Mass transfer between phases overall coefficients

Evaporation is generally described by a resistance in series model, commonly used to describe mass-transfer between phases. The overall transfer coefficient depends on the rate... 

In the case of mass transfer between two phases - for example, the absorption of a gas component into a liquid solvent, or the extraction of a liquid component by an immiscible solvent - we need to consider the overall as well as the individual phase coefficients of mass transfer. 

Mass transfer, an important phenomenon in science and engineering, refers to the motion of molecules driven by some form of potential. In a majority of industrial applications, an activity or concentration gradient serves to drive the mass transfer between two phases across an interface. This is of particular importance in most separation processes and phase transfer catalyzed reactions. The flux equations are analogous to Ohm s law and the ratio of the chemical potential to the flux represents a resistance. Based on the stagnant-film model. Whitman and Lewis [25,26] first proposed the two-film theory, which stated that the overall resistance was the sum of the two individual resistances on the two sides. It was assumed in this theory that there was no resistance to transport at the actual interface, i.e., within the distance corresponding to molecular mean free paths in the two phases on either side of the interface. This argument was equivalent to assuming that two phases were in equilibrium at the actual points of contact at the interface. Two individual mass transfer coefficients (Ld and L(-n) and an overall mass transfer coefficient (k. ) could be defined by the steady-state flux equations ... 

By suitably choosing the solubility, the concentration of the reactant and the rate of reaction, either the mass transfer coefficients, or the interfacial area or both groups of parameters can be deduced from the overall rate of absorption (lA). Generally but not always, a steady flow of each phase through the reactor is assumed. Indeed the competition between the phsyical and chemical kinetics at the level of mass transfer between gas and liquid (the mass transfer reaction regime where the reaction belongs) may allow for the choice of the type of gas-liquid contactor (I). This is clearly shown in Fig. I that represents schematically the concentration profiles for A and B on each side of the interface. 

One lumps the resistances into a single empirical overall resistance. This is the empiricism used in Illustration 1.6. It will be seen time and again throughout the text whenever mass transfer between two phases is expressed in terms of a single overall mass transfer coefficient K. ... 

Mass transfer between gas bubbles and the emulsion phase was discussed earlier in connection with the treatment of bubbles in fluidized beds thus the overall mass transfer coefficient between the bubble and the emulsion phase may be calculated with the aid of Eqs. (7.5.11)-(7.5.15). 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Some workers have attempted to base the design of humidifiers on the overall heat transfer coefficient between the liquid and gas phases. This treatment is not satisfactory since the quantities of heat transferred through the liquid and through the gas are not the same, as some of the heat is utilised in effecting evaporation at the interface. In fact, at the bottom of a tall tower, the transfer of heat in both the liquid and the gas phases may be towards the interface, as already indicated. A further objection to the use of overall coefficients is that the Lewis relation may be applied only to the heat and mass transfer coefficients in the gas phase. 

The mass transfer coefficients, Kg and Ky, are overall coefficients analogous to an overall heat transfer coefficient, but the analogy between heat and mass transfer breaks down for mass transfer across a phase boundary. Temperature has a common measure, so that thermal equilibrium is reached when the two phases have the same temperature. Compositional equilibrium is achieved at different values for the phase compositions. The equilibrium concentrations are related, not by equality, as for temperature, but by proportionality through an equilibrium relationship. This proportionality constant can be the Henry s law constant Kh, but there is no guarantee that Henry s law will apply over the necessary concentration range. More generally, Kyy is a function of composition and temperature that serves as a (local) proportionality constant between the gas- and liquid-phase concentrations. 

When Kh is a function of composition, the concept of overall mass transfer coefficient stops being useful. Instead, the overall resistance to mass transfer is divided between two him resistances, one for each phase. This is done by assuming that equilibrium is achieved at the interface. The equilibrium values are related by a function having the form of Henry s law ... 

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a the gas-liquid mass transfer coefficient, kx, and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kxa, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kxa reported in the literature are listed in Table 19. 

Mass transfer of ozone from the gas phase to the liquid phase strongly depends on the reactor system and the process conditions. Two characteristic factors are in general important the overall mass transfer coefficient between gas phase and water phase, k, and the specific surface area available for mass transfer, Am. 

The relationships between the overall mass transfer coefficient and the film mass transfer coefficients in both phases are not as simple as in the case of heat transfer, for the following reason. Unlike the temperature distribution curves in heat transfer between two phases, the concentration curves of the diffusing component in the two phases are discontinuous at the interface. The relationship between the interfacial concentrations in the two phases depends on the solubility of the diffusing component. Incidentally, it is known that there exists no resistance to mass transfer at the interface, except when a surface-active substance accumulates at the interface to give additional mass transfer resistance. 

The overall coefficients of liquid-liquid mass transfer are important in the calculations for extraction equipment, and can be defined in the same way as the overall coefficients of gas-liquid mass transfer. In liquid-liquid mass transfer, one component dissolved in one liquid phase (phase 1) will diffuse into another liquid phase (phase 2). We can define the film coefficients /C i (nr h" ) and k (m h ) for phases 1 and 2, respectively, and whichever of the overall coefficients A (m h ), defined with respect to phase 1, or Al2 (mh ) based on phase 2, is convenient can be used. Relationships between the two film coefficients and two overall coefficients are analogous to those for gas-liquid mass transfer that is,... 

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 ). 

Derive the relationship between the overall mass-transfer coefficient for liquid phase Kh and the individual mass-transfer coefficients, kL and kG. How can this relationship be simplified for sparingly soluble gases ... 

In the impinging streams of gas-liquid systems, high relative velocity between phases and collision between droplets favor surface renewing of droplets, resulting in reduced liquid film resistance and thus increased overall mass transfer coefficient. 

Because the concentration at the interface is difficult to determine, Eq. (94) is modified to define the mass transfer rate between the two phases in terms of bulk phase concentrations and an overall mass transfer coefficient ... 

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. 

O. Shell side of microporous hollow fiber module for solvent extraction Na, = V[dha-)/L]N%N°s M Nsh- D Nlt = K = overall mass-transfer coefficient (3 = 5.8 for hydrophobic membrane. (3 = 6.1 for hydrophilic membrane. [E] Use with logarithmic mean concentration difference. dh = hydraulic diameter 4 x cross-sectional area of flow wetted perimeter (p = packing fraction of shell side. L = module length. Based on area of contact according to inside or outside diameter of tubes depending on location of interface between aqueous and organic phases. Can also be applied to gas-liquid systems with liquid on shell side. [118]... 

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