Definition of Mass Transfer Coefficients

We shall adopt a simple model of the interface itself a surface that offers no resistance to mass transfer and where equilibrium prevails. Thus, the usual equations of phase equilibrium relate the mole fractions y and x j. 

The starting point for any analysis of the interphase mass transfer process will be Eqs. 

13 describing the continuity of molar fluxes with respect to the interface. The simpler form, Eq. 1.3.14, will suffice for a majority of the cases in which the interface remains stationary. We proceed with Eq. 1.3.14 with the understanding that if the interface moves, the fluxes must be referred to the interface and not a stationary coordinate reference frame. Furthermore, interphase mass transfer usually takes place in a direction normal to the interface and, therefore, it is sufficient to use the scalar form of Eq. 1.3.14, that is, 

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Depending on the driving force we choose to employ in our analysis, there are several definitions of mass transfer coefficients that may be considered appropriate for use. If we consider an arbitrary interface between a fluid and the external surface of a catalyst particle, we might choose to define a mass transfer coefficient based on a concentration driving force (kc) as... 

The general definition of mass transfer coefficients according to Eqs. (9.31)-(9.33) is also valid for the mass transfer coefficient in a centrifugal field. The... 

We also feel that portions of the material in this book ought to be taught at the undergraduate level. We are thinking, in particular, of the materials in Section 2.1 (the Maxwell-Stefan relations for ideal gases). Section 2.2 (the Maxwell-Stefan equations for nonideal systems). Section 3.2 (the generalized Fick s law). Section 4.2 (estimation of multicomponent diffusion coefficients). Section 5.2 (multicomponent interaction effects), and Section 7.1 (definition of mass transfer coefficients) in addition to the theory of mass transfer in binary mixtures that is normally included in undergraduate courses. 

The HTU is determined from experimental data or empirical correlations, and the NTU is related to equilibrium and operating data. Since both HTU and NTU depend on the particular definition of mass transfer coefficients and compositions in the mass transfer equations, it is important to use compatible pairs of HTU and NTU. For instance. Equations 15.24 and 15.25 are rewritten as... 

Although the definitions of mass transfer coefficients expressed in Eq, (2,4-1) are must commonly used, an alternative definition originally employed by Colburn and Drew1 is useful ueder conditions of large convective flow in the direction of transport. The flux across a transfer surface at position I is given as... 

Since concentrations may be defined in a number of equivalent ways, other definitions of mass-transfer coefficients for this case (NB - 0 dilute solutions) are frequently used, such as... 

Table 16-1. Definitions of mass transfer coefficients andHTUs.

I. Definition of mass-transfer coefficient. Since our understanding of turbulent flow is incomplete, we attempt to write the equations for turbulent diffusion in a manner similar to that for molecular diffusion. For turbulent mass transfer for constant c, Eq. (6.1-6) is... 

Here, x) is the vapor-phase mole fraction in equilibrium with the actual liquid-phase bulk composition (in mole fraction) Xm, and Xjg,- is the vapor-phase mole fraction of species i at the vapor-liquid interface. Using definitions of mass-transfer coefficients... 

Table 8.2-2 Common definitions of mass transfer coefficients ...

Fig. 8.2-1. Ammonia scrubbing. In this example, ammonia is separated by washing a gas mixture with water. As explained in the text, the example illustrates ambiguities in the definition of mass transfer coefficients. The ambiguities oeeur because the concentration difference causing the mass transfer changes and because the interfacial area between gas and liquid is unknown.

In the previous two sections we have presented definitions of mass transfer coefficients and have shown how these coefficients can be found from experiment. Thus we have a method for analyzing the results of mass transfer experiments. This method can be more convenient than diffusion when the experiments involve mass transfer across interfaces. Experiments of this sort include liquid liquid extraction, gas absorption, and distillation. 

These shortcomings lead to alternative definitions of mass transfer coefficients that include the effects of diffusion-induced convection. One such definition is... 

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