STABILITY OF FLOW IN A DEFORMABLE CHANNEL

Abstract

The effect of various parameters such as solid thickness H, interfacial tension and extent of deformability of the solid on the stability of Newtonian fluid flowing in a channel lined with an incompressible and impermeable neo-Hookean material at one end is examined in this work. The analysis was carried out using linear stability analysis at zero, low and high Reynolds number. A first normal stress difference whose magnitude depends on depth arises in the base state for solid, and linear stability analysis reveals that this leads to a short-wave instability. This instability continues in all the three ranges of Reynolds number. Contrary to the findings of Gkanis& Kumar (2005), for the values of less than 10 the short wave instability is absent because of the modifications in the stress balance equations. At low but non-zero Reynolds number, the unstable modes in the low wave-number reported by Gaurav & Shankar (2010) are absent. The effect of various parameters on the stability of the system is reported.