Unsteady-state diffusion resistance

Newman (N3), Geddes (G16), and others obtained the internal transfer efficiency, for the special case of zero resistance of the external film. By solving the unsteady-state diffusion equation, they obtained the following expression for the transfer efficiency ... 

Figure 7.1-2. Unsteady-state diffusion in a flat plate with negligible surface resistance.

Rate of leaching when diffusion in solid controls. In the case where unsteady-state diffusion in the solid is the controlling resistance in the leaching of the solute by an external solvent, the following approximations can be used. If the average diffusivity Da eff of the solute A is approximately constant, then for extraction in a batch process, unsteady-state mass-transfer equations can be used as discussed in Section 7.1. If the particle is approximately spherical. Fig. 5.3-13 can be used. 

With drops and bubbles the resistance to mass transfer in both phases may be significant. Diffusion inside a stagnant noncirculating) drop is an unsteady-state process, but for convenience in combining coefficients an effective internal coefficient can be used, as was done for heat transfer in spheres [see Eqs. (11.38) and (11,40)] ... 

A theory which incorporates some of the principles of both the two-film theory and the penetration theory has been proposed by TOOR and Marchello The whole of the resistance to transfer is regarded as lying within a laminar film at the interface, as in the two-film theory, but the mass transfer is regarded as an unsteady state process. It is assumed that fresh surface is formed at intervals from fluid which is brought from the bulk of the fluid to the interface by the action of the eddy currents. Mass transfer then takes place as in the penetration theory, except that the resistance is confined to the finite film, and material which traverses the film is immediately completely mixed with the bulk of the fluid. For short times of exposure, when none of the diffusing material has reached the far side of the layer, the process is identical to that postulated in the penetration theory. For prolonged periods of exposure when a steady concentration gradient has developed, conditions are similar to those considered in the two-film theory. 

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