Mass-transfer coefficients, analogy with rates

The treatment is divided into four sections. Section II deals with estimation of coefficients of heat transfer and of mass transfer. Because most, or all, of the latent heat of evaporation of the moisture is normally derived from the sensible heat of the carrier gas, our knowledge of the pertinent coefficients of heat transfer from the gas to the surface of the drying solid is summarized. A summary of the analogous mass-transfer coefficients records in condensed form gives our current knowledge of the means of estimating the rate of transport from the solid to the gas of the vapor evolved. 

Fig. 9.4-1. The Graetz-Nusselt problem. In this case, a pure solvent flowing laminarly in a cylindrical tube suddenly enters a section where the tube s walls are dissolving. The problem is to calculate the wall s dissolution rate and hence the mass transfer coefficient. The problem s solutions, based on analogies with heat transfer, are useful for designing artificial kidneys and blood oxygenators.

This review deals mainly with the discussion of various macroscopic hydro-dynamic, heat, and mass transfer characteristics of bubble columns, with occasional reference to the analogous processes in modified versions of bubble columns with a variety of internals. The hydrodynamic considerations include determination of parameters like flow patterns, holdup, mixing, liquid circulation velocities, axial dispersion coefficient, etc., which all exert strong influence on the resulting rates of heat and mass transfer and chemical reactions carried out in bubble columns. Different correlations developed for estimating the aforementioned parameters are presented and discussed in this chapter. 

In this section, microdisc electrodes will be discussed since the disc is the most important geometry for microelectrodes (see Sect. 2.7). Note that discs are not uniformly accessible electrodes so the mass flux is not the same at different points of the electrode surface. For non-reversible processes, the applied potential controls the rate constant but not the surface concentrations, since these are defined by the local balance of electron transfer rates and mass transport rates at each point of the surface. This local balance is characteristic of a particular electrode geometry and will evolve along the voltammetric response. For this reason, it is difficult (if not impossible) to find analytical rigorous expressions for the current analogous to that presented above for spherical electrodes. To deal with this complex situation, different numerical or semi-analytical approaches have been followed [19-25]. The expression most employed for analyzing stationary responses at disc microelectrodes was derived by Oldham [20], and takes the following form when equal diffusion coefficients are assumed ... 

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