Interfacial transfer film theory

Note that the transfer rate equation is based on an overall concentration driving force, (X-X ) and overall mass transfer coefficient, Kl. The two-film theory for interfacial mass transfer shows that the overall mass transfer coefficient, Kl, based on the L-phase is related to the individual film coefficients for the L and G-phase films, kL and ko, respectively by the relationship... 

Laubriet et al. [Ill] modelled the final stage of poly condensation by using the set of reactions and kinetic parameters published by Ravindranath and Mashelkar [112], They used a mass-transfer term in the material balances for EG, water and DEG adapted from film theory J = 0MMg — c ), with c being the interfacial equilibrium concentration of the volatile species i. 

In rate-based multistage separation models, separate balance equations are written for each distinct phase, and mass and heat transfer resistances are considered according to the two-film theory with explicit calculation of interfacial fluxes and film discretization for non-homogeneous film layer. The film model equations are combined with relevant diffusion and reaction kinetics and account for the specific features of electrolyte solution chemistry, electrolyte thermodynamics, and electroneutrality in the liquid phase. 

Like their random-packing efficiency model (above), the Bravo, Fair et al. structured-packing model is based on the two-film theory. The HTU is calculated from the mass transfer coefficients and interfacial areas using Eqs. (9.23) and (9.24). The HETP can be calculated from the HTU using Eqs. (9.12) and (9.13). The mass transfer coefficients are evaluated from... 

As the interface offers no resistance, mass transfer between phases can be regarded as the transfer of a component from one bulk phase to another through two films in contact, each characterized by a mass-transfer coefficient. This is the two-film theory and the simplest of the theories of interfacial mass transfer. For the transfer of a component from a gas to a liquid, the theory is described in Fig. 6B. Across the gas film, the concentration, expressed as partial pressure, falls from a bulk concentration Fas to an interfacial concentration Ai- In the liquid, the concentration falls from an interfacial value Cai to bulk value Cai-... 

The thickness of the fictitious film can neither be predicted nor measured experimentally. This limits the use of the film theory to directly calculate the mass transfer coefficients from the diffusivity. Nevertheless, the film theory is often applied in a two-resistance model to describe the interphase mass transfer between the two contacting phases (gas and liquid). This model assumes that the resistance to mass transfer only exists in gas and liquid films. The interfacial concentrations in gas and liquid are in equilibrium. The interphase mass transfer involves the transfer of mass from the bulk of one phase to the interfacial surface, the transfer across the interfacial surface into the second phase, and the transfer of mass from the interface to the bulk of the second phase. This process is described graphically in Fig. 1. 

The film theory is the simplest model for interfacial mass transfer. In this case it is assumed that a stagnant film exists near the interface and that all resistance to the mass transfer resides in this film. The concentration differences occur in this film region only, whereas the rest of the bulk phase is perfectly mixed. The concentration at the depth I from the interface is equal to the bulk concentration. The mass transfer flux is thus assumed to be caused by molecular diffusion through a stagnant film essentially in the direction normal to the interface. It is further assumed that the interface has reached a state of thermodynamic equilibrium. 

The result obtained from the film theory is that the mass transfer coefficient is directly proportional to the diffusion coefficient. However, the experimental mass transfer data available in the literature [6], for gas-liquid interfaces, indicate that the mass transfer coefficient should rather be proportional with the square root of the diffusion coefficient. Therefore, in many situations the film theory doesn t give a sufficient picture of the mass transfer processes at the interfaces. Furthermore, the mass transfer coefficient dependencies upon variables like fluid viscosity and velocity are not well understood. These dependencies are thus often lumped into the correlations for the film thickness, 1. The film theory is inaccurate for most physical systems, but it is still a simple and useful method that is widely used calculating the interfacial mass transfer fluxes. It is also very useful for analysis of mass transfer with chemical reaction, as the physical mechanisms involved are very complex and the more sophisticated theories do not provide significantly better estimates of the fluxes. Even for the description of many multicomponent systems, the simplicity of the model can be an important advantage. 

If an appropriate relation for the contact area as a function of the internal coordinates is available, the particle growth term due to interfacial mass transfer can be modeled in accordance with the well known film theory (although still of semi-empirical nature) and the ideal gas law [68]. The modeling of the source and sink terms due to fluid particle breakage and coalescence is less familiar and still on an early stage of development. Moreover, the existing theory is rather complex and not easily available. Further research is thus needed in order to derive consistent multifluid-population balance models. 

