More about Mass Transfer Coefficients

In Chapter 1 the notion of a mass transfer coefficient was introduced and the connection to what was termed film theory was shown. 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 was referred to as two-film theory. Chapter 1 was confined to simple applications of the mass transfer coefficient which is either assumed to be known or is otherwise evaluated numerically in simple 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. 

Mass Transfer and Separation Processes Principles and Applications 

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For particles with rough surfaces, e.g., with roughness elements of height less than 20% of d, the mass transfer coefficient is usually larger than predicted here (A5, J4, S3, S4), but at most by about 50%. Roughness is treated in more detail in Chapter 10. For a particle made up of a small number of particles in a cluster, the use of d in Eq. (6-35) gives good results (S4). 

Die difference from the real value (lm) is mainly due to the approximation made about the mass transfer coefficient as well as the complete wetting of the catalyst, as the actual wetting efficiency is 88%. Furthermore, the problem is more complicated because under incomplete wetting, the gas reactant reaches the catalyst surface more easily than the unwetted part, as Horowitz et al. found out experimentally. 

In general, diffusion is most useful for fundamental studies where we want to know the details about the system. For example, if we were concerned with a plastisizer inside a polymer film, we might want to know where and when the plasticizer is located. Diffusion will tell us. Dispersion can be important when there is convection, as in chromatography or atmospheric pollution. Mass transfer, on the other hand, tends to be useful in less fundamental, more practical problems. For example, if we want to know how to humidify and ventilate a house, we probably will use mass transfer coefficients. 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

Pilot plant work is essential as a basis for full scale design. It may be directed to finding suitable velocities, temperatures and drying times, or it may employ more basic approaches. The data provided for Example 9.8, for instance, are of particle size distribution, partial pressure of water in the solution, and heat and mass transfer coefficients. These data are sufficient for the calculation of residence time when assumptions are made about terminal temperatures. 

It is likely also that biofilms will become more dense with the passage of time since the voids within a biofilm, will gradually fill with cells as a result of reproduction. The effects of the age of a biofilm of Pseudomonas fluorescens on mass transfer through the biofilm were demonstrated by Vieira et al [1994]. Using Li Cl as the diffusing solute there was a fall of around 60% in mass transfer coefficient in a period of about 150 hours. The Reynolds numbers used in the experiments were 8250 and 14700 but there appeared to be little dependence as would be anticipated, of mass transfer through the biofilm due to changes in Reynolds number. 

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