Partho Neogi

Spreading kinetics of a drop on a rough solid surface

Abstract The effect of surface roughness on spreading rates has been analyzed using a model in which a liquid drop spreads over the surface of a porous medium filled with the same liquid. The equations of motion in the drop are simplified with the lubrication theory approximation and then solved for both zero and small but nonzero contact angles by the method of matched asymptotic expansions. Although the largest pressure gradients and velocity gradients occur near the contact line at the drop periphery, behavior in this region is not singular as found in previous analysis of spreading on perfectly smooth surfaces. The reason no singularities exist is that flow occurs in the “porous medium” underlying the drop, i.e., the region of surface irregularities which is present for all real surfaces. Because the solution is not valid in the initial stages of spreading where experimental data on spreading rates are available, a quantitative comparison of theory and experiment cannot be made at present. The theory does, however, explain all qualitative features observed for spreading drops, e.g., the increase in spreading rate with increasing roughness and the frequent appearance of apparent contact angles significantly different from equilibrium contact angles.

Spreading kinetics of a drop on a smooth solid surface

Abstract Spreading of a drop on a perfectly smooth solid surface is analyzed using the method of matched asymptotic expansions. The analysis includes the effect of intermolecular forces near the contact line both on surface diffusion of adsorbed molecules and on flow within the liquid phase itself near the contact line. The former effect produces slip and allows the contact line to advance, while the latter effect is found to be small for most situations of interest. Equations obtained for drop shapes and spreading rates are formally similar to those found previously for rough surfaces, the main difference being that the length scale for the effective range of intermolecular forces replaces the length scale of surface irregularities in the definition of the small parameter used in the perturbation expansions. Expressions for the spreading rate are given for both zero and small but nonzero equilibrium contact angles.

On One-dimensional Self-assembly of Surfactant-coated Nanoparticles

Nanometer-sized metal and semiconductor particles possess novel properties. To fully realize their potential, these nanoparticles need to be fabricated into ordered arrays or predesigned structures. A promising nanoparticle fabrication method is coupled surface passivation and self-assembly of surfactant-coated nanoparticles. Due to the empirical procedure and partially satisfactory results, this method still represents a major challenge to date and its refinement can benefit from fundamental understanding. Existing evidences suggest that the self-assembly of surfactant-coated nanoparticles is induced by surfactant-modified interparticle interactions and follows an intrinsic road map such that short one-dimensional (1D) chain arrays of nanoparticles occur first as a stable intermediate before further assembly takes place to form higher dimensional close-packed superlattices. Here we report a study employing fundamental analyses and Brownian dynamics simulations to elucidate the underlying pair interaction potential that drives the nanoparticle self-assembly via 1D arrays. We find that a pair potential which has a longer-ranged repulsion and reflects the effects of surfactant chain interdigitation on the dynamics is effective in producing and stabilizing nanoparticle chain arrays. The resultant potential energy surface is isotropic for dispersed nanoparticles but becomes anisotropic to favor the growth of linear chain arrays when self-assembly starts.

Tears-of-wine and related phenomena

Abstract The meniscus of a strong wine in a glass is drawn upward on the glass surface into a thin film. Due to a preferred evaporation of alcohol, the alcohol-lean liquid interface has a higher surface tension giving rise to a surface tension gradient and a flow which leads to the formation of the thin film. The accumulated liquid water forms “tears.” The tears-of-wine phenomenon has been generalized here to account for movement of thin films containing contact lines and driven by surface tension gradients. The fluid mechanical problem has been solved under lubrication theory approximation and a rough comparison with the experiments made. The results obtained here for the nonwetting liquids show that wettability plays an important role and the lack of wetting ability can give rise to receding contact lines even when the gradient of surface tension opposes such a movement.

