Wall polymer depletion effects on electrokinetic diffusioosmosis of power-law liquids in cylindrical capillaries

Abstract

We investigate electrokinetic diffusioosmotic flows of power-law liquids including the effects of a polymer-depleted Newtonian liquid layer near the wall boundaries in circular cylindrical capillaries. Semi-analytical solutions to the flow velocity distribution and volume flow rate are obtained for conditions involving finite double layer effects on the induced electric field of the electrokinetic diffusioosmosis. Results show that the flow behavior and responses of the electrokinetic diffusioosmotic flow depend not only on the wall zeta potential, diffusivity difference parameter, and flow behavior index, but also on the depletion layer thickness to Debye thickness ratio, the ratio of the flow consistency parameter of the power-law liquid core to the viscosity of the Newtonian depletion layer, as well as the exact numeric values of the flow consistency parameter and the Newtonian viscosity. Including the Newtonian depletion layer gives rise to wiggled-shaped zero flow rate border curves on the zeta potential versus diffusivity difference parameter map when the depletion layer thickness to Debye thickness ratio and the ratio of the flow consistency parameter of the power-law liquid core to the viscosity of the Newtonian depletion layer are close to one. These results are not identified in previous Newtonian or non-Newtonian electrokinetic diffusioosmosis literature and may likely open new possibilities and suggest new ideas in the analysis and design of diffusiophoretic separation and diffusioosmotic flow operations.