Individual phase transfer coefficient

This model was found to give a slightly better fit of the distillation data than did the Bolles-Fair model. It is somewhat more cumbersome to use, however, because of the need to evaluate individual-phase transfer coefficients. 

This shows that the relationship between the individual-phase transfer coefficients and the overall coefficient takes the form of addition of resistances (hence two-resistance theory). In similar fashion, is a measure of q and can be used to define another overall coefficient K... 

The individual phase transfer coefficients k, and k g are often of the same order of magnitude. However, the value of Ha can vary over a wide range depending on the nature of species A and the liquid phase. If a gas species is highly soluble in the liquid (Figure 3.3.3 illustrates such a system), has a small value, which makes... 

Equation (3.4.8) relates the overall mass-transfer coefficient Kxg to the individual mass-transfer coefficients kxg and kxi- Relations between the overaU transfer coefficient and the individual phase transfer coefficients for other types of concentration driving gradients are also of considerable use. Consider... 

The various results considered above for a gas-Uquid (or vapor-Uquid) system were obtained for absorption of species A from gas (or vapor) into a liquid. If species A is being stripped from the liquid into gas (or vapor) phase, only the direction of transport changes therefore the flux expressions (3.4.3)-(3.4.6) are changed by a minus sign, as are the concentration profiles in the two phases. However, the relations between the overall transfer coefficient K and the individual phase transfer coefficient k remain unaffected by the direction of transport. 

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 ... 

According to assumptions and concentration profiles, illustrated in Fig. 2.1 A, solute being extracted through a hydrophobic flat membrane can be described by the solute flux from the bulk aqueous phase to the bulk organic phase in terms of individual mass-transfer coefficients at steady state and additivity of a one-dimensional series of diffusion resistances. Overall mass-transfer coefficient, Ap/p ... 

Ai is the interfacial area between the liquid and vapor phases, xa and are the interfacial mole fractions, xa and y>A are the bulk-phase mole fractions, and ky are the individual mass transfer coefficients for the liquid and vapor phases, respectively. 

Under which circumstances does the gas phase individual mass transfer coefficient dominate a separation When is the liquid phase individual mass transfer coefficient dominant ... 

By convention, distillation calculations are based on the gas (vapor) phase, since usually most of the resistance is in that phase. Note also that since components are diffusing in both directions, the coefficient has a slightly different definition (see Table 8.3 for the individual mass transfer coefficients, which are primed). Further, the equilibrium ratio is replaced by the slope of the equilibrium curve, m. The overall coefficient is, then. 

Individual heat-transfer coefficient, W/m -°C or Btu/ft -h-°F Mass flux relative to a plane of zero velocity, kg mol/m -s or lb mol/ft -h J, Jg, of components A and B, respectively average value of component A, caused by turbulent action Colburn factor for heat transfer, hlCpG) Cgfifkfl, dimensionless Colburn j fector for mass transfer, (ky MlG lpD Y, dimensionless Overall mass-transfer coefficient in gas phase, kg mol/m -s-unit mole fraction or lb mol/ft -h-unit mole fraction Ky, new value in Example 21.5... 

Individual mass-transfer coefficient k, cm/s or ft/s k r, minimum coefficient for suspended particle (Fig. 21.6) k, effective internal coefficient [Eq. (21,65)] kc, average value over time tj, k, ky, in liquid phase and gas phase, respectively, based on mole-fraction differences, kg mol/m -s-unit mole fraction or lb mol/ft -h-unit mole fraction Effective mass-transfer coefficient in one-way diffusion kc, cm/s or ft/s k, in gas phase, kg mol/m -s-unit mole fraction or lb mol/ft -h-unit mole fraction also new values in Example 21.5 Length of pipe or tube, m or ft... 

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 ... 

The mass transfer resistances strongly depend on the nature of the hydrodynamics in the contacting device and the mode of operation. Many devices have been used to study two-phase mass transfer at or near the liquid-liquid interface. Hence, the hydrodynamic characteristics of ion transport through a membrane were presented to evaluate the feasibility that this permeation system can be calibrated as a standardized liquid-liquid system for studying the membrane-moderated PT-catalyzed reaction. The individual mass transfer coefficients and diffusivities for the aqueous phase, organic phase, and membrane phase were determined and then correlated in terms of the conventional Sh-Re-Sc relationship. The transfer time of quaternary salt across the membrane and the thickness of the hydrodynamic diffusion boundary layer are calculated and then the effect of environmental flow conditions on the rate of membrane permeation can be accurately interpreted [127]. 

Alternatively, the individual mass transfer coefficients can be estimated. In general, the resistance to mass transfer occurs in both phases and these partial resistances can be added together to obtain the overall value. Correlations for both sides of the phase boundaries are given in Table 3. For the inner side... 

Spray Towers. The performance of a spray tower will be a function of the variation of the individual mass-transfer coefficients k of the two phases and the interfacial area a with operating conditions. The value of k for the dispersed phase can be expected to depend on drop size, diffusivity, and... 

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