Boundary streaming with Navier boundary condition.dvi

In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness δ is so small that some non-negligible slip may occur at the fluid-solid interface. The classical problem of steady acoustic streaming over a flat boundary is therefore revisited to include the effect of slip modelled using the Navier boundary condition u|y=0 = Ls∂yu|y=0, where u is the velocity tangent to the boundary y = 0, and the parameter Ls is the slip length. A general expression is obtained for the streaming velocity outside the boundary layer as a function of the dimensionless parameter Ls/δ. Particularising to travelling and standing waves shows that the boundary slip respectively increases and decreases the streaming velocity. PACS numbers: 47.35.Rs, 43.25.+y, 47.61.Ne