Simple analytic model for peristaltic flow and mixing

Peristaltic flows occur when fluid in a channel is driven by periodic, traveling wall deformations, as in industrial peristaltic pumps, urethras, stomachs, and cochleae. Peristaltic flows often vary periodically at every point in space but nonetheless cause net transport and mixing of solutes because of Lagrangian (Stokes) drift. Direct numerical simulation can predict peristaltic flows but is computationally expensive, particularly for determining functional relationships between drive parameters and transport or mixing. We present a simple analytic model of peristaltic flow that expresses flow velocity and drift velocity in terms of deformation speed and amplitude. The model extends beyond prior studies by allowing arbitrary wave forms via Fourier series. To validate our analytic model, we present experiments and simulations; both closely match the analytic model over a range of deformation speeds and amplitudes. We demonstrate the applicability of the model by quantifying variations in the thickness of the reflux region (where fluid drifts opposite the direction of travel of deformations) and by modeling mixing in the cochlea, which is promoted by peristaltic flow.