Solution of Two-Dimensional Viscous Flow Driven by Motion of Flexible Walls

Abstract

An exact solution of the Navier–Stokes equations for a flow driven by motion of a flexible wall is developed. A simple two-dimensional channel with deforming walls is considered as the domain. The governing equations are linearized for low Reynolds and large Womersley number Newtonian flows. Appropriate boundary conditions for general deformation are decomposed into harmonic excitations in space by Fourier series decomposition. A model of harmonic boundary deformation is considered and the results are compared with computational fluid dynamics predictions. The results of velocity profiles across the channel and the centerline of the channel are in good agreement with CFD solution. The analytical model developed provides quantitative descriptions of the flow field for a wide spectrum of actuating frequency and boundary conditions. The presented model can be used as an effective framework for preliminary design and optimization of displacement micropumps and other miniature applications.