The contribution from electroosomosis is much greater than the contribution from electrophoresis (mainly because of the excess positive charge on the diffusive layer that drags the entire buffer solution (positive, negative and neutral ions) towards the cathode. In other words, this electroosmosis is originated mainly because of the nature of the negative charges on the inner wall of the capillary, which then acts accordingly to the applied voltage. For example, if no high voltage is applied across the capillary, only a double layer will form which is still rich with excess positive charge in the diffusive part to compensate the excess negative charge.
You can't have the electrophoretic mobility without also having the electroosmotic flow. As soon as you apply the electric field to the capillary, you get both.
