Electrokinetically-driven Viscoelastic Fluid Flow in a Microchannel with Hydrodynamic Slipwalls

In this work we conduct a numerical analysis of a purely electro-osmotic flow (EOF) of simplified Phan-ThienTanner (sPTT) fluids in a slit microchannel with hydrodynamic slip at the walls. We use the Debye-H¨uckel linearization together with the lubrication approximation in order to determine the flow and temperature fields in the microchannel. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, the relaxation time and electrical conductivity of the fluid are assumed temperature-dependent. The variation of the physical properties of the fluid, as a consequence of temperature gradients along the microchannel, causes that the flow field does not reach the fully developed hydrodynamic condition, and therefore the velocity gradients at the interface fluid-solid will change along the microchannel, which in turn yields variable slip velocity. In addition, it is pointed out that, depending on the slip condition and the used values of the dimensionless parameters associated with the rheology of the fluid, the velocity, temperature and pressure profiles in the fluid are substantially modified. The results show that the slippage over microchannel walls modifies in a notable manner the flow, temperature and electric fields.