Influence of slip wall effect on a non-isothermal electro-osmotic flow of a viscoelastic fluid

We present an analytical model that predicts the influence of Joule heating on the slip velocity in an electro-osmotic flow (EOF) of viscoelastic fluids. The viscoelasticity of the fluid is taken into account by employing the simplified Phan-Thien and Tanner constitutive model (sPTT). The Joule heating induces temperature gradients along the microchannel making properties non-uniform and hence alters the electric potential and the flow field. In consequence, the slip velocity and the velocity gradient on the microchannel surface are drastically modified in comparison with the case of uniform properties. Using the well-known lubrication theory, the momentum equations together with the energy, Poisson and Ohmic current conservation equations are considerably simplified. The dimensionless mathematical model is solved by using a regular perturbation technique, which is compared against a numerical solution. The results show that using hydrophobic microchannels, for the used values of the parameters involved in this analysis, the volumetric flow rate through microchannels can be massively amplified in about 400%, in comparison with the case of non-slipping surfaces. In addition, by using hydrophobic microchannels, the maximum temperature in the microchannel can be substantially reduced.