Electrokinetic transport in microchannels with random roughness.

We present a numerical framework to model the electrokinetic transport in microchannels with random roughness. The three-dimensional microstructure of the rough channel is generated by a random generation-growth method with three statistical parameters to control the number density, the total volume fraction, and the anisotropy characteristics of roughness elements. The governing equations for the electrokinetic transport are solved by a high-efficiency lattice Poisson-Boltzmann method in complex geometries. The effects from the geometric characteristics of roughness on the electrokinetic transport in microchannels are therefore modeled and analyzed. For a given total roughness volume fraction, a higher number density leads to a lower fluctuation because of the random factors. The electroosmotic flow rate increases with the roughness number density nearly logarithmically for a given volume fraction of roughness but decreases with the volume fraction for a given roughness number density. When both the volume fraction and the number density of roughness are given, the electroosmotic flow rate is enhanced by the increase of the characteristic length along the external electric field direction but is reduced by that in the direction across the channel. For a given microstructure of the rough microchannel, the electroosmotic flow rate decreases with the Debye length. It is found that the shape resistance of roughness is responsible for the flow rate reduction in the rough channel compared to the smooth channel even for very thin double layers, and hence plays an important role in microchannel electroosmotic flows.