Interphase mass transfers

Actual concentration profiles (Fig. 1.28) in the very near vicinity of a mass transfer interface are complex, since they result from an interaction between the mass transfer process and the local hydrodynamic conditions, which change gradually from stagnant flow, close to the interface, to more turbulent flow within the bulk phases. 

According to the Whitman Two-Film theory, the actual concentration profiles, as shown in Fig. 1.28 are approximated for the steady state with no chemical reaction, by that of Fig. 1.29. 

A thin film of fluid exists on either side of the interface. 

Each film is in stagnant or laminar flow, such that mass transfer across the films is by a process of molecular diffusion and can therefore be described by Pick s Law. 

There is zero resistance to mass transfer at the interface, itself, and therefore the concentrations at the interface are in local equilibrium. 

Thus far we have considered only the diffusion of substances within a single phase. In most of the mass-transfer operations, however, two insoluble phases are brought into contact in order to permit transfer of constituent substances between them. Therefore we are now concerned with the simultaneous application of the diffusional mechanism for each phase to the combined system. We have seen that the rate of diffusion within each phase is dependent upon the concentration gradient existing within it. At the same time the concentration gradients of the two-phase system are indicative of the departure from equilibrium which exists between the phases. Should equilibrium he-estahlished  

It is convenient first to consider the equilibrium characteristics of a particular operation and then to generalize the result for others. As an example, consider the gas-absorption operation which occurs when ammonia is dissolved from an ammonia-air mixture by liquid water. Suppose a fixed amount of liquid water is placed in a closed container together with a gaseous mixture of anunonia and air, the whole arranged so that the system can be maintained at constant temperature and pressure. Since ammonia is very soluble in water, some ammonia molecules will instantly transfer from the gas into the liquid, crossing the interfacial surface separating the two phases. A portion- oJLAe-ammonia 

If we now inject additional ammonia into the container, a new set of equilibrium concentrations will eventually be established, with higher concentrations in each phase than were at first obtained. In this manner we can eventually obtain the complete relationship between the equilibrium concentrations in both phases. If the ammonia is designated as substance A, the equilibrium concentrations in the gas and liquid,and mole fractions, respectively, give rise to an equilibrium-distribution curve of the type shown in Fig. 5.1. This curve results irrespective of the amounts of water and air that we start with and is influenced only by the conditions, such as temperature and pressure, imposed upon the three-component system. It is important to note that at equilibrium thc-con-Cjintrations in the lwQ phases.ai LJiot,.equal instead the chemical potential of the ammonia is the. same in. both phases, and it will be recalled (Chap. 2) that it is equality of chemical potentials, not concentrations, which causes the net transfer of solute to stop. 

The curve of Fig. 5.1 does not of course show all the equilibrium concentrations existing within the system. For example, the water will partially vaporize into the gas phase, the components of the air will also dissolve to a small extent in the liquid, and equilibrium concentrations for these substances will also be established. For the moment. we need not consider these equilibria, since they 

Generally speaking, whenever a substance is distributed between two insoluble phases, a dynamic equilibrium of this type can be established. The various equilibria are peculiar to the particular system considered. For example, replacement of the water in the example considered above with another liquid such as benzene or with a solid adsorbent such as activated carbon or replacement of the ammonia with another solute such as sulfur dioxide will each result in new curves not at all related to the first. The equilibrium resulting for a two-liquid-phase system bears no relation to that for a liquid-solid system. A discussion of the characteristic shapes of the equilibrium curves for the various situations and the influence of conditions such as temperature and pressure must be left for the studies of the individual unit operations. Nevertheless the following principles are common to all systems involving the distribution of substances between two insoluble phases  

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 

Let us define two overall mass transfer coefficients one for the rich phase, Ky, and one for the lean phase, Kj,. Hence, the rate of interphase mass transfer for 

Correlations for estimating overall mass-transfer coefficients can be found in McCabe et al. (1993), Perry and Green (1984), Geankoplis (1983), Henley and Seader (1981), King (1980) and Treybal (1980). 

For equimolar counterdiffusion we have the simple result that [p] = [/]. Departures from the identity matrix signify the increasing importance of the convective term in the mass transfer process. 

