17. Convective Material Transport

In this Chapter we study the material transport (in terms of mass or moles) of a dilute solute dissolved in a solvent. As we have seen in Sect. 14.​3, at leading order the average velocity of a mixture in the dilute limit equals the solvent velocity, so that the material transport reduces to a linear problem, as both diffusive and convective fluxes are linear functions of the concentration difference. Accordingly, the governing equations of mass transport in the dilute limit are identical as those of heat transport, so that most of the considerations that we made in Chap. 13 can be extended here. In particular, in Sects. 17.1 and 17.2 we study the mass boundary layer, with its dependence on the fluid velocity and the geometry of the problem. Then, in Sect. 17.3, we focus on the case where there is a mass boundary layer, with no momentum boundary layer, occurring when the material Peclet number is large and concomitantly the Reynolds number is small. The material boundary layer is further examined in Sect. 17.4, using the integral approximation described in Sect. 7.​7. Finally, in Sect. 17.5, we apply the quasi steady state approximation to solve important problems of mass transfer, related to particle growth or consumption.