The Analogy with Single-Solute Mass Transfer

The Analogy with Single-Solute Mass Transfer 

We may note that the problem defined by (9-7) and (9-8) is identical mathematically to the corresponding single-solute mass transfer problem, provided the conditions at the body surface and at infinity are such that we can specify the solute concentration as known constants. In this case, we can substitute concentration c (measured as mass fraction of solute) for the temperature T in the definition (9-3) of 9. Then the boundary conditions are identical to (9-8), and the governing equation for solute transport is also the same as (9-7), with the exception that the Peclet number must now be defined in terms of the diffrisivity D for the solute in the solvent, rather than the thermal diffusivity k. Hence, in this case 

Another important practical difference between the heat and mass transfer problems is the magnitude of the Prandtl number and the Schmidt numbers. In the present chapter, these parameters appear in only the relationship between the Peclet number and the Reynolds number. However, we shall see in Chap. 11 that this is not always true. In any case, the magnitude of the Schmidt number is typically larger than the magnitude of the Peclet number. For liquids, typical values of the Schmidt number are 

Finally, one fundamental difference between heat and mass transport is that mass transfer may modify the fluid flow and/or produce a convective contribution to the transport rate to (or from) a surface, even when natural convection effects are completely negligible, because the mass transfer process produces a nonzero normal velocity at the transport boundary. To see that this is the case, we must carefully reconsider the mass balance at the boundary. First, let us introduce some convenient notation. If we denote the solvent as A and the solute as B, then by c we mean the concentration c . Because cA and cb(= c) are specified as mass fractions, the sum cA + cn = cA + c = 1, and hence dcA/dn = —dc/dn, where we can denote the surface as n = 0 and derivatives normal to the surface as dc/dn. The key to the correct mass balance is to note that there can be no net flux of the (inert) solvent at the mass transfer surface. Hence there must be a normal velocity away from the surface to balance the diffusive flux of solvent toward the surface because of the gradient in the solvent concentration, dcA/dn  

Here we include the primes on v and n to remind us that these are dimensional quantities. It follows that 

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