Although the additive approach traditionally used for coupling Fickian diffusion with convection appears logical and works for calculating total fluxes of \(A\) and \(B\), this is not the only way one could tackle the problem. For binary systems this approach has the advantages of forcing \(D_{\mathrm{AB}}=D_{\mathrm{BA}}\) (see Problem 15.C1), and \(D_{\mathrm{AB}}\) is the same for any choice of \(\mathrm{v}_{\text {ref }}\) (see Problem 15.C2). Instead of treating diffusion and convection terms as additive Eqs. (15-15a) and (15-15b), what other approaches could be used to analyze simultaneous convection and diffusion?

Data From Problem 15.B1

In Example 15-2, operation is at a pseudo-steady state. Brainstorm alternative designs for this diffusion measurement.

Example 15-2

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Pure ethanol is contained at the bottom of a long, vertical tube (cross-sectional area = 0.9 cm), as shown in Figure 15-2. Above the liquid is a quiescent layer of air. The liquid at the bottom of the tube is carefully adjusted so that distance from the air-liquid interface to the open top of the tube is constant at 15.0 cm. No liquid is withdrawn from the tube. At the open end of the tube air is blown perpendicular to the vertical tube so that the concentration of ethanol at the top of the tube is essentially zero. The entire apparatus is kept at 0C, and Ptot = 0.98 atm. The tube is carefully arranged so that there is so little convection in the tube that we can ignore it. Over the course of several days, we find that the average evaporation rate is 0.9190 x 10-3 cm/h. What is the value of the diffusion coefficient of ethanol in air at 0C? Air Z L 15 cm Liquid level in reservoir z = 0