Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability

TL;DR

This paper investigates how convective transport influences the linear stability of free surface polymer films with binary mixtures, revealing that convection can destabilize films and alter stability regimes compared to diffusive transport alone.

Contribution

It provides a detailed analysis of the impact of convective transport on film stability, extending previous diffusive models to include convection effects and their qualitative influence.

Findings

Convective transport destabilizes films more than diffusion alone.

Increased film thickness can stabilize or destabilize depending on conditions.

Convective effects significantly alter the stability behavior and parameter dependencies.

Abstract

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.