Mass transfer coefficients definitions

The concentration difference can also be re-defined in different ways, thus there exists a variety of modifications of the basic mass transfer coefficient definition as well. Therefore, care should to be taken to ensure that the mass transfer coefficient parameterizations adopted for modeling purposes, correspond to the model formulation used. 

Table 16.3 shows some possible forms of mass transfer coefficient definitions and the relationships between the coefficients based on EMD and UMD. In addition to Ky and Ky coeflScients, we can also define Ky and Kx coefficients based on mole ratio f(T— Tj) and (Xj — X)] driving forces. 

This value is typical of those found in liquids. This type of mass transfer coefficient definition is preferable to that used first, a point explored further in Section 8.2. 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

It is important to understand that when chemical reactions are involved, this definition of Cl is based ou the driving force defined as the difference between the couceutratiou of un reacted solute gas at the interface and in the bulk of the liquid. A coefficient based ou the total of both uureacted and reached gas could have values. smaller than the physical-absorption mass-transfer coefficient /c . 

Now R0 (the shear stress in the fluid at the surface) is equal and opposite to R, the shear stress acting on the surface, —q jQs is by definition the heat transfer coefficient at the surface (h), and (—NA)y=o/ CAjl - CAw) is the mass transfer coefficient ho). Then dividing both sides of equation 12.100 by pu, and of equation 12.101 by u, to make them dimensionless ... 

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... 

Fig. 9.20 Definition of individual and overall mass transfer coefficients.

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... 

This is simply the definition of the mass transfer coefficient km, the subject of mass transfer courses is to find suitable correlations in order to estimate k A (units of lengthAime). The mass transfer coefficient is in turn defined through the Sherwood number,... 

Relationships between the gas-phase mass transfer coefficient the liquid-phase mass transfer coefficient and the overall mass transfer coefficients Kq and were discussed in Section 6.2. With the definitions used in this book, all of these coefficients have a simple dimension (L T ). 

Equating the two representations of the wall mass flux (Eqs. 5.31 and 5.32) provides the operational definition for the mass-transfer coefficient,... 

This chapter will first provide some basics on ozone mass transfer, including theoretical background on the (two-) film theory of gas absorption and the definition of over-all mass transfer coefficients KLa (Section B 3.1) as well as an overview of the main parameters of influence (Section B 3.2). Empirical correction factors for mass transfer coefficients will also be presented in Section B 3.2. These basics will be followed by a description of the common methods for the determination of ozone mass transfer coefficients (Section B 3.3) including practical advice for the performance of the appropriate experiments. Emphasis is laid on the design of the experiments so that true mass transfer coefficients are obtained. 

The mass-transfer coefficients, by definition, are equal to the ratios of the molar mass flux to the concentration driving forces. The mass-transfer coefficients are related to each other as follows ... 

Earlier it,was noted that a definite relationship exists between the heat transfer coefficient and the mass transfer coefficient. Chilton and Colburn [10] developed Equation 3.31, which will be restated here ... 

Note that the usual definition of the mass transfer coefficient is related to limiting diffusion conditions or nemstian conditions (mo, no = yDo/nt for a planar electrode see Sect. 1.8.4). The definition given in Eq. (3.43) is general for any reversibility degree of the electrode process at planar electrodes. 

By definition, the mass transfer coefficient (k) relates the rate of mass transport (AW) to a difference in concentration at two identifiable locations ... 

Mass transfer coefficients are frequently regarded as a difficult subject, not because the subject is inherently difficult, but because of different definitions and because of complexities for mass transfer from one solution into a second solution. These differences merit further discussion. 

Each of these units of concentration may be used to define a different mass transfer coefficient, as exemplified by the definitions in Table III. It is not a difficult task to convert a value from one form of coefficient into another form of coefficient (Cussler, 1997 Treybal, 1980). However, it is complicated and requires care. It s like balancing a checkbook it doesn t always work out the first time you try it. Still, we normally find that with the definitions like those in Table III held firmly in mind, we can readily convert from one form of coefficient to another. 

The definition of the mass-transfer coefficient according to the film model is ... 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

Which is less than 2300 and thus the flow is laminar. Therefore, based on the analogy between heat and mass transfer, the Nusselt and the Sherv/ood numbers in this case are Nu = Sh = 3.66, Using the definition of Sherwood number, itie mass transfer coefficient is determined to be... 

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