Power-law electrokinetic behavior as a direct probe of effective surface viscosity

An exact solution to the Poisson-Boltzmann and Stokes equations is derived to describe the electric double layer with inhomogeneous dielectric and viscosity profiles in a lateral electric field. In the limit of strongly charged surfaces and low salinity, the electrokinetic flow magnitude follows a power law as a function of the surface charge density. Remarkably, the power-law exponent is determined by the interfacial dielectric constant and viscosity, the latter of which has eluded experimental determination. Our approach provides a novel method to extract the effective interfacial viscosity from standard electrokinetic experiments. We find good agreement between our theory and experimental data.