An apparatus and method of using the same are provided for generating a gradient of particles within a microfluidic device. The microfluidic device includes a channel having an input and an output. The channel is filled with a predetermined fluid. Thereafter, particles from a source pass through a porous membrane into the input of the channel. A second membrane is provided adjacent the output of the channel to minimize convection therein. A sink communicates with the output of the channel. The source/sink combination creates a pseudo-steady state in the channel wherein the concentration of particles at a point does not vary dramatically with time.