An exact solution for electroosmosis of non-Newtonian fluids in microchannels

Microfluidics usually processes biofluids which may be treated as non-Newtonian fluids. This study presents an analysis of the electroosmotic flow of power-law fluids in a parallel-plate microchannel. The Cauchy momentum equation is first simplified by incorporation of the electrostatic body force in the electric double layer and the power-law fluid constitutive model. Closed-form exact solutions are then obtained for the electroosmotic velocity profile and the average velocity in terms of hypergeometric functions. The exact solutions not only can recover the generalized Smoluchowski velocity derived in a previous work for the power-law fluids, but also can reproduce several known electroosmotic velocity distributions for power-law fluids with special fluid behavior indices (e.g., n= 1, 1/2, 1/3). Moreover, the effects of two important dimensionless parameters, (i) the fluid behavior index n and (ii) the electrokinetic parameter κH, on the characteristics of electroosmotic flows are examined. In addition, based on the generalized Smoluchowski velocity, we also propose an experimental method for determining the rheological properties of power-law fluids, which has the potential for constructing a micro-rheometer.