A Peristaltic Meso-Scale Mixer

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Abstract
We consider incompressible, viscous fluid confined in a rectangular cavity. One or more of the cavity walls are made of a thin membrane. Traveling waves are transmitted in a cavity’s wall and induce peristaltic motion. The induced velocity profiles are determined analytically for small amplitude waves (ε) and numerically for waves of arbitrary amplitude. The analysis consists of a perturbation expansion in terms of the wave amplitude (ε). Solutions for large amplitude oscillations are obtained through the use of a finite element code that employs a moving grid. The effect of the peristaltic motion on the stretching and deformation of material lines is discussed. The study is relevant to the analysis and design of micro and meso-scale mixers and stirrers.

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