Questions for Discussion
1. If the concentration difference for diffusion across a thin film is doubled, what happens to the flux?
2. If it is doubled for diffusion into a semi-infinite slab, what happens to the flux?
3. If the diffusion coefficient across a thin film is doubled, what happens to the flux?
4. If it is doubled for diffusion into a semi-infinite slab, what happens to the flux?
5. What is the average flux into a semi-infinite slab over a time t1?
6. What are some different ways in which an effective diffusion coefficient in a porous medium could be defined?
7. Explain Fig. 2.2-2 to someone without scientific training.
8. Explain why the funnel data in Fig. 2.1-3 curve downwards.
9. Imagine that you have a thin film separating two identical well-stirred solutions.
At time zero, the solute concentration in one solution is doubled. Sketch the concentration profiles in the film vs. position and time.
10. Estimate the flux in the previous question at a very short time.
11. Estimate it at a very long time.
12. How would the width of a spreading pulse change if the diffusion coefficient doubled?
13. Would the steady flux across a thin film increase if there was fast reaction producing a mobile product?
14. Imagine you have two films clamped together. The diffusion coefficient in one film is constant, but that in the other depends on concentration. If you reverse the concentration difference, the flux will reverse. Will its magnitude change?
Questions for Discussion
1. How does the total flux n1 differ from the diffusion flux j1?
2. When does the volume average velocity v0 equal the mass average velocity v?
3. When does v0 equal the molar average velocity v*?
4. Is there convection in distillation?
5. Suggest a problem where the Fick's law form of diffusion equation is easiest to use.
6. Suggest one where the Maxwell-Stefan form of the diffusion equation is easiest
8. Write the equations for steady-state diffusion across a flat membrane, across the wall of a tube, and out of a spherical shell.
9. Show that these equations reduce to the same limit when the membrane, wall, and shell are thin.
10. Heat and mass transfer are often said to be equivalent processes. What heat transfer property corresponds to the diffusion coefficient?
11. What heat transfer property corresponds to chemical reaction?
12. What mass transfer variable corresponds to thermal radiation?
13. We usually expect that doubling the concentration difference in a single phase will double the diffusion flux. When will this not be true?
Questions for Discussion
1. What are the dimensions of the dispersion coefficient?
2. What is the difference between a diffusion coefficient and a dispersion coefficient?
3. How will the maximum concentration in a stream vary with the distance traveled?
4. Why is the dispersion coefficient in turbulent flow independent of the diffusion coefficient?
5. Why does the dispersion coefficient in laminar flow depend inversely on the diffusion coefficient?
6. How does the dispersion coefficient vary with viscosity?
7. In a packed bed, radial dispersion is usually much larger than axial dispersion. Why?
8. At what velocity will dispersion in turbulent flow be smallest?
9. At what velocity will dispersion in laminar flow be smallest?
10. When in chromatography a solute is absorbed, how will its elution time change?
11. When in chromatography a solute is absorbed, how will its dispersion change?
12. What is the physical meaning of the capacity factor k0, defined by Equation 4.4-33?
13. What are the limits of the Golay equation (Equation 4.4-31) when the absorption is strong?