An extensive series of laboratory experiments is used to quantify the circumstances under which fluids can be mixed by natural convection at high flux Rayleigh number. A compositionally buoyant fluid was injected at a fixed rate into an overlying layer of ambient fluid from a planar, horizontally uniform source. The nature of the resulting compositional convection was found to depend on two key dimensionless parameters: a Reynolds number Re and the ratio U of the ambient fluid viscosity to the input fluid viscosity. Increasing the Reynolds number corresponded to increasing the vigor of the convection, while the viscosity ratio was found to determine the spacing between plumes and whether buoyant fluid rose as sheets (U1). From measurements of the final density profile in the fluid after the experiments we quantified the extent to which buoyant liquid was mixed in terms of a thermodynamic mixing efficiency E. The mixing efficiency was found to be high (E>0.9) when either the Reynolds number was large (Re>100) or the viscosity ratio was small (U200. The amount of mixing was related to whether ascending plumes generated a large-scale circulation in the ambient fluid. When our results are applied to the differentiation of the Earth's core, we suggest that the convection resulting from the release of buoyant residual liquid into the liquid outer core due to crystallization at the boundary between the inner and the outer core will probably lead to nearly complete mixing. In the dynamically very different context of the mantle, mantle plumes are predicted to ascend through the mantle and pond beneath the lithosphere, whereas convection driven by the subduction of oceanic lithosphere is expected to produce moderate to extensive mixing of the mantle. When the competing plate and plume modes of mantle convection are considered together, we find that owing to a larger driving buoyancy flux, the plate-scale flow will destroy any stratification at the top of the mantle produced by mantle plumes. Applying our results to the stagnant lid style of thermal convection predicted to occur in the mantles of the Moon, Mercury, Mars, Venus, and pre-Archean Earth, we expect the respective flows to produce minor thermal stratification at the respective core-mantle boundaries. In part 2 of this study <Jellinek and Kerr, this issue> we apply our results to the differentiation of magma chambers and komatiite lava flows. ¿ 1999 American Geophysical Union