The absence of a rheological effect on the spreading of small drops

The fluid mechanics of the movement of the contact line region for non-Newtonian fluids has been analyzed using the method of Joanny and de Gennes [C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Univers Terre 299, 279 (1984)] where under lubrication theory approximation the rate of viscous dissipation is equated to the rate of surface work to get the expression for the rate of spreading. Two kinds of fluids are considered, one where the viscosity is dependent on shear rate but there are no normal stresses, and another where there are normal stresses but the coefficients are not dependent on the shear rate. Both show the spreading rates to be independent of the non-Newtonian nature of the fluids to a good approximation, with the zero shear viscosity replacing the Newtonian viscosity in the result of Joanny and de Gennes. This appears to be in keeping with the available experimental data.

Three- and two-dimensional effects in wetting kinetics

Abstract Wetting at equilibrium is reviewed in brief, and it is then suggested that a wider class of nonequilibrium problems can exist where an equilibrium-like behaviour is reached simply because the mechanisms for spreading are suppressed. The mechanisms of spreading are reviewed to suggest that experiments of wetting kinetics of liquids with varying volatilities on mica would lead to interesting results. Such experiments were conducted and the results are supportive of the models. It was also observed that when volatility and surface roughness, two important mechanisms of spreading, are removed, the drop motion presumed to be controlled by surface diffusion at the contact line virtually ceases, although scanning electron microscopy results show that they are indeed moving. The role of films of ultra-low thicknesses are examined. It is seen that the dynamics of molecular scale droplets are understandable, and can be modelled in many ways, and the features these moving molecular scale drops exhibit can in some cases affect the movement of microscale drops as well. We are able to identify and define two- and three-dimensional volatilities and mobilities that help one to classify the spreading phenomena, as far as the liquids are concerned. The surfaces can be smooth or rough, a difference that has a strong effect.

Hydrocarbon Extraction into Surfactant Phase with Nonionic Surfactants. II. Model

Abstract The solubilization kinetics of an extraction process of oil with an aqueous micellar solution of a nonionic surfactant has been modeled. The model is directly related to the phase diagram, allowing a simple form which explains the main effects. The theoretical results show the adsorption process of surfactant at the phase interfaces to provide the main resistance to the mass transfer processes. The values of adsorption rates, and of some of the diffusion coefficients obtained, compare well with the earlier experimental results.

Sorption of benzene and n-hexane in polyethylene

Abstract Differential sorption data of benzene and n-hexane vapors in polyethylene have been obtained over wider ranges of temperatures and activities than available before. The data are used to develop a better model or help in the choice of the appropriate theory and modeling assumption from the available ones. Whereas the swelling of the walled-in amorphous region, with some modifications, provides the best correlation for the solubilities, in contrast, the integrated giant crosslink model shows remarkable agreement with the experimental values of diffusivities.

Sorption of Methylene Chloride in Semicrystalline Polyethylene Terephthalate

Abstract Differential sorption has been used to obtain diffusivities and solubilities of methylene chloride vapor in semicrystalline polyethylene terephthalate (PET) up to moderately high activities. The results show that clusters form. In one instance pseudo-Fickian diffusion is observed.

Ostwald ripening of oil drops in a micellar solution

A model for Ostwald ripening of oil-in-water emulsion in the presence of small amount of surfactants is presented. It accounts for the transfer of oil from small to larger drops when the interfacial resistance is rate controlling. In this case, the continuous breakdown and reformation of the micellar structure during mass transfer through the interface, is assumed to be the rate-controlling step. A discretized population balance equation for the change in the number concentration of drops due to Ostwald ripening is solved using the method of characteristics. The third moment of the distribution (average volume) is found to increase linearly with time, consistent with available experimental observations, before reaching an abrupt equilibrium. The rate of change of drop volume is found to be strongly dependent on the solubility and is fairly insensitive to the volume fraction. The transients of the drop size distributions indicate an initial rapid decrease in the small droplets with a corresponding increase in the larger drops followed by a very slow change in the number distributions at longer times. The rate constants involved can be roughly correlated with the components of several experimental measurements, and allow comparison with the data of Kabalnov (Langmuir 10 (1994) 680), but only at small surfactant concentrations. The numerical agreement is not good but it is able to predict the anomalous direction of change with increased surfactant concentrations. The basis of the lack of numerical agreement is discussed.