Fluid mixing induced by vibrating walls

Recent progress in micro-fluid dynamics has identified an increased demand for efficient mixing of highly viscous fluids in small channels and cavities. One way to do this is through the steady streaming generated by the vibration of solid boundaries. In this paper we investigate the mixing properties of such streaming flows in an infinite channel. A Newtonian fluid is confined within flexible walls with transverse motion in the form of standing waves of small amplitude. The velocity field is determined using a perturbation approach with the slope of the wall as a small parameter [Phys. Fluids 16 (2004) 1822]. Streaming occurs at second order with the formation of cellular flow patterns in the channel. The Lagrangian velocities were found to mimic the Eulerian except for flows at large channel half-widths and low frequencies. Most effective mixing is observed for flows at channel half-widths of similar, or lower, order than the vibratory wavelength and for sufficiently high frequencies.