Effects of slip velocity and surface acoustic wave on the laminar flow stability

The stability of slip flows when a surface acoustic wave (SAW) propagating along the walls of a microchannel in the laminar flow regime is investigated. The governing equation which was derived by considering the weakly nonlinear coupling between the deformable wall and streaming slip flow is linearized and then the eigenvalue problem is solved by a numerical code together with the associated interface and slip velocity boundary conditions. The value of the critical Reynolds number was found to be near 1,441 for a Knudsen number being 0.001 (associated with a physical parameter K ₀ characterizing the SAW effect) which is much smaller than the static-wall case for conventional pressure-driven flows.