George Karapetsas

Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

We study the thermocapillary-driven spreading of a droplet on a nonuniformly heated substrate for fluids associated with a non-monotonic dependence of the surface tension on temperature. We use lubrication theory to derive an evolution equation for the interface that accounts for capillarity and thermocapillarity. The contact line singularity is relieved by using a slip model and a Cox-Voinov relation; the latter features equilibrium contact angles that vary depending on the substrate wettability, which, in turn, is linked to the local temperature. We simulate the spreading of droplets of fluids whose surface tension-temperature curves exhibit a turning point. For cases wherein these turning points correspond to minima, and when these minima are located within the droplet, then thermocapillary stresses drive rapid spreading away from the minima. This gives rise to a significant acceleration of the spreading whose characteristics resemble those associated with the superspreading of droplets on hydrophobic substrates. No such behavior is observed for cases in which the turning point corresponds to a surface tension maximum.

Linear and nonlinear stability of hydrothermal waves in planar liquid layers driven by thermocapillarity

A shallow planar layer of liquid bounded from above by gas is set into motion via the thermocapillary effect resulting from a thermal gradient applied along its interface. Depending on the physical properties of the liquid and the strength of the gradient, the system is prone to departure from its equilibrium state and to the consequent development of an oscillatory regime. This problem is numerically investigated for the first time by means of two-phase direct numerical simulations fully taking into account the presence of a deformable interface. Obliquely travelling hydrothermal waves (HTWs), similar to those first described by Smith and Davis [J. Fluid Mech. 132, 119–144 (1983)]10.1017/S0022112083001512, are reported presenting good agreement with linear stability theory and experiments. The nonlinear spatiotemporal growth of the instabilities is discussed extensively along with the final bulk flow for both the liquid and gas phases. Our study reveals the presence of interface deformations which accomp...

On phase change in Marangoni-driven flows and its effects on the hydrothermal-wave instabilities

This paper investigates the effects of phase change on the stability of a laterally heated liquid layer for the first time. The interface is open to the atmosphere and vapor diffusion is the rate-limiting mechanism for evaporation. In this configuration, the planar layer is naturally vulnerable to the formation of travelling thermal instabilities, i.e., hydrothermal waves (HTWs), due to the presence of temperature gradients along the gas-liquid interface. Recent work carried out for deformable interfaces and negligible evaporation indicates that the HTWs additionally give rise to interface deformations of similar features, i.e., physical waves. The study presented here reveals that phase change plays a dual role through its effect on these instabilities: the latent energy required during the evaporation process tends to inhibit the HTWs while the accompanying level reduction enhances the physical waves by minimizing the role of gravity. The dynamics of the gas phase are also discussed. The HTW-induced convective patterns in the gas along with the travelling nature of the instabilities have a significant impact on the local evaporation flux and the vapor distribution above the interface. Interestingly, high (low) concentrations of vapor are found above cold (hot) spots. The phase-change mechanism for stable layers is also investigated. The Marangoni effect plays a major role in the vapor distribution generating a vacuum effect in the warm region and vapor accumulations at the cold boundary capable of inverting the phase change, i.e., the capillary flow can lead to local condensation. This work also demonstrates the inefficiencies of the traditional phase change models based on pure vapor diffusion to capture the dynamics of thermocapillary flows.