Electroosmotic and pressure-driven slip flow of fractional viscoelastic fluids in microchannels

Abstract

This study investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate microchannel under the combined effect of electroosmotic and pressure gradient forcings. Analytical solutions for velocity and potential distributions are derived using the Debye–Hackel linearization, Laplace transform, and residue theorem. Numerical solutions are also provided based on the finite difference method. The process through which the velocity and flow rate attain a steady state is related to the governing groups, including the fractional calculus parameter α, slip coefficient L, Deborah number De, normalized electrokinetic width K and ratio Π of the pressure to electroosmotic driving forces. Results show that an increase in α, De, L or Π increases the time required to reach a steady state. The steady flow rate depends on L and K but is independent of α and De. For the same slip coefficient, increases in α, De or K increase the slip velocity at the wall.