We present a novel means of transporting molecules in solution by applying a zero-time-average alternating motive force to the molecules, and perturbing the molecular drag coefficient synchronously with the applied force, thus causing a net drift in a direction determined by the phase of the alternating drag perturbation relative to the alternating force. We apply an electrophoretic form of the method to transport and concentrate DNA in a gel, such that all molecules migrate on average away from the nearest electrode and toward a central region. Since an electrode does not occupy this central region, this method presents the possibility of transporting and focusing DNA and other charged molecules in regions free from electrodes and the associated electrochemistry.