We discuss techniques for calculating the amount of crustal assimilation possible in lunar magma chambers and dikes based on thermal energy balances, kinetic rates, and simple fluid mechanical constraints. Assuming parent magmas of picritic compositions, we demonstrate the limits on the capacity of such magmas to melt and dissolve wall rock of anorthitic, troctolitic, noritic, and KREEP (quartz monzodiorite) compositions. Significant melting of the plagioclase-rich crustal lithologies requires turbulent convection in the assimilating magma and an efficient method of mixing in the relatively buoyant and viscous new melt. Even when this occurs, the major element chemistry of the picritic magmas will change by less than 1--2 wt %. Diffusion coefficients measured for Al2O3 from an iron-free basalt and an orange glass composition are 10-12 m2 s-1 at 1340 ¿C and 10-11 m2 s-1 at 1390 ¿C. These rates are too slow to allow dissolution of plagioclase to significantly affect magma compositions. Picritic magmas can melt significant quantities of KREEP, which suggests that their trace element chemistry may still be affected by assimilation processes; however, mixing viscous melts of KREEP composition with the fluid picritic magmas could be prohibitively difficult. We conclude that only a small part of the total major element chemical variation in the mare basalt and volcanic glass collection is due to assimilation/fractional crystallization processes near the lunar surface. Instead, most of the chemical variation in the lunar basalts and volcanic glasses must result from assimilation at deeper levels or from having distinct source regions in a heterogeneous lunar mantle. ¿ American Geophysical Union 1994