Fig 4. Peristaltic mixing is generated by a geometric phase.
(a) The minimal geometry of a model for the stomach. A peristaltic wave propagates along the upper and lower boundaries of a closed cavity z w(x, t) = 1+bsin(kx − ωt) of aspect ratio π. (b) Contours of concentration of a passive scalar whose initial spatial distribution at t = 0 is given by a blurred step with δ = 0.1. The temporal evolution of the spatial concentration is obtained integrating the advection–diffusion equation for Pe = 15 × 103. (c) The spatial concentration after 20 peristaltic cycles. (d) The geometric phase of the system. Pink solid lines show some representative trajectories with initial conditions marked by thick black dots.