Linear stability of an electroosmotic pressure-driven flow in a viscoelastic sub-diffusive channel

The linear stability analysis of a viscoelastic sub-diffusive fluid for a plane Poiseuille flow configuration subjected to an external electric field is reported. The viscoelastic fluid is modeled using the fractional upper-convected Maxwell model. The electric field induces electroosmotic forces due to the presence of an electric double layer near the channel walls. Analytical solution of the steady base flow is obtained under the Debye–Hückel approximation. The governing equations, incorporating both hydrodynamic and electrokinetic effects, are linearized about the steady base state and solved using the compound matrix method. Analysis reveals a fascinating interplay of the sub-diffusive exponent, elasticity, and the applied electric field, collectively impacting the flow stability. The present results provide new insights into the electrohydrodynamic behavior of viscoelastic fluids and have direct relevance to microfluidic applications involving electrically driven polymeric flows.