Session BD: Interfacial and Thin-Film I: Instabilities

Modeling of evaporating ultra-thin films and contact lines

A new lubrication-type model applying to evaporating ultra-thin films is presented. This evolution equation generalizes earlier ones found in the literature by incorporating the effects of finite thermal conductivity of the vapor and of temperature discontinuity across the evaporating/condensing interface. The latter effect is accounted for through a set of generalized interfacial conditions derived from irreversible thermodynamics. The model is first applied to determine the conditions under which a film of given thickness is stable to hydrodynamic disturbances. Then, steady nonlinear solutions in the form of contact lines connecting a constant-slope region with an adsorbed film are found, and particular attention is devoted to the peak of the mass flux at the contact line, as well as to the apparent contact angle. The influence of various effects on these quantities is also considered.   

Instabilities of Evaporating Droplets on Immiscible Liquid Substrates

We report a new class of convective instabilities observed in thin (lens-shaped) droplets of volatile liquids floating on a thick layer of an immiscible liquid. Two types of behavior are observed: internal axisymmetric fingering and one-dimensional spreading. For sufficiently low substrate viscosities ($\nu < 100$ cSt), a hole quickly develops near the center of the volatile liquid lens ($\nu \sim 1$ cSt). The hole rapidly forms fingers which grow radially outward into the remainder of the droplet. This instability is axisymmetric, but in some cases the droplet also spreads rapidly in one dimension, yielding aspect ratios $> 50$. The one-dimensional spreading is observed at all substrate viscosities tested (up to $1000$ cSt), with or without internal fingering; any holes that do form (at lower viscosities) are stretched into a long groove that extends the entire length of the droplet. Both instabilities are frequently observed concurrently, giving rise to ``fishbone'' structures with complicated dynamics. In this presentation we survey the observations and analyze the results in terms of evaporation-induced convection in the context of lubrication theory.   

Octopus-shaped Instabilities of Evaporating Droplets

We report on curious phenomena recorded recently during spreading of evaporating isopropyl alcohol droplets on silicon wafer surfaces \footnote[1]{see http://m.njit.edu/\~kondic/thin\_films/octopi.html}. Novel ``octopus''-shaped instabilities were noticed appearing close to the contact line. In addition to our desire to understand the instability, a motivation for this study is the fact that the region close to the contact line carries significant amounts of solid residue which can deteriorate electrical and other properties of the semiconductor devices. After presenting the experimental results, we discuss a lubrication-based mathematical model describing spreading of volatile drops. Through linear stability analysis and numerical simulations, we show that essential factors influencing occurrence of ``octopus''-shaped instabilities include volatility of liquid, and thermal conductivity of both liquid and solid.   

Evaporative and Convective Instabilities for the Evaporation of a Binary Mixture in a Bilayer System

Evaporative convection in binary mixtures arises in a variety of industrial processes, such as drying of paint and coating technology. There have been theories devoted to this problem either by assuming a passive vapor layer or by isolating the vapor fluid dynamics. Previous work on evaporative and convective instabilities in a single component bilayer system suggests that active vapor layers play a major role in determining the instability of the interface. We have investigated the evaporation convection in binary mixtures taking into account the fluid dynamics of both phases. The liquid mixture and its vapor are assumed to be confined between two horizontal plates with a base state of zero evaporation but with linear vertical temperature profile. When the vertical temperature gradient reaches a critical value, the evaporative instability, Rayleigh and Marangoni convection set in. The effects of vapor and liquid depth, various wave numbers and initial composition of the mixture on the evaporative and convective instability are determined. The physics of the instability are explained and detailed comparison is made between the Rayleigh, Marangoni and evaporative convection in pure component and those in binary mixtures.   

Stability of evaporating thin liquid film

In this study, we revisit the problem of an evaporating thin film in the presence of a surfactant. Instead of the conventional Hertz-Knudsen-Langmuir equation we impose a configurational momentum balance. This balance, which supplements the conventional conditions enforcing the balances of mass, momentum, and energy on the film surface, arises from a consideration of configurational forces within a thermodynamical framework. In addition to classical term involving the difference between the temperatures of the film surface and the adjacent vapor, the configurational momentum balance includes two additional terms. One of these terms involves the pressure at the film surface relative to the pressure of the vapor. The other term involves the difference between the surfactant concentration at the film surface and the saturation value of the surfactant concentration. We find that time-dependant base state of evaporating liquid film is affected by the effective pressure and the surfactant activity terms. Both effects reduce the disappearance time. In particular, we find that the effective pressure strongly affects the film rupture processes and is an important factor in the consideration of liquid films with thicknesses of one or two monolayers. These factors lead to a revised understanding of the stability of an evaporating film. Parameter domains where the contributions of the newly introduced terms is important are determined.   

The transition to thermocapillary convection during evaporation

Experiments have been conducted to investigate thermocapillary convection in water during evaporation from a spherical liquid-vapor interface. The Marangoni number (Ma) is found to be an indicative parameter for the Marangoni transition. When Ma is less than 100, the interface is quiescent with a uniform liquid temperature, an interfacial temperature discontinuity, and a temperature gradient in the vapor phase. Thermal conduction provides the energy required to evaporate the liquid at the observed rate. When Ma is greater than 100, significant temperature gradients exist along the interface, and in each bulk phase. If thermocapillary convection is neglected, thermal conduction does not provide enough energy to evaporate water at the observed rate. To satisfy energy conservation, a new property of water, the surface-thermal capacity, is introduced. The local evaporation flux is then calculated from an interfacial energy balance, and statistical rate theory is applied to predict the local interfacial pressure. The mean of the predicted pressures agrees with the measured vapor-phase pressure.   

Marangoni instability in an evaporating layer of binary liquid in the presence of the Soret effect

The one-sided model of evaporation is applied to the investigation of the Marangoni instability in an evaporating layer of binary liquid in the presence of the Soret effect. In the limit of both small evaporation and Lewis numbers, the time evolution of the base state for the solute concentration is studied numerically under assumption of non-deformability of the liquid-gas interface. Linear stability analysis of the time- dependent base state is carried out. In the limit considered here, the solutocapillary effect is found to be dominant with respect to the thermocapillary effect.   

Dynamics of Marangoni Driven thin film flows

We study the dynamics of thermally driven Marangoni flows of Polydimethylsiloxane(PDMS or silicone oil) on a completely wetting silicon wafer. A thin film of silicone oil is driven up the inclined plane against gravity by imposing a temperature gradient. Previous work has focused on the formation of `shock' structures and the analysis of fingers in thermally driven thin film flows. In this study we will perform a detailed analysis of how the contact line emerges from the meniscus. As the contact line emerges from the reservoir, the formation of a `precursor' or `foot' is seen. We study the emergence of this `precursor' as a function of the temperature gradient, angle of inclination and the deposited film thickness. In particular we consider the case where the meniscus typically shows a `dip' before decaying into the flat film as opposed to a `monotonic' decay. Such a meniscus shape has been predicted on theoretical grounds for very thick films by Muench and Evans.