Instabilities of volatile films and drops

We report on instabilities during spreading of volatile liquids, with emphasis on the novel instability observed when isopropyl alcohol (IPA) is deposited on a monocrystalline silicon (Si) wafer. This instability is characterized by emission of drops ahead of the expanding front, with each drop followed by smaller, satellite droplets, forming the structures which we nickname “octopi” due to their appearance. A less volatile liquid, or a substrate of larger heat conductivity, suppress this instability. In addition, we examine the spreading of drops of water (DJW)-JPA mixtures on both Si wafers and plain glass slides, and describe the variety of contact line instabilities which appear. We find that the decrease of IPA concentration in mixtures leads to transition from “octopi” to mushroom-like instabilities. Through manipulation of our experimental set up, we also find that the mechanism responsible for these instabilities appears to be mostly insensitive to both the external application of convection to the gas phase, and the doping of the gas phase with vapor in order to create the saturated environment. In order to better understand the “octopi” instability, we develop a theoretical model for evaporation of a pure liquid drop on a thermally conductive solid substrate. This model includes all relevant physical effects, including evaporation, thermal conductivity in both liquid and solid, (thermocapillary) Marangoni effect, vapor recoil, disjoining pressure, and gravity. The crucial ingredient in this problem is the evaporation model, since it influences both the motion of the drop contact line, and the temperature profiles along the liquid-solid and liquid-gas interfaces. We consider two evaporation models: the equilibrium “lens” model and the non-equilibrium one-sided (NEOS) model. Along with the assumption of equilibrium at the liquid-gas interface, the “lens” model also assumes that evaporation proceeds in a (vapor) diffusion-limited regime, therefore bringing the focus to the gas phase, where the problem of vapor mass diffusion is to be solved, which invokes analogy with the problem of lens-shaped conductor from electrostatics. On the other hand, NEOS model assumes non-equilibrium at the liquid-gas interface and a reaction-limited regime of evaporation; the liquid and gas phases are decoupled using the one-sided assumption, and hence, the problem is to be solved in the liquid phase only. We use lubrication approximation and derive a single governing equation for the evolution of drop thickness, which includes both models. An experimental procedure is described next, which we use in order to estimate the volatility parameter corresponding to each model. We also describe the numerical code, which we use to solve the governing equation for drop thickness, and show how this equation can be used to predict which evaporation model is more appropriate for a particular physical problem. Next, we perform linear stability analysis (LSA) of perturbed thin film configuration. We find excellent agreement between our numerical results and LSA predictions. Furthermore, these results indicate that the IPA/Si configuration is the most unstable one, in direct agreement with experimental results. We perform numerical simulations in the simplified 2d geometry (cross section of the drop) for both planar and radial symmetry and show that our theoretical model reproduces the main features of the experiment, namely, the formation of “octopus” -like features ahead of the contact line of an evaporating drop. Finally, we perform quasi-3d numerical simulations of evaporating drops, where stability to azimuthal perturbations of the contact line is examined. We recover the “octopi” instability for IPA/Si configuration, similarly as seen in the experiments

Dynamics of particle settling and resuspension in viscous liquids

We derive and study a dynamical model for suspensions of negatively buoyant particles on an incline. Our theoretical model includes the settling/sedimentation due to gravity as well as the resuspension of particles induced by shear-induced migration, leading to disaggregation of the dense sediment layer. Out of the three different regimes observed in the experiments, we focus on the so-called settled case, where the particles settle out of the flow, and two distinct fronts, liquid and particle, form. Using an approach relying on asymptotics, we systematically connect our dynamic model with the previously developed equilibrium theory for particle-laden flows. We show that the resulting transport equations for the liquid and the particles are of hyperbolic type, and study the dilute limit, for which we derive the analytic solution. We also carry out a systematic experimental study of the settled regime, focusing on the motion of the liquid and the particle fronts. Finally, we carry out numerical simulations of our transport equations. We show that the model predictions for small to moderate values of the particle volume fraction and the inclination angle of the solid substrate agree well with the experimental data

Dynamics of particle settling and resuspension in viscous liquid films

We develop a dynamic model for suspensions of negatively buoyant particles on an incline. Our model includes settling due to gravity and resuspension of particles by shear-induced migration. We consider the case where the particles settle onto the solid substrate and two distinct fronts form: a faster liquid and a slower particle front. The resulting transport equations for the liquid and the particles are of hyperbolic type and we study the dilute limit for which we compute exact solutions. We also carry out systematic laboratory experiments, focusing on the motion of the two fronts. We show that the dynamic model predictions for small to moderate values of the particle volume fraction and the inclination angle of the solid substrate agree well with the experimental data