Effect of finite Debye layer in electromigration Taylor-Aris dispersion of charged species in a thin channel

We investigate the effect of Debye layer thickness and the surface electro-chemical interactions in electromigration Taylor-Aris dispersion of charged species dissolved in a Newtonian fluid. The local electroneutrality condition has been extensively used in previous studies to decipher the role of electromigration dispersion within charged capillaries with infinitely thin Debye layers. However, in most cases of experimental interest, finitely thin Debye layers are better suited than the condition of infinitely thin Debye layers. This problem is circumvented by invoking the global electroneutrality condition and the Kohlrausch function to arrive at an expression for the local electric field, which is found to depend upon the background concentration of the negative ion, surface charge density, and the channel height. The fluid flow in the 2D channel is modeled by using lubrication approximation in the limit of the small channel aspect ratio. Time scale analysis is used to study the Nernst-Planck equation for concentration evolution within the channel coupled with the appropriate wall reaction kinetics. With the aid of the above computations, we arrive at an expression for Taylor Aris dispersion of the charged species with non-linear dependence of the advection and the dispersion terms on the species concentration. Finally, the reduced equation is used for numerical computations and to investigate the role of the various parameters in the dispersion of the species.