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Transient electroosmotic flow of general Maxwell fluids through a slit microchannel. (English) Zbl 1302.76011
Summary: Using the Laplace transform method, semi-analytical solutions are presented for transient electroosmotic flow of Maxwell fluids between micro-parallel plates. The solution involves solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the Maxwell constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Maxwell fluids and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. In addition, the Maxwell stress is incorporated to describe the boundary condition at the interface. The velocity expressions of these two layers were obtained respectively. By numerical computations of inverse Laplace transform, the influences of viscosity ratio \(\mu\), density ratio \(\rho\), dielectric constant ratio \(\epsilon\) of layer II to layer I, relaxation time \(\bar\lambda_1\), interface charge density jump \(Q\), and interface zeta potential difference \(\Delta\bar\psi\) on transient velocity amplitude are presented.

76A05 Non-Newtonian fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
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