Thermodiffusive effect on the local Debye-length in an electroosmotic flow of a viscoelastic fluid in a slit microchannel

This work theoretically studies the influence of the thermodiffusive effect on the local Debye length thickness in a purely electroosmotic flow in a parallel flat plate microchannel. An imposed electric field between the ends of the microchannel interacts with an ionized viscoelastic fluid causing Joule heating, which induces a temperature gradients along the microchannel, affecting the fluid's physical properties, and in a notable manner, the ionic distribution into the electric double layer (EDL), resulting in thermodiffusion. Consequently, an induced pressure field counterbalances the axial variation of the plug-like electroosmotic velocity to maintain the fluid mass continuity. Also, the ionic distribution and electrical potential based on the non-isothermal Poisson-Boltzmann equation are modified. To estimate the local Debye length thickness, the coupled set of the Poisson-Boltzmann, momentum, and energy equations are solved numerically in the limit of the lubrication approximation theory (LAT). Our results indicate that the thermodiffusion has an important effect on the thickness of the local Debye-length, particularly in the warm zone of the fluid. Besides, the ionic response to thermal fields is given by a positive Soret coefficient, which indicates that the ionic particles move from warm to cold regions in the fluid, giving place to a thinner Debye length and lower ionic concentration around the warming zone; this migration of ions confirms that the dimensionless mass-flow rate is affected with the Soret coefficient compared with the non-thermodiffusion case.