Theoretical analysis of non-linear Joule heating effects on an electroosmotic flow with patterned surface charges

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, Fχ and Fv,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, M_χ, 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.