Slip hydrodynamics of combined electroosmotic and pressure driven flows of power law fluids through narrow confinements

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.