Parallel Diffusion and Convection

The idea that diffusion is better described by a chemical potential gradient than by a concentration gradient appears frequently. It is basic to estimates of diffusion in liquids, as proposed by Einstein and discussed in Section 5.2. It is correct for dilute solutions of electrolytes, covered in Section 6.1. However, it is certainly wrong near spinodals or consolute points (Section 6.3), and it seems untested for other, highly nonideal solutions. I use it confidently for dilute solutions but cautiously elsewhere. 

We now want to combine the equations developed above with mass balances to calculate fluxes and concentration profiles. This is, of course, the same objective as in Chapter 2. The difference here is that both diffusion and convection are significant. The analysis of the more comphcated problems of diffusion and convection is aided by the parallels in the case of a thin film and an infinite slab around which Chapter 2 is organized. Such parallels produce powerful pedagogy. 

The first problem that we consider involves the same rapid evaporation that was used as the key example in Section 3.1. We recall that at intermediate temperatures, the evaporation rate depends on both diffusion and convection up the tube. 

We want to calculate the flux and the concentration profile where both diffusion and convection are important. To make this calculation, we must parallel our earlier scheme, but with a more exact physical understanding and a more complicated mathematical analysis. Just as before, the scheme starts with a mass balance, combines this balance with Pick s law, and then runs through the math to the desired result. 

This mass balance is written on the differential volume AAz shown in Fig. 3.3-1  

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