Electroosmosis with step changes in zeta potential in microchannels

Abstract

This article presents an analytical solution for two-dimensional fluid flow in a rectangular microchannel in the vicinity of a step change in the zeta (f) potential. The stream function is determined from the creeping flow approximation to the NavierStokes equations assuming a fixed volumetric axial flow, a constant electric field, and thin symmetric double layers. The resulting biharmonic equation is solved using a double-sided Laplace transformation, which is then inverted by Heaviside expansion. The resulting series solution provides closed-form expressions for the velocity and pressure fields that help explain how the recirculating flows generated by an abrupt change in the surface potential may contribute both locally and globally to the hydrodynamic dispersion in straight microchannels.

Analytical Solution of Time-Periodic Electroosmotic Flow through Cylindrical Microchannel with Non-Uniform Surface Potential

“…For example, Ajdari [17] theoretically showed that a surface with a sinusoidal charge can create vorticities within the bulk flow. Vortices formation within the bulk flow was also shown by Horiuchi et al [18] for a step change in the surface charge in a DC EOF. Through a numerical investigation, Erickson and Li [19] showed that surface heterogeneity increases the mixing efficiency and reduces the required mixing length.…”

Transient electroosmotic flow of Maxwell fluids in a slit microchannel with asymmetric zeta potentials

“…On the other hand, in order to induce recirculating flows, an analytical solution for two-dimensional fluid flow in a rectangular microchannel in the vicinity of a step change in the zeta potential was presented by Horiuchi et al [30]. Therefore, the technique related to change in surface or zeta potentials of the walls, modifies electrical potential distribution and thus the electrical body force in the flow field, allows significant effects on the flow characteristics into microchannel as various types of velocity profiles, variable flow rates and inverse flows [31][32][33].…”

Taylor dispersion in equilibrium gradient focusing at steady state

“…It is no longer separable, not even by Ramkrishna‐Amundson decomposition , and not even if the axial diffusion term is ignored. While the model is linear and could be attacked using two‐sided Laplace transforms in ζ or Hankel transforms in η , these are very difficult both to apply toward a solution in transformed‐variable space and, later, to invert the solution if that is needed to obtain moments. However, by applying the method of moments serially as demonstrated by Aris , analytic forms for the mean peak position and variance can be used to determine the dispersion coefficient.…”

“…(27) tells us that mass is conserved, the first central moment tells us that the time required to transit 99% of the distance from L to zero is about 5/(F 1 ), and the second central moment tells us that the time required for the dispersion coefficient to reach 99% of its final value is about half that of the transit…”