(296h) Linear Stability of Layered Two-Phase Flow through Soft Gel Coated Walls

Two phase stratified flows between soft-gel coated walls arise in flows in micro-channels. It is important to understand the elastohydrodynamic coupling between the soft-gel layers and the fluids to design lab on a chip devices. In this work, a theoretical model is developed in a generalized framework and different types of instabilities that arise due to the fluid flow are understood. The solid membrane is modelled as an incompressible linear viscoelastic material. To simplify the analysis, inertia in the solid is neglected as a first step. Linear stability analysis is carried around the base state velocity of the fluid and displacement field of the solid. The flow is perturbed by a small disturbance and a normal mode analysis is carried out to study the growth rate of the disturbance. An eigenvalue problem in formulated using Chebyshev spectral method and is solved to obtain the growth rate of the disturbance. The effect of different parameters such as thickness of the flexible membrane, Reynolds number, viscosity ratio, density ratio, Capillary number and Weissenberg number on the stability characteristics of the flow is studied in detail. Dispersion curves are obtained which explain the stability of the flow. A detail energy analysis is carried out to determine different ways through which energy transfers from the base flow to the disturbed flow. Three instability modes are identified a liquid-liquid long wave mode, a liquid-liquid short wave mode and a gel-liquid mode. Parameters for which the liquid-liquid long wave mode is unstable for flow between rigid plates gets stabilized by introducing a soft-gel layer near to the more viscous fluid. For parameters for which the liquid-liquid long wave mode is stable for flow between rigid plates gets destabilized by introducing a soft-gel layer near to the less viscous fluid.