The fractionation of small particles in a liquid based on their size in a micropost array by deterministic lateral displacement was recently demonstrated with unprecedented resolution (L. R. Huang, E. C. Cox, R. H. Austin and J. C. Sturm, Science, 2004, 304, 987-990, ). In this paper, we present a model of how the critical particle size for fractionation depends on the micropost geometry, depending specifically on the gap between posts, the offset of posts in one row with respect to another, and whether the fluid is driven by hydrodynamics or by electroosmosis. In general the critical particle diameter is much smaller than the gap, which prevents clogging. The model is supported by data with particles from 2.3 to 22 microm.