Streaming potential and electroviscous effect in heterogeneous microchannels

This communication presents a theoretical analysis of the streaming potential and the electroviscous effect on pressure-driven flow in heterogeneous microchannels. Compact formulae in terms of phenomenological coefficients are derived for the streaming potential and the apparent viscosity ratio in channels with surface charge variations perpendicular and parallel to the applied pressure gradient. In the latter case, the streaming potential per unit liquid flow in a multi-section channel is found to be simply the summation of that in each homogeneous section. The apparent viscosity ratio is a weighted average of each section where the hydrodynamic resistance serves as the weighting factor. The phenomenological coefficients are specified using electrokinetic flow analysis, through which the streaming potential and electroviscous effect in a two-section slit channel are examined. It is found that they both depend on the arrangement of surface heterogeneity in small microchannels. This dependence, however, gets weak in large microchannels, which is consistent with the prediction of thin double layer approximation.