We explore the potential effects of magmatic assimilation on mineral growth and mineral zoning in an alkali olivine basaltic magma using both equilibrium thermodynamics and kinetics. The equilibrium-model calculations simulate fractional crystallization alone (closed system) and coupled assimilation-fractional crystallization (AFC) (open system); the models predict the assemblages of magmatic minerals expected and the ranges of mineral compositions. The AFC simulations are varied to show the consequences of bulk assimilation of granite versus the selective assimilation of minerals of the same granite. The resulting paths are strongly affected by the nature and type of assimilation; differences between the paths are reflected in the predicted patterns of compositional zoning in feldspar and pyroxene. These results strongly support the concept of using patterns of mineral zoning a) to identify open-system behavior, b) to restrict the identity or nature of the assimilant, and c) to constrain the extent of assimilation. In particular, these results could provide important constraints in determinations of ratios of assimilation to crystallization in the context of trace-element and isotopic studies of AFC. Mineral zoning may also help to identify the specific mechanisms that control how xenoliths react with their host magmas, since kinetic models indicate that in most cases, magmatic assimilation operates selectively. Integration of kinetic constraints with current thermodynamic models of magmatic phase-equilibria should ultimately produce accurate chemical models of magmatic assimilation and a greater understanding of mineral-zoning patterns.