Transient electroosmotic flow of Maxwell fluids in a slit microchannel with asymmetric zeta potentials

In this work, the transient electroosmotic flow through a slit microchannel formed by two parallel walls with asymmetric zeta potentials is studied. An appropriate combination of the momentum equation together with the rheological Maxwell model leads to a hyperbolic partial differential equation that permits to determine the velocity profile, which is found analytically by the method of separation of variables. Adopting the nondimensionalized version of the governing equations allows us to obtain the following dimensionless parameters that control the fluid flow conditions: the dimensionless relaxation time of the fluid, λ̄1, and the ratio of the zeta potentials for both walls of the microchannel, Rζ. The significance of the former is based on that the fluid flow of Maxwell fluids reaches the steady state just controlled by the value of this parameter. For the Newtonian case, the steady state is directly established depending on values of Rζ. The velocity profiles of the fluid flow exhibit a symmetric or asymmetric shape and a peculiar oscillatory behavior in the transient stage, depending on the competition between the viscous and elastic forces.