Dispersion of solute by electrokinetic flow through post arrays and wavy-walled channels

In this work, we simulate electrokinetically driven transport of unretained solute bands in a variety of two-dimensional spatially periodic geometries (post arrays as well as sinuous/varicose channels), in the thin Debye layer limit. Potential flow fields are calculated using either an inverse method or a Schwarz-Christoffel transform, and transport is modeled using a Monte Carlo method in the transformed plane. In this way, spurious "numerical diffusion" transverse to streamlines is completely eliminated, and streamwise numerical diffusion is reduced to arbitrary precision. Late-time longitudinal dispersion coefficients are calculated for Peclet numbers from 0.1 to 3162. In most geometries, a Taylor-Aris-like scaling law for the dispersion coefficient D(L)/D(L0) = 1 + Pe2/alpha underpredicts dispersion when Pe approximately O(alpha1/2) (here D(L0) is the effective axial diffusion coefficient in the periodic geometry). A two-parameter correlation widely used in the porous media literature, D(L)/D(L0) = 1 + Pe(n)/alpha, agrees slightly better, but much better agreement can be obtained using a new quadratic form: D(L)/D(L0) = 1 + Pe/alpha1 + Pe2/alpha2. A quasi-universal relationship for stream-wise dispersion is offered that predicts 96% of the simulation data to within a factor of 2 in all geometries studied. Comparison with previous work shows that in circular post arrays, the dispersion coefficient for electrokinetic flow is a factor of 3-10 less (depending on Pe and relative post size) than for pressure-driven flow.