A Survey of Mass Transfer Coefficients

Chapter 1 introduced the reader to the notion of a mass transfer coefficient and has shown the connechon to what is termed film theory. In essence, this approach assumes the resistance to mass transfer to be confined to a thin film in the vicinity of an interface in which the actual concentration gradient is replaced by a linear approximation. The result is that the rate of mass transport can be represented as the product of a mass transfer coefficient and a linear concentration difference, or concentration driving force. Thus, 

It was further shown that individual transport coefficients could be combined into overall mass transfer coefficients to represent transport across adjacent interfacial layers. The underlying concept is referred to as two-film theory. Chapter 1 has been confined to simple applications of the mass transfer coefficient which is either assumed to be known, or is otherwise evaluated numerically in simple fashion. 

This chapter seeks to enlarge our knowledge of mass transfer coefficients by compiling quantitative relations and data for use in actual calculations applied to practical systems. There are evidently a host of such systems, and our aim here is to convey the coefficients perhnent to these systems in an organized fashion. 

When the system under consideration is in laminar flow, it is often possible to give precise analytical expressions of the transport coefficients. In most other cases, including the important case of turbulent flow, the analytical approach generally fails and we must resort to semiempirical correlations, arrived at by the device known as dimensional analysis, which involves the use of dimensionless groups. 

To represent these facts in an organized fashion, we start our deliberations with a brief survey of the dimensionless groups pertinent to mass transfer operations. We next turn to transport coefficients that apply to systems in laminar flow and show how these coefficients are extracted from the solutions of the pertinent PDE models. This is followed by an analysis of systems in turbulent flow where the approach of dimensional analysis is used. We 

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Mass-transfer coefficients seem to vary as the 0.7 exponent on the power input per unit volume, with the dimensions of the vessel and impeller and the superficial gas velocity as additional factors. A survey of such correlations is made by van t Riet (Ind Eng. Chem Proc Des Dev., IS, 3.57 [1979]). Table 23-12 shows some of the results. 

The mass transfer between phases is, of course, the very basis for most of the diffusional operations of chemical engineering. A considerable amount of experimental and empirical work has been done in connection with interphase mass transfer because of its practical importance an excellent and complete survey of this subject may be found in the text book of Sherwood and Pigford (S9, Chap. Ill), where dimensionless correlations for mass transfer coefficients in systems of various shapes are assembled. 

The second part of the chapter is devoted to the effect of pressure on heat and mass transfer. After a brief survey on fundamentals the estimation of viscosity, diffusivity in dense gases, thermal conductivity and surface tension is explained. The application of these data to calculate heat transfer in different arrangements and external as well as internal mass transfer coefficients is shown. Problems at the end of the two main parts of this chapter illustrate the numerical application of the formulas and the diagrams. 

In the following sections a survey of the elementary diffusion theories that are determining the basis for the mass transfer coefficient concepts is given. No heat and mass transfer models dealing with simultaneous chemical reactions are considered to maintain attention to the fundamental principles. 

In addition, it is worth noting that a survey of 14 experimental studies where sufficient data were presented to make the analysis showed that the ratio of the maximum to minimum measured mass transfer coefficient for a particular solid-liquid pair, respectively, was always less than 2 ... 

Gogate, P.R., and Pandit, A.B. (1999b), Survey of measurement techniques for gas-liquid mass transfer coefficient in bioreactors, Biochemical Engineering Journal, 4(1) 7-15. 

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