Electrokinetic flow of non-Newtonian fluid through a micro-channel with deformable surfaces: An analytical approach

The study of the electroosmotic flow in deformable microchannels is crucial for developing a deep insight into the hydrodynamics of physiological flows. The effectiveness of these microchannels is determined by their load-carrying capacity, which specifies the highest load the deformable wall can handle. In this study, the intricate coupling between fluid flow and wall deformation is analyzed under the influence of an externally applied electric field. The microchannel walls are assumed to be elastic in response to the deformation, and the non-Newtonian behavior of the fluid is governed by the simplified Phan-Thein-Tanner model. The hydrodynamics of ion and fluid transport are studied through the Poisson-Nernst-Planck-based Navier-Stokes model, coupled with the system of forces endured by both induced and external electric potential. The resulting coupled nonlinear equations are solved to capture the dynamics of wall deformations using continuum mean-field theories in the solid-liquid coupled system following the conservation principle. The electroosmotic flow deals with the lubrication approximation theory in the limit of the small channel aspect ratio. The result is validated with the pure electroosmotic flow of viscoelastic fluid for undeformed channels and also for the Newtonian fluid with deformable channels. Additionally, the coupling effect between wall deformation and electrokinetic transport modifies the quantitative response of wall relaxation dynamics and flow within the channel, which can provide a significant contribution to comprehending electrokinetic flow through charged viscoelastic media for microfluidic fabrications.