Influence of grafting properties on electrokinetic flow of polyelectrolyte solutions in brush-grafted microchannels*

Brush-grafted channels have the advantage of a tunable and wide range of response to external stimuli, allowing us to use them in various applications. We modeled the electrokinetic flows of Newtonian as well as polyelectrolyte (PE) solutions in PE brush-grafted microchannels, on the basis of the continuum approach. In our model framework, the Poisson-Nernst-Planck equations are explicitly solved for the electrostatic field incorporated with the Alexander-de Gennes model for PE brush-layer and each ion concentration estimated by multi-species ion balance. Accounting for the Brinkman hydrodynamic friction inside the brush-layer, Bird-Carreau constitutive model is applied in the Cauchy momentum equation to describe the PE solution of anionic polyacrylic acid (PAA). This presentation reports in-detail the new results regarding the effects of grafting properties in terms of grafting density and Kuhn segment length. The electrostatic potential increases with increasing grafting density, whereas the surface potential decreases with increasing Kuhn length clearly unlike in the bulk. It is emphasized that the flow velocity decreases with either higher grafting density owing to enhanced PAA chain friction or larger Kuhn length according to higher flow retardation due to chain stiffness. The corresponding viscosity profile inside the channel is also examined with variations of pH and concentration of PAA dispersion.