Separating particles from the liquid in which they are suspended is often an important step in processing multiphase materials such as suspensions and emulsions. We describe a new method to separate neutrally buoyant particles from viscous liquids. The method is based on the low Reynolds number motion of freely-suspended particles at bifurcations -points where a tube or channel splits into multiple tubes. We show experimentally that the partitioning of particles at a bifurcation differs from the partitioning of the suspending fluid. The effects of particle size, particle volume fraction, and shape of the bifurcation on particle partitioning are examined. Furthermore, we demonstrate that when tubes and bifurcations are arranged in certain ways, the particles can take preferentialpaths through the network and can be separated from the liquid in which they are suspended. The data show that the particle separation can be enhanced in relatively simple networks consisting of just a few interconnected channels.