small-sized channels

This paper investigates the effect of evaporation on the shape of liquid/vapor interfaces in small-scale systems. Vapor bubbles are generated due to localized heating in a small-sized channel (with an inner dimension of 3x3x200 mm) filled with pentane, for which heat fluxes and temperature distributions are simultaneously measured. The length of the resulting vapor bubble is studied as a function of the power input and heater temperature, and is found to be not only repeatable but nonhysteretic. The bubble length depends nearly linearly on the power input, in qualitative agreement with an approximate theory of Ajaev and Homsy [V.S. Ajaev, G.M. Homsy, J. Colloid Interface Sci. 244 (2001) 180]. In addition, it is found that vapor bubbles oscillate very slowly due to the effect of thermal relaxation.