Analytical Study of Nonlinear Electroosmotic Flow in Xanthan Gum Solutions

Introducing rheology, such as shear thinning and elasticity, into Newtonian buffers has been demonstrated to enhance the performance of electrokinetic microfluidic devices. Understanding electroosmotic flow in non-Newtonian fluids through microchannels is essential for device design and operation. We present in this work an analytical model that incorporates a near-wall polymer depletion layer (PDL) to investigate the experimentally measured electroosmotic velocity in xanthan gum (XG) solutions. The derived analytical solution for the electroosmotic velocity has two components stemming from the Newtonian fluid in the PDL and the power-law fluid in the bulk, respectively, with the PDL thickness being the only fitting parameter. We also derived an analytical formula for the PDL thickness to match the experimental electroosmotic velocity. Furthermore, we develop an analytical formula for the effective electric field exponent of the Newtonian and non-Newtonian electroosmotic velocity components. The predictions of this formula in the intermediate-field region closely match the experimentally obtained nonlinear electric field index of the electroosmotic velocity in XG solutions with varying polymer and buffer concentrations.