Analysis of a viscoelastic fluid flow in a microchannel with asymmetric zeta potentials under a combination of electroosmotic and magnetohydrodynamic driven forces

In this paper an analytical solution to describe the velocity profiles and flow rate of combined electroosmotic and magnetohydrodynamic flows in a microchannel is obtained. A fully-developed flow is considered and the fluid obeys a constitutive relation based in a simplified Phan-Thien-Tanner model. Asymmetric boundary conditions with different zeta potentials at the walls are specified to provide a perturbation to the fluid flow. The effect of the dimensionless parameters on the flow field as viscoelastic parameter, the Hartmann number, the ratio of applied electric fields on the fluid field and the ratio of the wall zeta potentials is predicted. The analysis permits to establish the conditions for which the flow rate is increased respect to a purely electroosmotic flow, therefore, in the limit of small Hartmann numbers and low electrical conductivity in the buffer solution correspond to the range where the electric and magnetic effects can be used to move a charged solution in the flow control and sample handling in biomedical and chemical analysis. In addition, we determine the conditions that must be met to prevent the undesirable lateral electroosmotic flow, which is present in this kind of applications. Finally, the combined effect of asymmetric zeta potentials and electro-magnetic fields on viscoelastic fluid flows in microchannels is discussed as future application of mixed in microfluidics devices.