However, as with the penetration theory analysis, the difference in magnitude of the mass and thermal diffusivities with cx 100 D, means that the heat transfer film is an order of magnitude thicker than the mass transfer film. This is depicted schematically in Fig. 8, The fall in temperature from T over the distance x is (if a = 100 D) about 0% of the overall interface excess temperature above the datum temperature T.. Furthermore, in considering the location of heat release oue to reaction in the mass transfer film, this is bound to be greatest closest to the interface, and this is especially the case when the reaction becomes fast. Therefore, two simplifications can be introduced as a result of this (i) the release of heat of reaction can be treated as am interfacial heat flux and (ii) the reaction can be assumed to take place at the interfacial temperature T. The differential equation for diffusion and reaction can therefore be written... 

Presence of an interfacial resistance can be incorporated easily into the film theory by introduction of an additive resistance terra R so that the expression for the overall resistance to mass transfer becomes... 

Heat and Mass Transfer Using the film theory, both phenomena mainly depend on the film and gas stream thickness and the type of reaction. Other parameters are the interfacial area, the residence time and the axial dispersion. Good mass and heat transport presume a good fiow equipartition in the channels. In mesh reactors the mesh open area determines the interfacial area. Mass transfer coefficients ki a from 3 to 8 L s and higher values in catalytic systems can be achieved [25]. 

Film Theory and Gas-Liquid and Liquid-Liquid Mass Transfer. The history and literature surrounding interfacial mass transfer is enormous. In the present context, it suffices to say that the film model, which postulates the existence of a thin fluid layer in each fluid phase at the interface, is generally accepted (60). In the context of coupled mass transfer and reaction, two common treatments involve 1) the Hatta number and (2) enhancement factors. Both descriptions normally require a detailed model of the kinetics as well as the mass transfer. The Hatta number is perhaps more intuitive, since the numbers span the limiting cases of infinitely slow reaction with respect to mass transfer to infinitely fast reaction with respect to mass transfer. In the former case all reaction occurs in the bulk phase, and in the latter reaction occurs exclusively at the interface with no bulk reaction occurring. Enhancement factors are usually categorized in terms of reaction order (61). In the context of nonreactive systems, a characteristic time scale (eg, half-life) for attaining vapor-liquid equilibrium and liquid-liquid equilibrium, 6>eq, in typical laboratory settings is of the order of minutes. 

The main transport parameters to be estimated are the mass transfer coefficients (gas-liquid (liquid side) fc , gas-liquid (gas side) kg, and liquid-solid fc )). Coupled to that is the estimation of the interfacial area per unit volume a, and often it is the combination (i.e., kia or kgO) that is estimated in a certain experimental procedure. Thermodynamic parameters, such as Henry s law constant (fZ) can be estimated in a simpler manner since their estimation on the flow or on any time-dependent phenomenon. Mass transfer coefticients may be evaluated in well-defined geometries with known flow fields using classical theories like film theory, penetration theory, surface renewal... 

Interfacial mass transfer processes can be described by the two-film theory (Figure 4.4.1) based on the following assumptions ... 

Interfacial mass transfer processes can be described by the two-film theory. Both the gas and the liquid phase can be divided into a stagnant film located near the interface and well-mixed bulk phases without concentration gradients. The two-film theory certainly lacks physical reality in postulating the existence... 

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. 

Fig. 9.1-1. The film theory for mass transfer. In this model, the interfacial region is idealized as a hypothetical film or unstirred layer. Mass transfer involves diffusion across this thin film. Note that the constant value cio implies no resistance to mass transfer in the gas.

In the above theory, the interfacial concentrations Coi and Cli are not measurable directly and are therefore of relatively little immediate use. In order to overcome this apparent difficulty, overall mass transfer rate equations are defined by analogy to the film equations. These are based on overall... 

The conclusions we may draw from these results are that, in general, interfacial turbulence will occur, and that it will increase the rate of mass transfer in these otherwise unstirred systems. Monolayers will prevent this turbulence, and theory and experiment are then in good agreement, in spite of spontaneously formed emulsion. There are no interfacial barriers greater than 1000 sec. cm. due to the presence of a mono-layer, though polymolecular films can set up quite considerable barriers. Usually there are no appreciable barriers due to re-solvation however, in the passage of Hg from the liquid metal into water, the change between the metallic state and the Hg2++ (aq) ion reduces the transfer rate by a factor of the order 1000. 

---