We study solute transport in a microfluidic channel, where the walls hold an array of tilted rigid nanopillars. By solving numerically the flow equations in the channel, we show that a combination of hydrodynamic effects with excluded volume interactions between the solute particles and the pillars leads to a hydrodynamic lift effect, which varies with the particle size, and depends in a strongly nonlinear fashion on the flow rate. We show that the lift force can be sufficiently strong to drive the solute accumulation or removal from the pillar region and can be switched to the opposite direction by variation of the shear rate or driving pressure. We also demonstrate that the nanopillar array can be used to selectively attract particles of certain size and enhance solute trapping at the surface.