Straight Mass Transfer

Unsteady-state operations (semibatch) where the liquid composition changes with time 

Mixed G/batch uniform L Plug G/batch uniform L 

Fi = F CijlCj, downward molar flow rate of inerts in the liquid phase (mol/s). 

With this nomenclature, we have the following relationships among the various concentration measures. 

The performance equations which are written in terms of F and Fi are useful when the flowing streams have inert carrier material. The equation written in terms of F and F are useful when the flowing streams only contain reactive materials and no inerts. 

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The Rate Equation for Straight Mass Transfer (Absorption) of A... 

Figure 23.1 Setting up the rate equation for straight mass transfer based on the two film theory.

The absorption of A from gas is larger when reaction occurs within the liquid film than for straight mass transfer. Thus for the same concentrations at the two boundaries of the liquid film we have... 

The liquid side coefficients are for straight mass transfer without chemical reaction and are therefore based on flow through the whole film of thickness Xq. 

Since the approach for reacting systems is a straightforward extension of straight mass transfer, let us first develop equations for absorption alone of A by liquid... 

Figure 24.3 Illustration of the design procedure for straight mass transfer in countercurrent towers.

The relationship of the overall gas-phase mass transfer coefficient to the individual film coefficients maybe found from equations 4 and 5, assuming a straight equiHbrium line ... 

Equation 28 and its liquid-phase equivalent are very general and valid in all situations. Similarly, the overall mass transfer coefficients may be made independent of the effect of bulk fiux through the films and thus nearly concentration independent for straight equilibrium lines ... 

Sedimentation is also used for other purposes. For example, relative motion of particles and Hquid iacreases the mass-transfer coefficient. This motion is particularly useful ia solvent extraction ia immiscible Hquid—Hquid systems (see Extraction, liquid-liquid). An important commercial use of sedimentation is ia continuous countercurrent washing, where a series of continuous thickeners is used ia a countercurrent mode ia conjunction with reslurrying to remove mother liquor or to wash soluble substances from the soHds. Most appHcations of sedimentation are, however, ia straight sohd—Hquid separation. 

Comparison of Eqs. (5-255) and (5-257) shows that for systems in which the eqmlibrium line is straight, the overall mass transfer coefficients are related to each other by the equation... 

The concept of a mass-transfer unit was developed many years ago to represent more rigorously what happens in a differential contactor rather than a stagewise contactor. For a straight operating line and a straight equilibrium line with an intercept of zero, the equation for calculating the number of mass-transfer units based on the overall raffinate phase N r is identical to the Kremser equation except for the denominator when the extraction factor is not equal to 1.0 [Eq. (15-23)]. 

It is seen that the Van Deemter equation predicts that the total resistance to mass transfer term must also be linearly related to the reciprocal of the solute diffusivity, either in the mobile phase or the stationary phase. Furthermore, it is seen that if the value of (C) is plotted against 1/Dni, the result will be a straight line and if there is a... 

Figure 9-69. Mass transfer diagrams. The number of transfer units can be determined by the difference in concentration or vapor pressure, particularly over ranges where the equilibrium line is essentially straight. Used by permission of Czermann, J. J., Gyokheqyi, S. L, and Hay, J. J., Petroleum Refiner, V. 37, No. 4 (1958) p. 165 all rights reserved.

Figure 3.11 illustrates the mass transfer coefficient for batch-grown R. rubrum and was computed with various acetate concentrations at 200 rpm agitation speed, 500 lux light intensity, and 30 °C. As the experiment progressed, there was an increase in the rate of carbon monoxide uptake in the gas phase and a gradual decrease in die partial pressure of carbon monoxide. Also, a decrease in the partial pressure of carbon monoxide was affected by acetate concentration in the culture media. The value of the slope of the straight line increased with the decrease in acetate concentrations, i.e. 2.5 to 1 g-l. The maximum mass transfer coefficient was obtained for 1 g-l 1 acetate concentration (KLa = 4.3-h 1). The decrease in mass transfer coefficient was observed with the increase in acetate concentration. This was due to acetate inhibition on the microbial cell population as acetate concentration increased in the culture media. The minimum KLa was 1.2h 1 at 3g l 1 acetate concentration. 

As mentioned earlier, in curved channels a secondary flow pattern of two counter-rotating vortices is formed. Similarly to the situation depicted in Figrue 2.43, these vortices redistribute fluid volumes in a plane perpendicular to the main flow direction. Such a transversal mass transfer reduces the dispersion, a fact reflected in the dependence in Eq. (108) at large Dean numbers. For small Dean numbers, the secondary flow is negligible, and the dispersion in curved ducts equals the Taylor-Aris dispersion of straight ducts. 

Richardson, D. H., Sekulic, D. P., Campo, a.. Low Reynolds number flow inside straight micro channels with irregular cross sections. Heat Mass Transfer 36 (2000) 187-193. 

The analyses of simultaneous reaction and mass transfer in this geometry are similar mathematically to those of the straight cylindrical pore model considered previously, because both are essentally one-dimensional models. In the general case, the Thiele modulus for semiinfinite, flat-plate problems becomes... 

Values for the average vapor-transfer coefficient from the gas phase to the airway epithelium can also be estimated from heat-transfer data in straight, curved, or bifurcating cylindrical tubes by using the analogy between heat transfer and mass transfer. Such an approach has been used by Yeh to predict the diffusional deposition of small particles in the conducting airways. 

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