Theoretical study of stability problems for transport in a deformable microfabricated channel

We investigate the stability problem related to the basic flows induced by peristaltic transport within the bounded deformable walls which are common in micro- and/or nanobiotechnological applications. The neutral stability boundary is obtained by solving the relevant Orr-Sommerfeld equation via a verified preconditioned complex-matrix solver. The critical Reynolds number (when the wall is deformable) is 2886.5 which is much less than the conventional rigid-wall case (~5772, obtained by Orszag based on the spectral method).