Equations 7.2.9-7.2.21 apply at all points along the diffusion path in the bulk fluid 

One important difference between the binary and the general multicomponent case is worth recording here. For a binary system all matrices reduce to scalar quantities and we must have 

As noted earlier, we assume that at the interface itself the two phases are in equilibrium with each other. The compositions on either side of the interface are, therefore, related by 

It will sometimes prove useful to linearize the vapor-liquid equilibrium relationship for the interface over the range of compositions obtained in passing from the bulk to the interface conditions 

An additional example of Eq. (2.2) is the distribution function commonly used in solvent extraction  

Flgare 2.4 A schematic diagram of a multistage mass exchanger. 

Altefnatively, for the case of i nhomal, dilute nmss exchange with lii ar equilibrium, NTP can be determined through the Kremser (1930) equation  

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The contrihution to the section on Interphase Mass Transfer of Mr. WiUiam M. Edwards (editor of Sec. 14), who was an author for the sixth edition, is acknowledged. 

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

Rate equations are used to describe interphase mass transfer in batch systems, packed beds, and other contacting devices for sorptive processes and are formulated in terms of fundamental transport properties of adsorbent and adsorbate. 

This chapter sets out to provide a means of handling these types of interphase mass transfer problems taking into consideration their fundamental characterizing variables, the conservation of mass, and appropriate constitutive relationships. 

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. 

This objection is supported by recent results of Moffat ef al. (109, 110), who observed severe interphase mass transfer limitations for the same system, in spite of calculations which predicted the mass transfer rate to be several orders of magnitude greater than the observed rate. As... 

Beek and Kramers (B6) studied the case of interphase mass transfer where the interfacial area expands or contracts as the transfer proceeds. As examples where the interfacial area may change, they mention mass transfer between... 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

Chapter 11 treats reactors where mass and component balances are needed for at least two phases and where there is interphase mass transfer. Most examples have two fluid phases, typically gas-liquid. Reaction is usually confined to one phase, although the general formulation allows reaction in any phase. A third phase, when present, is usually solid and usually catalytic. The solid phase may be either mobile or stationary. Some example systems are shown in Table 11.1. 

An overall mass balance is written for the system as a whole. Interphase mass transfer does not appear in the system mass balance since gains in one phase exactly equal losses in the other. The net result is conceptually identical to Equation (1.3), but there are now two inlets and two outlets and the total inventory is summed over both phases. The result is... 

The phase mass balances are more complicated since the mass in a phase can grow or wane due to interphase mass transfer. The phase balances are... 

Surface Renewal Theory. The film model for interphase mass transfer envisions a stagnant film of liquid adjacent to the interface. A similar film may also exist on the gas side. These h5q>othetical films act like membranes and cause diffu-sional resistances to mass transfer. The concentration on the gas side of the liquid film is a that on the bulk liquid side is af, and concentrations within the film are governed by one-dimensional, steady-state diffusion ... 

Interphase mass transfer between liquid-liquid slugs... 

Figure 4.58 Interphase mass-transfer coefficient obtained for a reaction engineering model [94. Reactor model...

Schrage, R. W., A Theoretical Study of Interphase Mass Transfer. Columbia Univ. Press, New York, 1953. 

Biomass containment in continuously operated bioreactors is an essential prerequisite for the feasibility of practical industrial-scale dye biodegradation. Biofilm airlift reactors have demonstrated excellent performance for their ability to control mixing, interphase mass transfer and biofilm detachment rate. Further studies are required to further exploit the potential of this type of reactors with either aggregated cells or biofilm supported on granular carriers. 

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]. 

Fig. 1.7 Balance region showing convective and diffusive flows as well as interphase mass transfer in and out.

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. 

In 1976 he was appointed to Associate Professor for Technical Chemistry at the University Hannover. His research group experimentally investigated the interrelation of adsorption, transfer processes and chemical reaction in bubble columns by means of various model reactions a) the formation of tertiary-butanol from isobutene in the presence of sulphuric acid as a catalyst b) the absorption and interphase mass transfer of CO2 in the presence and absence of the enzyme carboanhydrase c) chlorination of toluene d) Fischer-Tropsch synthesis. Based on these data, the processes were mathematically modelled Fluid dynamic properties in Fischer-Tropsch Slurry Reactors were evaluated and mass transfer limitation of the process was proved. In addition, the solubiHties of oxygen and CO2 in various aqueous solutions and those of chlorine in benzene and toluene were determined. Within the framework of development of a process for reconditioning of nuclear fuel wastes the kinetics of the denitration of efQuents with formic acid was investigated. 

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