Analytical Solution of Mixed Electroosmotic/Pressure Driven Flow of Viscoelastic Fluids between a Parallel Flat Plates Micro-Channel: The Maxwell Model Using the Oldroyd and Jaumann Time Derivatives

In the present work, an analytical approximate solution of mixed electroosmotic/pressure driven flow of viscoelastic fluids between a parallel plates microchannel is reported. Inserting the Oldroyd, Jaumann, or both time derivatives into the Maxwell model, important differences in the velocity profiles were found. The presence of the shear and normal stresses is only close to the wall. This model can be used as a tool to understand the flow behavior of low viscosity fluids, as most of them experiment on translation, deformation and rotation of the flow. For practical applications, the volumetric flow rate can be controlled with two parameters, namely the gradient pressure and the electrokinetic parameter, once the fluid has been rheologically characterized.