Numerical Simulations of Peristaltic Mixing

Abstract

Numerical simulations of two-dimensional flow and species transport in a peristaltically driven closed mixer are performed as a function of the Reynolds number (Re⩽6288) and the normalized traveling wave amplitude (ε⩽0.3) at low to moderate Schmidt number (Sc⩽10) conditions. The mixer consists of a rectangular box with a traveling wave motion induced on its bottom surface. Flow and species mixing are produced by the surface motion. The numerical algorithm, based on an arbitrary Lagrangian–Eulerian spectral element formulation, is verified using the asymptotic solutions for small wave amplitude cases. Kinematics of large-deformation conditions are studied as a function of the Reynolds number. Species mixing is simulated at various Re and Sc conditions. Mixing index inverse (M−1) is utilized to characterize the mixing efficiency, where M−1∝exp(Pe−αt) is observed as the long-time behavior. Simulation data are utilized to determine the exponent α at various Re and Sc conditions. For all simulations, 0.28⩽α⩽0.35, typical of partially chaotic flows, have been observed. The effect of flow kinematics and species diffusion on mixing is interpreted.