Heterogeneities convective mixing

The analogy between the problem of convective diffusion in a channel with semipermeable walls and the problem of mixed heterogeneous reaction makes it possible to consider these problems together. Conclusions that are true for one problem would be true for the other problem as well, even though these processes are distinct from both physical and chemical viewpoints. Besides, the analogy with chemical reactions allows us to introduce a dimensionless parameter of the problem (see (6.16)) - the Damkoler number ... 

Normally, crystals do not exhibit convective flow and, therefore, mixing by convection at atomic dimensions is not possible. As a consequence, diffusive transport and heterogeneous reactions are the only processes which can be anticipated at this point. 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

In summary, we have recently witnessed a shift away from the classically layered mantle model in favor of whole mantle convection models, where the buoyancy of sinking slabs is the dominant driving force. Slabs can penetrate deep into the lower mantle and with the induced return flow we would expect the mantle to mix efficiently. This leaves us with an interesting dilemma. If the mantle convects as a whole, how can it preserve the large-scale and long-hved heterogeneity seen in the geochemistry of oceanic basalts ... 

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