Electroosmotic Flow in Microchannel with Pressure-Dependent Slip Boundary Condition

The study of microsystems that considers different flow patterns with arbitrary geometrical configurations for microchannel design permits us to understand that the combined influence of surface and non-isothermal effects occupies a privileged place in predicting electroosmotic behavior. For this reason, in this work, we develop a theoretical analysis based on a perturbative scheme that permits us to predict the hydrodynamic effects generated in an electroosmotic flow when the slip condition on the walls of the microchannel is taken as a function of pressure, together with the Joule heating effect, and when these effects operate together to determine the fluid dynamics. For this purpose, when the governing equations are written in dimensionless form, we can identify some relevant dimensionless parameters associated with the previous condition. In this manner, the dimensionless volumetric flow rate that occurs in the microchannel is controlled by the combined influence of the previous effects, causing the volumetric flow rate to increase or decrease depending on the assumed values of the combined influence of these effects.