We describe a microfluidic technique for separation of particles and cells and a device that employs this technique to separate white blood cells (WBC) from whole human blood. The separation is performed in cross-flow in an array of microchannels with a deep main channel and large number of orthogonal, shallow side channels. As a suspension of particles advances through the main channel, a perfusion flow through the side channels gradually exchanges the medium of the suspension and washes away particles that are sufficiently small to enter the shallow side channels. The microfluidic device is tested with a suspension of polystyrene beads and is shown to efficaciously exchange the carrier medium while retaining all beads. In tests with whole human blood, the device is shown to reduce the content of red blood cells (RBC) by a factor of approximately 4000 with retention of 98% of WBCs. The ratio between WBCs and RBCs reached at an outlet of the device is 2.4 on average. The device is made of a single cast of poly(dimethylsiloxane) sealed with a cover glass and is simple to fabricate. The proposed technique of separation by perfusion in continuous cross-flow could be used to enrich rare populations of cells based on differences in size, shape, and deformability.