We describe a microfluidic device for on-chip chemical processing, such as staining, and subsequent washing of cells. The paper introduces "separator walls" to increase the on-chip incubation time and to improve the quality of washing. Cells of interest are concentrated into a treatment stream of chemical reagents at the first separator wall for extended on-chip incubation without causing excess contamination at the output due to diffusion of the unreacted treatment chemicals, and then are directed to the washing stream before final collections. The second separator wall further reduces the output contamination from diffusion to the washing stream. With this approach, we demonstrate on-chip leukocyte staining with Rhodamine 6G and washing. The results suggest that other conventional biological and analytical processes could be replaced by the proposed device.