Effect of variable slip boundary conditions on flows of pressure driven non-Newtonian fluids

In microfluidic devices it has been suggested a scheme for enhancing the mixing of two fluids is to use patterned, slip boundary conditions. This has been shown to induce significant transverse flow for Newtonian fluids S.C. Hendy, M. Jasperse, J. Burnell, Effect of patterned slip on micro- and nanofluidic flows, Phys. Rev. E 72 (2005) 016303]. Here we study the effect of patterned slip on non-Newtonian fluids. Using a power-law model it is shown for shear-thickening fluids patterned slip can induce significant transverse flows comparable in size to those produced for Newtonian fluids. However, for shear-thinning fluids this transverse flow is suppressed. We predict a convenient way to increase the transverse flow for shear-thinning fluids is to use a patterned slip boundary condition coupled to a sinusoidally time-varying pressure gradient. This system is studied using a simple linearized White–Metzner model which has a power-law viscosity function R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, John Wiley & Sons, New York, 1987]. In this case it is shown the two variations combine to produce transverse flow, which can be increased by increasing the frequency of the sinusoidal time-dependent fluctuation.