The disclosure relates to an apparatus for segregating particles on the basis of their ability to flow through a stepped passageway. At least some of the particles are unable to pass through a narrower passageway bounded by a segregating step, resulting in segregation of the particles. The breadth of the leading edge of at least one step of the apparatus is significantly greater than the overall width of the passageway in which the step occurs, permitting high and rapid sample throughput. The apparatus and methods described herein can be used to segregate particles of a wide variety of types. By way of example, they can be used to segregate circulating tumor cells from a human blood sample.