Interfacial equilibrium relation

Hence, the liquid-phase resistance controls interphase mass transfer and, for aU practical purposes, yj yji. This is analogous to drawing horizontal tie-lines between the equilibrium and operating lines during graphical analysis of a gas absorber, where vapor-phase mole fraction is plotted on the vertical axis and liquid-phase mole fraction is on the horizontal axis. This assumption allows one to re-express interphase transport on the liquid side of the gas-liquid interface, liquid(C —Cji)aLVL, using the interfacial equilibrium relations given by (24-36) ... 

Hence, the interfacial equilibrium relations, given by (24-42), can be rewritten as... 

The previous three types of liquid-solid equilibria considered equilibrium between two bulk phases we will now briefly look at two types of interfacial adsorption systems where the two bulk phases are either fluid-fluid or fluid-solid. Consider first the interfacial equilibrium relation for a nonelectrolytic surface active solute in an air-water system (a fluid-fluid system). If the surface active solute i is such that the interfacial tension decreases linearly with the surfactant concentration C,i as... 

The interfacial mole fractions yj and Xj can be determined by solving Eq. (5-252) simultaneously with the equilibrium relation = F(x,) to obtain y and Xj. The rate of transfer may then be calculated from... 

If the equilibrium relation y° = F Xi) is sufficiently simple, e.g., if a plot of yfversus Xi is a straight hne, not necessarily through the origin, the rate of transfer is proportional to the difference between the bulk concentration in one phase and the concentration (in that same phase) which would be in equilibrium with the bulk concentration in the second phase. One such difference isy — y°, and another is x° — x. In this case, there is no need to solve for the interfacial compositions, as may be seen from the following derivation. 

Pi =f Ci) or Pi = HCi, equilibrium relation at the interface a = interfacial area/iinit volume Zg, Z-L = film thicknesses The steady rates of solute transfer are... 

Because the interfacial slippage is assumed to be caused by the thin TLCP-rich interlayers, we can form a stress equilibrium relation as ... 

The interfacial concentration x, is computed by combining the equilibrium relation y, = irtx, with the equation kdy - yi) = kdxi - x) to obtain... 

At the other extreme, when the ratio kjmke is much smaller than unity, the interfacial concentration of reactant A may be approximated by the equilibrium relation, = y/m, and the specific absorption rate expression is... 

Calculations of the relations between the input and output amounts and compositions and the number of extraction stages are based on material balances and equilibrium relations. Knowledge of efficiencies and capacities of the equipment then is applied to find its actual size and configuration. Since extraction processes usually are performed under adiabatic and isothermal conditions, in this respect the design problem is simpler than for thermal separations where enthalpy balances also are involved. On the other hand, the design is complicated by the fact that extraction is feasible only of nonideal liquid mixtures. Consequently, the activity coefficient behaviors of two liquid phases must be taken into account or direct equilibrium data must be available. In countercurrent extraction, critical physical properties such as interfacial tension and viscosities can change dramatically through the extraction system. The variation in physical properties must be evaluated carefully. 

Interfacial equilibrium concentrations in the extraction side are related through the expression of the chemical equilibrium parameter... 

To derive a relation for the overall mass transfer coefficient we consider a gas-liquid interface, as sketched in Fig 5.15. Formulate the expressions for the fluxes at both sides of the interface and relate the two unknown interfacial concentrations to each other by use of an equilibrium relation like Henrys law. The flux relations can then be combined in order to eliminate the interfacial concentrations obtaining an overall driving force. 

Finally, the interfacial component mole fractions in each phase must add up to unity and satisfy the equilibrium relations. 

Interfacial equilibrium work of adhesion was calculated using the values of polar and dispersive components of the surface energy according to the relation ... 

This was not the case with the toluene and xylene systems but the mass transfer rate then apparently depends on the direction of solute transfer. In this respect the butanol system was better as the rate was equal in both directions and, in addition, the equilibrium relation was linear. However, for this system the interfacial tension is very low so that general conclusions cannot be drawn from experiments carried out on this system alone. 

At the beginning of this section, it was indicated that the route of overall mass-transfer coefficients was a convenient way of avoiding the difficulties created by the difficult-to-obtain interfacial concentrations Ca/ Pav Xau, etc. We have found it to be so. It is also possible to solve for the interfacial concentration Cab or JCAgi/ otc. from either equations (3.4.3) (3.4.4) if k i, k g and the equilibrium relation are known for given bulk concentrations. For example, from equation (3.4.3),... 

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