Over-all mass-transfer

Fig. 11. Plot of K (ReiReay (in cm. sec. " ) against C, (dynes cm." ) for spread monolayers of bovine plasma albumin. K refers to the over-all mass-transfer coefficient for isopropanol transferring from water to benzene, and various stirring speeds are employed in the apparatus of Fig. 5(b). R refers to the runs using redistilled water, H to those using 0.01 N HCl, N to those using 0.01 NaOH, and T to those using tap water (60).

Results of experiments in annular flow showed that the over-all mass-transfer coefficient, Kq, based on the tube surface area and the liquid-film compositions, was a function of both gas and liquid superficial Reynolds number, but depended much more strongly on that of the liquid. When plotted as jo factors, that is. 

On the basis of the familiar two-film theory, the over-all mass transfer coefficients, as well as the over-all heights and times of transfer units,... 

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 experimental determination of the film coefficients kL and kc is very difficult. When the equilibrium distribution between the two phases is linear, over-all coefficients, which are more easily determined by experiment, can be used. Over-all coefficients can be defined from the standpoint of either the liquid phase or gas phase. Each coefficient is based on a calculated over-all driving force Ac, defined as the difference between the bulk concentration of one phase (cL or cc) and the equilibrium concentration (cL or cc ) corresponding to the bulk concentration of the other phase. When the controlling resistance is in the liquid phase, the over-all mass transfer coefficient KLa is generally used ... 

The connection between the film mass transfer coefficients and the over-all mass transfer coefficients is provided by the two-film theory from Lewis and Whitman (1924) the total resistance to mass transfer is the sum of the resistances in each phase. 

Rearranging equation 3-8 yields an equation relating the over-all mass transfer coefficient to the individual film coefficients ... 

Many parameters affect the mass transfer between two phases. As we discussed above, the concentration gradient between the two phases is the driving force for the transfer and this, together with the over-all mass transfer coefficient, determines the mass transfer rate. The influence of process parameters (e. g. flow rates, energy input) and physical parameters (e. g. density, viscosity, surface tension) as well as reactor geometry are summed up in the mass transfer coefficient. The important parameters for Kta in stirred tank reactors are ... 

The over-all resistance is then the sum of the individual resistances (see equation 3-8) and the over-all mass transfer coefficient KLa takes all of them into account. In practice, it is often not possible to determine the mass transfer coefficient for a dispersed liquid or solid... 

Since it is difficult to measure interfacial concentrations of the gas and liquid film (PAi and cAi) and the distance in direction of diffusion (Zg and Z.), this problem can be eliminated by using the over-all mass transfer coefficients, K( and Kg, for the liquid and gas respectively. The rate of absorption of the solute depends on the concentration difference or gradient of the solute between the liquid and gas phases. This concentration gradient can also be expressed in terms of the difference between... 

Hixson and Knox also suggest an over-all mass transfer coefficient, Fo, defined by the relationship... 

Mass transfer data in the region of transition between molecular flow and laminar flow have been recently gathered by Cooke (C2). In a study of sublimation of naphthalene spheres, under vacuum, he discovered that the data collected can be correlated by a concept of over-all mass-transfer coefficient equal to the reciprocal of the sum of the resistance in the gas phase and a resistance corresponding to the Langmuir equation for the interface. An emission or accommodation coefficient of 0.10 was found to fit the data. 

K = over-all mass transfer coefficient, k = mass transfer film coefficient,... 

Over-all Transfer Units. As explained in Chap. 5, the practical difficulties entering into the use of true equilibrium interfacial concentrations xe% and xrx have led to the introduction of over-all mass-transfer coefficients Ke and Kr which express the rate of diffusion in terms of over-all concentration gradients xr — x r) and x% — Xe) [Eqs. (5.57) and (5.59)]. Their use requires that the distribution coefficient. 

A number of attempts have been made to relate the values of kA obtained for one system with those for other systems. The coefficients involve resistances to mass transfer for both the vapor and the liquid phases, and it has been customary to apply relations based on the Lewis and Whitman two-film theory. It is doubtful that such a theory is applicable in this case since it is difficult to visualize the conditions inherent in this theory for a liquid phase in a packed tower. Further studies of the mechanism of mass transfer between the vapor and the liquid for systems approximating the conditions in a packed tower are needed to furnish a sound basis for correlating the over-all mass-transfer coefficients. 

Kq over-all mass-transfer coefficient, (mols)/(unit time) (unit pressure difference) (unit interfacial surface) a interfacial area of bubble 6 = contact time of bubble with liquid Assuming G, P, i/ , and Koa are constant, this equation can be integrated to give... 

Walter and Sherwood (Ref. 31) gave a correlation for the plate efficiency based on the derivation of Eq. (17-3). Using the two-film absorption concept (Ref. 33), they separated the over-all mass-transfer resistance into a liquid- and vapor-fiilm resistance. 

Ka over-all mass-transfer coefficient kaa gas-ffim mass-transfer coefficient Kl over-all mass-transfer coefficient kua liquid-film mass-transfer coefficient L liquid in slug... 

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