Peristaltically induced motion in a closed cavity with two vibrating walls

We consider incompressible, viscous fluid confined in a rectangular cavity. Both the bottom and top walls are made of thin membranes. Traveling waves with the same amplitude and frequency but opposite phase are transmitted in these membranes and induce peristaltic motion in the fluid. The induced velocity profiles are determined analytically for small-amplitude waves (ε) and numerically for waves of any amplitude. The analysis consists of a perturbation expansion in terms of the wave amplitude (ε) up to O(ε²). Solutions for large-amplitude oscillations are obtained through the use of a finite element code that employs a moving grid. The numerical code is verified by critically comparing the simulations' predictions with analytical results.