Dispersion in electroosmotic flow generated by oscillatory electric field interacting with oscillatory wall potentials

Abstract

An analytical study is presented in this article on the dispersion of a neutral solute released in an oscillatory electroosmotic flow (EOF) through a two-dimensional microchannel. The flow is driven by the nonlinear interaction between oscillatory axial electric field and oscillatory wall potentials. These fields have the same oscillation frequency, but with disparate phases. An asymptotic method of averaging is employed to derive the analytical expressions for the steady-flow-induced and oscillatory-flow-induced components of the dispersion coefficient. Dispersion coefficients are functions of various parameters representing the effects of electric double-layer thickness (Debye length), oscillation parameter, and phases of the oscillating fields. The time-harmonic interaction between the wall potentials and electric field generates steady as well as time-oscillatory components of electroosmotic flow, each of which will contribute to a steady component of the dispersion coefficient. It is found that, for a thin electric double layer, the phases of the oscillating wall potentials will play an important role in determining the magnitude of the dispersion coefficient. When both phases are zero (i.e., full synchronization of the wall potentials with the electric field), the flow is nearly a plug flow leading to very small dispersion. When one phase is zero and the other phase is p, the flow will be sheared to the largest possible extent at the center of the channel, and such a sharp velocity gradient will lead to the maximum possible dispersion coefficient.

On the time development of dispersion in electroosmotic flow through a rectangular channel

“…For numerical discussions, the range of the dimensionless Debye-Hückel parameter is taken as 1 <k 100. These values are frequently reported in the literature [18][19][20] for typical scenarios of electroosmotic flows. Figure 2a shows the dimensionless convection coefficient −K 1 = u m /U, given in Eq.…”

Dispersion in oscillatory electro-osmotic flow through a parallel-plate channel with kinetic sorptive exchange at walls

“…The derived result is the same as the dispersion coefficient due to the interaction of the oscillatory electric field with the steady component of the wall potentials presented in Paul and Ng [14] .…”

“…where e is the electron charge, z is the valence of the co-and counter-ions in the carrier liquid, 0 c is the ion concentration far from the charged walls, B R is the Boltzmann constant, T is the absolute temperature, and ψ is the electric potential. Here, for the static Boltzmann distribution to be valid, the flow frequency shall be limited to around 1 MHz to avoid EDL relaxation effects [14] . The electric potential can be expressed by the following Poisson equation, where η is the permittivity of the liquid medium.…”

“…When at equilibrium, s C can be related to C by, α = C C s (17) We now introduce the homogenization approach with the multiple-scale perturbation analysis. For EOFs in micro-channels, the assumptions for the homogenization approach to be applicable are typically satisfied [14] . Adopting three sharply distinct time scales 0 t , 1 t and 2 t to represent the three different transport processes, i.e.…”

“…Kuo et al [13] studied a directional EOF due to a nonlinear interaction between oscillatory axial electrical fields and oscillatory wall potential. Paul and Ng [14] further investigated the dispersion behavior in such kind of flows. They found that the phase of wall potential plays an important role in determining the dispersion coefficient magnitude.…”