Interphase mass transfers equilibrium

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Under certain conditions, it will be impossible for the metal and the melt to come to equilibrium and continuous corrosion will occur (case 2) this is often the case when metals are in contact with molten salts in practice. There are two main possibilities first, the redox potential of the melt may be prevented from falling, either because it is in contact with an external oxidising environment (such as an air atmosphere) or because the conditions cause the products of its reduction to be continually removed (e.g. distillation of metallic sodium and condensation on to a colder part of the system) second, the electrode potential of the metal may be prevented from rising (for instance, if the corrosion product of the metal is volatile). In addition, equilibrium may not be possible when there is a temperature gradient in the system or when alloys are involved, but these cases will be considered in detail later. Rates of corrosion under conditions where equilibrium cannot be reached are controlled by diffusion and interphase mass transfer of oxidising species and/or corrosion products geometry of the system will be a determining factor. 

First, we must consider a gas-liquid system separated by an interface. When the thermodynamic equilibrium concentration is not reached for a transferable solute A in the gas phase, a concentration gradient is established between the two phases, and this will create a mass transfer flow of A from the gas phase to the liquid phase. This is described by the two-film model proposed by W. G. Whitman, where interphase mass transfer is ensured by diffusion of the solute through two stagnant layers of thickness <5G and <5L on both sides of the interface (Fig. 45.1) [1—4]. 

Sorption/desorption is one of the most important processes influencing movemement of organic pollutants in natural systems. Sorption with reference to a pollutant is its transfer from the aqueous phase to the solid phase on the other hand, desorption is its transfer from the solid phase to the aqueous phase. Similar to all interphase mass-transfers, the sorption/ desorption process can be defined by the final-phase equilibrium of the pollutant at the aqueous-solid phase interface and the time required to approach final equilibrium. 

If the T and P of a multiphase system are constant, then the quantities capable of change are the individual mole numbers rf of the various chemical species i in the various phases p. In the absence of chemical reactions, which is assumed here, the ft may change only by interphase mass transfer, and not (because the system is closed) by the transfer of matter across the boundaries of the system. Hence, for phase equilibrium in a 7T-phase system, equation 212 is subject to a set of material balance constraints ... 

Tray Efficiencies in Tray Absorbers ana Strippers Computations of the theoretical trays N assume that the liquid on each tray is completely mixed and that the vapor leaving the tray is in equilibrium with the liquid. In practice, complete equilibrium cannot exist since interphase mass transfer requires a finite driving force. This leads to the definition of an overall tray efficiency... 

In this case, as shown in Figure 4, the subsystems are stoichiometry, material balance, energy balance, chemical kinetics, and interphase mass transfer. The mass transfer phenomena can be subdivided into (1) phase equilibrium which defines the driving force and (2) the transport model. In a general problem, chemical kinetics may be subdivided into (1) the rate process and (2) the chemical equilibrium. The next step is to develop models to describe the subsystems. Except for chemical kinetics, generally applicable mathematical equations based on fundamental principles of physics and chemistry are available for describing the subsystems. 

The so-called Two Film Theory (Lewis and Whiteman, 1923-24) assumes the formation of laminar boundary layers on both sides of the interphase. Mass transfer through these boundary layers can only be effected by means of diffusion, while the phase transition is immeasurably fast, Fig. 86. Consequently, an equilibrium predominates in the interphase and the saturation concentration cG of the gas in the interphase ( ) obeys Henry s law ... 

If the adsorption equilibrium is not attained instantaneously, a different analysis is needed. Toei et al. (T18) studied the mechanism of heat and mass transfer between bubbles and emulsion phase under such circumstances. The dependence of diffusion rate on bulk flow across the bubble interface also becomes important when coarse particles are fluidized (H16). For two-dimensional bubbles Chavarie and Grace (C7a) compared various interphase mass-transfer models. 

Fig. 5 illustrates a physical model of the chromatography process. Initially, there is a dynamic equilibrium of molecules between the phases. Then, one phase is moved relative to the other with an average velocity, v. In the stationary phase, molecules do not move while in the mobile phase, molecules move with a velocity equal to v. Provided that the interphase mass transfer rate is fast relative to the flow rate of the mobile phase, the time-average distribution of a molecule between the phases is statistically equal to the equilibrium distribution as determined by the distribution constant. 

The thickness of the fictitious film can neither be predicted nor measured experimentally. This limits the use of the film theory to directly calculate the mass transfer coefficients from the diffusivity. Nevertheless, the film theory is often applied in a two-resistance model to describe the interphase mass transfer between the two contacting phases (gas and liquid). This model assumes that the resistance to mass transfer only exists in gas and liquid films. The interfacial concentrations in gas and liquid are in equilibrium. The interphase mass transfer involves the transfer of mass from the bulk of one phase to the interfacial surface, the transfer across the interfacial surface into the second phase, and the transfer of mass from the interface to the bulk of the second phase. This process is described graphically in Fig. 1. 

Clearly, from these results, it is a species partial molar Gibbs energy difference between phases, rather than a concentration difference, that is the driving force for interphase mass transfer in the approach to equilibrium. See, for example, of J. W. Tester and M. Modell, Thermodynamics and Its Applications, 3rd ed., Prentice Hall, Englewood Cliffs. N.J. (1997) Chapter 7. 

Separation operations are interphase mass transfer processes because they involve the creation, by the addition of heat as in distillation or of a mass separation agent as in absorption or extraction, of a second phase, and the subsequent selective separation of chemical components in what was originally a one-phase mixture by mass transfer to the newly created phase. The thermodynamic basis for the design of equilibrium staged equipment such as distillation and extraction columns are introduced in this chapter. Various flow arrangements for multiphase, staged contactors are considered. 

In order to achieve a separation of chemical species, a potential must exist for the different species to partition between the two phases to different extents. This potential is governed by equilibrium thermodynamics, and the rate of approach to the equilibrium composition is controlled by interphase mass transfer. By intimately mixing the two phases, we enhance mass transfer rates, and the maximum degree of partitioning is more quickly approached. After sufficient phase contact, the separation operation is completed by employing gravity and/or a mechanical technique to disengage the two phases. 

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) ... 

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