The evolution partial differential equations describing the transport processes induced by hydrodynamic flow in free-flow electrophoresis (FFE) are solved by the generalized dispersion theory. Our theoretical analysis demonstrates that the central injection of solutes into a relatively fast hydrodynamic flow enables to transport them to the channel outlet well before they are spread through the width of the channel and their migration is negatively affected by a contact with walls. In this case, the axial zone spreading decreases by increasing the linear velocity of hydrodynamic flow. The resulting dependencies of convective and dispersion coefficients on the velocity of flow and parameters of the separation channel show the optimum separation conditions with respect to resolution and analysis time. Due to the unsteady character of transport processes, effective FFE separations can potentially be performed in a microfluidic device in seconds. This is a reasonable time to separate low-molecular mass impurities in the electric field. Thus, a fast and efficient sample cleaning before subsequent analysis by electrospray ionization-mass spectrometry (ESI-MS) or another separation method can be performed.