Stability of stratified flows through neo-Hookean soft-gel-coated walls

The work focuses on the effect of elastohydrodynamic coupling between the fluids and the soft-gel-coatings on different instabilities that arise in the flow. The fluids are assumed to be Newtonian and incompressible. The dynamics in the soft-gel layers is captured using a neo-Hookean solid model. There is a first normal stress difference which characterizes the base state in this model. The neo-Hookean model is relevant in the context of large displacement fields. First the effect of using a consistent neo-Hookean model for soft-gel layers on different instabilities in two-phase flows is analysed. We then determine the effect of soluble surfactants on the stability of the system. The dynamics of the solute is captured using a species transport equation. The results obtained from linear stability theory of single phase flows show the same scaling laws as those found experimentally in the literature. A long wave interfacial instability arises at the liquid-liquid interface. A Tollmien-Schlichting wave type instability is seen at higher Reynolds numbers. A new gel-liquid instability arises at gel-liquid interface. It is shown that these instabilities can be stabilized by the soft-gel layers . Insights into the physical mechanism driving the instabilities are discussed.