We study mixed brushes under shear flow by molecular dynamics simulation with an explicit solvent. The primary brush is formed by chemically grafting polymers to a solid substrate, the secondary brush is comprised of shorter, physically end-adsorbed molecules that can laterally diffuse. By virtue of the immobility of the grafted end-points of the primary brush, its individual macromolecules perform a cyclic motion. If there is a well defined solvent-brush interface, this cyclic motion of the primary brush molecules will collectively result in the reversal of the flow inside of the primary brush. This backflow, linear in the shear rate, gives rise to the transport of the shorter, physically end-adsorbed molecules in the opposite direction of the solvent flow. We discuss which conditions are necessary to observe this counter-intuitive phenomenon. Comparing Poiseuille and Couette flow we demonstrate that the magnitude of the local shear rate at the brush-liquid interface dictates the cyclic motion and concomitant inversion of transport but that these universal effects are independent of the type of driving the flow.