Lagrangian transport by peristalsis in a closed cavity

In the context of fluid mixing in microelectromechanical systems, Lagrangian mass transport induced by peristaltic waves traveling on the boundaries of a two-dimensional rectangular closed channel is studied analytically. Based on the Lagrangian description, an asymptotic analysis is performed to generate explicit expressions for the leading-order oscillatory as well as the higher-order time-mean mass transport velocities as functions of the wave properties. For small steady-streaming Reynolds number, we have revisited the problem studied previously in the literature, but with all the results fully presented in the Lagrangian sense.