The present study is concerned with broadening of neutral solute band in electrically driven flow through a straight channel with longitudinally varying zeta potential. The present analysis takes into account effects that are important for submicron channels, namely, variation of the excess conductivity in the diffuse part of the electric Double Layer and the non-uniformity of the velocity profile within the Double Layer. Initially, the combined, electroosmotic and pressure driven flow through a straight channel is addressed for the case of longitudinal variation of zeta potential. Using the obtained distribution of the hydrodynamic velocity, the plate height for a non-electrolyte neutral solute is interrelated with the longitudinal distribution of the electrokinetic potential. Several examples of cross-section geometry and electrolyte composition are discussed.