Dispersion in Electro-Osmotic Flow Through a Slit Channel With Axial Step Changes of Zeta Potential

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Chiu-On Ng ◽  
Bo Chen
Keyword(s):  
Dispersion Coefficient ◽  
Hydrodynamic Dispersion ◽  
Plate Height ◽  
Cross Sectional ◽  
Ζ Potential ◽  
Osmotic Flow ◽  
Long Wave ◽  
Cross Sectional Dimension ◽  
Limiting Case ◽  
Electro Osmotic Flow

An analytical study is presented in this paper on hydrodynamic dispersion due to steady electro-osmotic flow (EOF) in a slit microchannel with longitudinal step changes of ζ potential. The channel wall is periodically patterned with alternating stripes of distinct ζ potentials. Existing studies in the literature have considered dispersion in EOF with axial nonuniformity of ζ potential only in the limiting case where the length scale for longitudinal variation is much longer than the cross-sectional dimension of the channel. Hence, the existing theories on EOF dispersion subject to nonuniform charge distributions are all based on the lubrication approximation, by which cross-sectional mixing is ignored. In the present study, the general case where the length of one periodic unit of wall pattern (which involves a step change of ζ potential) is comparable with the channel height, as well as the long-wave limiting case, are investigated. The problem for the hydrodynamic dispersion coefficient is solved numerically in the general case, and analytically in the long-wave lubrication limit. The dispersion coefficient and the plate height are found to have strong, or even nonmonotonic, dependence on the controlling parameters, including the period length of the wall pattern, the area fraction of the EOF-suppressing region, the Debye parameter, the Péclet number, and the ratio of the two ζ potentials.

Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential

2018 ◽  
Vol 839 ◽  
pp. 348-386 ◽  
Author(s):  
J. C. Arcos ◽  
F. Méndez ◽  
E. G. Bautista ◽  
O. Bautista
Keyword(s):  
Dispersion Coefficient ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Debye Length ◽  
Rheological Behaviour ◽  
Governing Equations ◽  
Regular Perturbation ◽  
Axial Distribution ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

The dispersion coefficient of a passive solute in a steady-state pure electro-osmotic flow (EOF) of a viscoelastic liquid, whose rheological behaviour follows the simplified Phan-Thien–Tanner (sPTT) model, along a parallel flat plate microchannel, is studied. The walls of the microchannel are assumed to have modulated and low $\unicode[STIX]{x1D701}$ potentials, which vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient was solved using the lubrication approximation theory (LAT). The solution of the electric potential is based on the Debye–Hückel approximation for a symmetric $(z:z)$ electrolyte. The viscoelasticity of the fluid is observed to notably amplify the axial distribution of the effective dispersion coefficients due to the variation in the $\unicode[STIX]{x1D701}$ potentials of the walls. The problem was formulated for two cases: when the Debye layer thickness (EDL) was on the order of unity (thick EDL) and in the limit where the thickness of the EDL was very small compared with the height of the microchannel (thin EDL limit). Due to the coupling between the nonlinear governing equations and the sPTT fluid model, they were replaced by their approximate linearized forms and solved in the limit of $\unicode[STIX]{x1D700}\ll 1$ using the regular perturbation technique. Here $\unicode[STIX]{x1D700}$ is the amplitude of the sinusoidal function of the $\unicode[STIX]{x1D701}$ potentials. Additionally, the numerical solution of the simplified governing equations was also obtained for $\unicode[STIX]{x1D700}=O(1)$ and compared with the approximate solution, showing excellent agreement for $0\leqslant \unicode[STIX]{x1D700}\leqslant 0.3$. Note that the dispersion coefficient primarily depends on the Deborah number, on the ratio of the half-height of the microchannel to the Debye length, and on the assumed variation in the $\unicode[STIX]{x1D701}$ potentials of the walls.

Exact Solution of AC Electro-Osmotic Flow in a Microannulus

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Ali Jabari Moghadam
Keyword(s):  
Exact Solution ◽  
Double Layer ◽  
Electric Double Layer ◽  
Maximum Velocity ◽  
Velocity Profiles ◽  
Radius Ratio ◽  
Dimensionless Frequency ◽  
Ζ Potential ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

The time-periodic electro-osmotic flow in a microannulus is investigated based on the linearized Poisson–Boltzmann equation. An exact solution of the velocity distribution is obtained by using the Green's function approach. The influences of the geometric radius ratio, the wall ζ potential ratio, the electrokinetic radius, and the dimensionless frequency on velocity profiles are presented. Variations of the geometric radius ratio (between zero and one) can lead to quite different flow behaviors. The wall ζ potential ratio affects the magnitude and direction of the velocity profiles within the electric double layer near the two walls of a microannulus. Depending on the frequency and the geometric radius ratio, the walls identically and/or oppositely charged, both may result in the two-opposite-direction flow in the annulus. For high frequency, the electro-osmotic velocity variations are restricted mainly within a thin layer near the two cylindrical walls. Increasing the electrokinetic radius leads to decrease the electric double layer thickness as well as the maximum velocity near the walls.

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