Approximate Solution for Electroosmotic Flow of Power-Law Fluids in a Planar Microchannel with Asymmetric Electrochemical Boundary Conditions.

Electroosmotic flow (EOF) is widely used in microfluidic systems and chemical analysis. It is driven by an electric force inside microchannel with highly charged boundary conditions. In practical applications, electrochemical boundary conditions are often inhomogeneous because different materials as walls are commonly utilized in routine fabrication methods. In the present study, we focus on the analytic solutions of the EOF generated in a planar microchannel with asymmetric electrochemical boundary conditions for non-Newtonian fluids. The velocity profile and flow rate are approximated by employing the power-law model of fluids in the Cauchy momentum equation. The hydrodynamic features of the EOF under asymmetric zeta potentials are scrutinized as a function of the fluid behavior index of the power-law fluid, thickness of Debye length, and zeta potential ratios between planes. The approximate solutions of the power-law model are comparable to the numerically obtained solutions when the Debye length is small and the fluid behavior index is close to unity. This study provides insights into the electrical control of non-Newtonian fluids, such as biological materials of blood, saliva, and DNA solution, in lab-on-a-chip devices.

An Exact Solution for Power-Law Fluids in a Slit Microchannel with Different Zeta Potentials under Electroosmotic Forces.

Electroosmotic flow (EOF) is one of the most important techniques in a microfluidic system. Many microfluidic devices are made from a combination of different materials, and thus asymmetric electrochemical boundary conditions should be applied for the reasonable analysis of the EOF. In this study, the EOF of power-law fluids in a slit microchannel with different zeta potentials at the top and bottom walls are studied analytically. The flow is assumed to be steady, fully developed, and unidirectional with no applied pressure. The continuity equation, the Cauchy momentum equation, and the linearized Poisson-Boltzmann equation are solved for the velocity field. The exact solutions of the velocity distribution are obtained in terms of the Appell's first hypergeometric functions. The velocity distributions are investigated and discussed as a function of the fluid behavior index, Debye length, and the difference in the zeta potential between the top and bottom.