A microfluidic device for increasing convective clearance of particles from a fluid is provided. A network of first channels can be separated from a network of second channels by a first membrane. The network of first channels can also be separated from a network of third channels by a second membrane. Fluid containing an analyte can be introduced in the network of first channels. Infusate can be introduced into the network of second channels, and waste-collecting fluid can be introduced into the network of third channels. A pressure gradient can be applied in a direction perpendicular to the direction of fluid flow in the network of first channels, such that the analyte is transported from the network of first channels into the network of third channels through the second membrane.