Instability of creeping Couette flow past a neo-hookean solid

Fluid flow over a deformable solid can become unstable due to the fact that waves may propagate along the solid–fluid interface. In order to understand the role that nonlinear rheological properties of the solid play in these elastohydrodynamic instabilities, we apply linear stability analysis to investigate creeping Couette flow of a Newtonian fluid past an incompressible and impermeable neo-Hookean solid of finite thickness. As inertial effects are assumed to be negligible, the problem is governed by three dimensionless parameters: an imposed strain, a thickness ratio, and an interfacial tension. In the base state, there is a first normal stress difference in the neo-Hookean solid, and this leads to instability behavior that is significantly different from what is observed with a linear constitutive equation. In the absence of interfacial tension, the first normal stress difference gives rise to a shortwave instability. For sufficiently thin solids, a large range of high-wavenumber modes becomes unstabl...