Peristalsis of a viscoelastic fluid in a cavity with closed ends

Theoretical studies in microfluidics have examined a ``peristaltic mixer" - one that consists of a fluid filled cavity bounded above and below by flexible membranes which vibrate mechanically in a prescribed fashion. We use Lagrangian coherent structure (LCS) methods to identify geometric flow regions in a finite channel with closed ends due to low amplitude, high frequency peristaltically driven walls. The presence of sidewalls introduces a return flow in the system. We observe consistency with the asymptotic solutions in the Newtonian case. Cellular flow patterns are observed for Newtonian and Oldroyd-B fluids, and striking differences emerge when viscoelasticity is introduced.