Mass transfer resistance penetration equation

A plot of H/(2mq) versus 1/Ug is a straight line with a slope equal to Di and an ordinate equal to 3f + S )/Sq. The coefficient of external mass transfer is estimated using one of the several correlations available for it (see Chapter 5, subsection 5.2.5, correlation of Wilson and Geankoplis [62], Kataoka et al. [87], or the penetration theory [88]). Correcting for the contribution due to the external mass transfer resistance gives the last term in the plate height equation, 5, hence the intraparticle diffusion coefficient, Dg. 

This equation illustrates that when there is incomplete S penetration in thick films, the observed rate depends only on the magnitude of the depth of penetration and not of the total thickness (La Motta, 1976b). This so-called active depth was specified by Kornegay and Andrews (1969), and it is often used for design purposes. The significance of internal mass transfer resistance to the interpretation of the kinetic data of suspended growth systems will be explained quantitatively. The biological rate equation, written as... 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

If potential flow and constant surface temperature are assumed, an equation analogous to Eq. (18) is obtained for the internal Nusselt number. Note, however, that the reference velocity in the internal Peclet number is the drop velocity. Similar results will be obtained from the penetration theory, according to which the film is assumed infinite with respect to the depth of heat penetration during the short contact time of a fluid element sliding over the interface. Licht and Pansing (L13) report West s equation, based on the transient film concept, for the case of mass transfer through the combined film resistance. In terms of the overall heat-transfer resistance, l/U (= l//jj + I/he) and if the contact time is that required for the drop to traverse a distance equal to its diameter. West s equations yield... 

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