Numerical and Analytical Investigation of Induced Voltage in the Liquid Pressure-Driven Micro-Flows

In the present study, the interplaying effects of a pressure-driven flow and the induced electric potential, corresponding to the zero net electrical current, have been numerically investigated. The governing equations, which consist of the Poisson equation for the distribution of electric potential, the Nernst-Planck equation for the distribution of charge density, and the modified Navier-Stokes equations for the flow field are solved numerically for an incompressible steady flow of a Newtonian fluid using the finite-volume method. In the presence of electric double layer and the maximum induced voltage condition, the mass flow rate decreases negligibly with respect to the corresponding pure pressure-driven fellow. Surprisingly, the absolute value of induced voltage approaches a maximum value at zeta potentials smaller than 100 mV and then drops. The exponentially increase of the average electric conductivity coefficient beyond 100 mV is accounted for this behavior. Thus the common practice of assuming constant electric conductivity is justified at low zeta potentials.