Mass transfer theories

The actual stage can be a mixing vessel, as in a mixer-settler used for solvent extraction applications, or a plate of a distillation or gas absorption column. In order to allow for non-ideal conditions in which the compositions of the two exit streams do not achieve full equilibrium, an actual number of stages can be related to the number of theoretical stages, via the use of a stage-efficiency factor. 

In this type of apparatus, the two phases do not come to equilibrium, at any point in the contactor and the simulation approach is based, therefore, not on a number of equilibrium stages, but rather on a consideration of the relative rates of transport of material through the contactor by flow and the rate of interfacial mass transfer between the phases. For this, a consideration of mass transfer rate theory becomes necessary. 

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Mass-transfer theory (eq. 17) iadicates that the overall mass-transfer resistance 1 /consists of contributions from each phase, so that the overall HTU is also the sum of two contributions ... 

The factors and Xbm cannot be justified on the basis of mass-transfer theory since they are based on overall resistances. These factors therefore are included in the equations by analogy with the corresponding film equations. 

Simplified Mass-Transfer Theories In certain simple situations, tne mass-transfer coefficients can be calculated from first principles. The film, penetration, and surface-renewal theories are attempts to extend tnese theoretical calculations to more complex sit-... 

Mass-transfer theory indicates that for trays of a given design the factors most hkely to inflnence E in absorption and stripping towers are the physical properties of the flnids and the dimensionless ratio Systems in which the mass transfer is gas-film-controlled may be expected to have plate efficiencies as high as 50 to 100 percent, whereas plate efficiencies as low as 1 percent have been reported for the absorption of gases of low sohibility (large m) into solvents of relatively high viscosity. 

Applying mass transfer theory to a component / in the liquid, assumint good mixing and neglecting atmospheric concentrations, the evaporation molar rate of a single component can be expressed as... 

Sherwood. T.K. Chemical Engineering Education (Fall, 1974), 204. A review of the development of mass transfer theory. ... 

The application of RHSE is primarily in the laminar boundary layer flow regime of Re < 15000, where the edge effect is negligible and the mass transfer theory has been confirmed by experimental investigations. An important consideration in the design of a practical RHSE system is to conform to the theoretical requirement that the boundary layer thickness be thin in comparison to the radius of the RHSE (<5 a). 

The validity of Eq. (12) for correlations of limiting-current measurements was first questioned by Arvia et al. (A5), and later by Wragg and Ross (W13a). The latter found that limiting currents in an annular flow cell could be correlated in better agreement with the Leveque mass-transfer theory if a lower mobility (Stokes-Einstein) product were employed, such as... 

Mass transfer rate processes, 25 279 Mass-transfer resistance, 11 808 external, 25 290—293 Mass-transfer theory, 10 761 Mass transport, electrochemical cell, 9 658-659... 

Ibl, Application of mass transfer theory. The formation of powdered metal deposits, in Advances in Electrochemistry and Electrochemical Engineering (eds. P. Delahay and C. W. Tobias), Vol. 2, J. Wiley and Sons, New York (1962), p. 58. 

Chapter 9 Air-Water Mass Transfer in the Field. The theory of interfacial mass transfer is often difficult to apply in the field, but it provides a basis for some important aspects of empirical equations designed to predict interfacial transport. The application of both air-water mass transfer theory and empirical characterizations to field situations in the environment will be addressed. 

From the viewpoint of the chemical engineer, the application of the fundamentals just discussed takes the form of mass-transfer theory, and the constants Kj are called mass-transfer coefficients. However, some care must be exercised in determining the potential difference between two phases. One cannot simply take the difference between the thermodynamic activities in two phases without ensuring that they are adjusted to the same reference state. The point is illustrated with a brief consideration of the boundary-layer model. 

Several theories have been developed to describe the rate of interphase mass transfer. These include film theory, boundary layer theory, penetration theory, and surface renewal theory. In this chapter we will review the first two, along with an overview of empirical correlations that are used to describe mass transfer. A more thorough overview of mass transfer theories can be found in Bird, Stewart and Lightfoot [48], Clark [49], Logan [50], and Weber and DiGiano [51]. 

As Eg is usually small the detrimental effect of gas phase dispersion on the performance of bubble columns can be neglected in columns less than 20 cm in diameter (61). For illustrating the influence of gas phase dispersion some computed conversions are presented in Fig. 10 (J ). The simulations refer to CO2 absorption in carbonate buffer in a column 5 m in length. Eq was calculated from eqn. (15). The liquid phase dispersion does not affect the conversion in the present case as the process takes place in the diffusional regime of mass transfer theory. As shown in Fig. 10, the decrease in conversion due to gas phase dispersion increases with increasing diameter and gas velocity. However, in the favorable bubbly flow regime and in small diameter columns the effect is less pronounced. 

Bubble columns are convenient for catalytic slurry reactions also (67). It is therefore important to know how the hydrodynamic properties of the gas-in-liquid dispersion is influenced by the presence of suspended solid particles. In the slurry reactor absorption enhancement due to chemical reaction cannot be expected. However, if particle sizes are very small, say less than 5 yum, and if, in addition, the catalytic reaction rate is high a small absorption enhancement can occur ( 8). Usually the reaction is in the slow reaction regime of mass transfer theory. Hence, it is sufficient to know the volumetric mass transfer coefficient, kj a, and there is no need to separate k a into the individual values. 

Kokini, J. L., Bistany, K., Poole, M., and Stier, E. 1982. Use of mass transfer theory to predict viscosity-sweetness interactions of fructose and sucrose solutions containing tomato solids. J. Texture Stud. 13 187-200. 

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