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In this work the purely electro-osmotic flow of a viscoelastic liquid, which obeys the simplified Phan-Thien–Tanner (sPTT) constitutive equation, is solved numerically and asymptotically by using the lubrication approximation. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, relaxation time and electrical conductivity of the liquid are assumed to be temperature-dependent. Owing to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the microchannel, altering the electric potential and flow fields. A consequence of the above is the appearance of an induced pressure gradient along the microchannel, which in turn modifies the normal plug-like electro-osmotic velocity profiles. In addition, it is pointed out that, depending on the fluid rheology and the used values of the dimensionless parameters, the velocity, temperature and pressure profiles in the fluid are substantially modified. Also, the finite thermal conductivity of the microchannel wall was considered in the analysis. The dimensionless temperature profiles in the fluid and the microchannel wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled momentum, thermal energy and potential electric equations are examined in detail. A comparison between the numerical predictions and the asymptotic solutions was made, and reasonable agreement was found.

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In this work, non-linear Joule heating effects induced on an electroosmotic flow with patterned surface charges driven inside of a slit microchannel are analyzed. Here, the movement of the fluid is controlled by placing electro-thermal forces, which are induced through an imposed longitudinal electric field, E0, and the wall electric potential generated by electrodes inserted along the surface of the microchannel wall. For this analysis, the physical properties of the fluid are included as known functions, which depend on the temperature. Therefore, in order to determine the flow, temperature, and electric potential fields together with their simultaneous interactions, the governing equations have to be solved in a coupled manner. For a strong Joule heating, the non-isothermal flow regime reveals that with the presence of thermal gradients, the local electro-thermal and viscous forces, F¯χ and F¯v,χ, are affected in a sensible manner, which results in changes in the flow pattern causing the interruption or intensification of recirculations along the microchannel. In parallel, increments of flow rate or pressure are observed due to electro-thermal interactions associated with the mentioned thermal dependence of the physical properties; here the corresponding effects induced in those regions where thermal gradients are located prevail. The present analytical formulation allows determining the local electro-thermal rotational moment, Mχ, which clearly reveals the fundamental importance of when thermal gradients interact with the electric and flow fields. Thus, the local electro-thermal rotational moment can be used to interpret alterations in the flow pattern linked to the temperature rise.