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

• Published in: Journal of non-Newtonian fluid mechanics Vol. 166; no. 17; pp. 1076 - 1079
• Main Authors: Zhao, Cunlu, Yang, Chun
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 18.09.2011; Elsevier
• Subjects: Applied fluid mechanics; Computational fluid dynamics; Cross-disciplinary physics: materials science; rheology; Electroosmotic flows; Exact sciences and technology; Exact solutions; Fluid dynamics; Fluid flow; Fluidics; Fluids; Fundamental areas of phenomenology (including applications); Generalized Smoluchowski velocity; Mathematical analysis; Mathematical models; Micro-rheometry; Microchannels; Microfluidics; Non Newtonian fluids; Non-newtonian fluid flows; Non-Newtonian power-law fluids; Physics; Rheological measurements; Rheology; Techniques and apparatus; Generalized Smoluchowski velocity; Micro-rheometry; Microfluidics; Non-Newtonian power-law fluids; Electroosmotic flows; Velocity distribution; Non-Newtonian fluids; Exact solution; Power law fluid; Microchannel; Electroosmosis; Modelling; Microstructure; Rheometer; Parallel plate; Rheological properties
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2011.05.006

► We present an exact solution for electroosmosis of power-law fluids. ► The fluid rheology substantially affects the velocity profiles. ► We propose a potential method for constructing micro-rheometers. 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 κ H , 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.