The D″ region of the mantle has been interpreted as a variable-thickness layer of hot, chemically heterogeneous material at the base of the mantle. This paper reports the results of numerical simulations testing whether growth of a chemically distinct layer at the base of the mantle is possible by influx of molten iron alloy from the core to the mantle. A finite-element model of thermo-chemical mantle convection was used to simulate exchange of material between the mantle and core. Growth of a significant layer at the base of the mantle depends on several factors; we focus on the effect of density of the material in the chemical boundary layer. Relatively low density material was swept away from the core-mantle boundary by mantle upwellings. Very high density material, in contrast, was not swept away, but flowed into the mantle too slowly to form a layer as thick as D″. For moderate density contrasts between material in a chemical boundary layer and the overlying mantle, a laterally heterogeneous layer formed. The stable layer results in an elevated temperature contrast between the core and the mantle. High temperatures in this layer are associated with broad regions of elevated temperature in the overlying mantle.