Kronig-Brink solution

Solutions have been obtained for a rigid sphere with Pep = 0 (G8), and the results are shown in Fig. 3.21. We have complemented these with solutions for a sphere circulating with the Hadamard-Rybczynski velocities at PCp/(l + k) 00, assuming Shi proportional to sin 0 and with the overall mean Sh used to define Bi. These results are shown in Fig. 3.22. For Bi oo (i.e., negligible external resistance), the limiting curves are the Newman solution in Fig. 3.21 and the Kronig-Brink solution in Fig. 3.22. For Bi < 0.2 the internal resistance... 

For a circulating sphere with Pep/(1 + /c) oc, the time required for diffusion is much greater than that for fluid circulation, so that surfaces of uniform concentration coincide with the Hadamard-Rybczynski streamlines. Kronig and Brink (K6) showed that the solution is then... 

Stagnant cap, o- Results lie between the solutions of Newman and Kronig and Brink. This model can easily be extended to include changes of cap angle with time. 

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