Asymptotic analysis of non-newtonian fluid flow in a microchannel under a combination of EO and MHD micropumps

Asymptotic solution for the shear stress distributions and velocity profiles of steady electroosmotic (EO) and magnetohydrodynamic (MHD) flows are obtained in a parallel flat plate microchannel. A fully-developed flow is considered and the fluid obeys a constitutive relation based in a simplified Phan-Thien-Tanner model. The effect of the following dimensionless parameters on the fluid flow control is predicted: the viscoelastic parameter and the Hartmann number. The momentum equation, boundary conditions and the constitutive rheological model are combined to formulating a nonlinear differential equation to solve the shear stress, which is expanded in a regular expansion series in powers of small Hartmann numbers. This 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.