Ice lenses are formed during soil freezing by the migration and solidification of premelted water that is adsorbed to ice-particle interfaces and confined to capillary regions. We develop a model of ice lens growth that clearly illustrates how the freezing rate dependence on particle size and soil microstructure changes in response to changes in the relative importance of permeable flow and thin-film flow in governing the water supply. The growth of an ice lens in fine-grained porous media is primarily constrained by low permeability in the unfrozen region. In contrast, the constraints offered by the film flow decrease the lens growth rate adjacent to larger particles. The trade-off between resistance to permeable flow and film flow causes the growth rate for ice lenses to be maximized for particles of intermediate size. Moreover, because film flow along particle surfaces adjacent to a growing lens is not strongly affected by the microstructure of the pore space, our analysis predicts that lensing in coarse-grained porous media is insensitive to the pore microstructure and porosity, but the permeable flow that governs lens formation in fine-grained porous media causes their growth to be much more affected by these details.