Voltage-step transient problem, useful in electrodiffusion diagnostics of the near-to-wall flow kinematics, is solved for microdispersion liquids that manifest non-linear velocity profile close to the wall. The known solution of this problem for circular probes in a diffusion-layer approximation (DLA), assuming a power-law representation of the velocity profiles, Wein and Kovalevskaya [11], is corrected on the edge effects, important at low Peclet number, i.e. for the small probes and slow flows. A model of the transient process, controlled by convective diffusion at finite Peclet number, is developed here as a generalization of the approach by Wein et al. [9]. The model is applied for treating primary voltage-step transient data of several aqueous high-molecular polysaccharide solutions, displaying strongly non-linear velocity profiles close to the wall (C) 2010 Elsevier Ltd All rights reserved