Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil

Abstract

We investigate interfacial stability of an evaporating viscous liquid layer above/below a horizontal heated substrate in the framework of a long-wave model that accounts for surface tension, positive/negative gravity, and evaporation effects of mass loss and vapor recoil. With the time-dependent linear stability analysis, it is found that the interface instability is enhanced by vapor recoil with time using an effective growth rate. The destabilizing mechanism of vapor thrust competes with the stabilizing surface tension, and the effects of the latter are not asymptotically negligible near rupture, reflected by a rescaled effective interfacial pressure. A two-dimensional nonlinear evolution is investigated for the quasi-equilibrium evaporating layers with different evaporative conditions for Rayleigh–Taylor unstable and sessile layers. For weak mass loss and strong vapor recoil, the well-defined capillary ridges emerge around a deepening narrow valley with increasing wavelength under a positive gravity, while, on the basis of initial condition, main and secondary droplets are either coalesced partially or separated by a sharp dry-out point under a negative gravity. The rupture location depends strongly on the characteristics of a given initial condition, except for the random perturbation. For both the cases, an increase in the modified evaporation number tends to reduce the rupture time tr and droplet thickness remarkably. Similarity analysis along with numerical strategy is presented for the final stage of touch-down dynamics, determined by a physical balance between the vapor recoil and capillary force. The evaporation-driven rupture with a significant vapor recoil and negligible mass loss is shown to contain a countably infinite number of similarity solutions whose horizontal and vertical length scales behave as (tr − t)1/2 and (tr − t)1/3. The first similarity solution represents a stable single-point rupture.