Interphase mass transfer rate

By comparing interfacial inactivation rates in a stirred-cell (low and controlled area of exchange) and an emulsion system (high interfacial area), these authors have shown that the use of an emulsion system can be exploited to obtain high solute interphase mass-transfer rates since the rate of specific interfacial inactivation remains low. However, in this system, the presence of an epoxide substrate at high concentration in the organic phase increases the rate of interfacial inactivation. Addition of a sacrificial protein to the system, which can prevent adsorption of the catalytic enzyme at the interface, could provide a method to reduce the rate of interfacial inactivation. 

The interphase mass-transfer rates for the components A, B, and I in the condenser are governed by rate expressions of the form ... 

The linear driving force model (a form of Fick s first law) is often used to determine interphase mass transfer rate coefficients. This equation is expressed as... 

Any of the curves in Fig. 10, which refer to different values of the modified Prater number fi, tend to approach a certain limiting value of the Weisz modulus for which the overall effectiveness factor obviously becomes infinitely small. This limit can be easily determined, bearing in mind that the effective reaction rate can never exceed the maximum interphase mass transfer rate (the maximum rate of reactant supply) which is obtained when the surface concentration approaches zero. To show this, we formulate the following simple mass balance, analogous to eq 62 ... 

K Interphase mass-transfer rate of solute A per interfacial area with respect to fixed coordinates kmol/(s-m2) (lbmoOAh-ft2)... 

INTERPHASE MASS TRANSFER RATES OF CHEMICAL REACTIONS WITH CROSSLINKED POLYSTYRENE Gabriella Schmuckler and Shimon Goldstein... 

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. 

If it is sufficiently rapid, the reaction will also take place in the liquid film adjacent to the phase interface, and very fast reactions may occur only in the film. In either case the continuity equations for the film are required for taking into account the effect of the reaction on the interphase mass-transfer rates... 

Figure 8 Dependence of interphase mass transfer rate on has adsorptivity. (From Bohle and van Swaaij, 1978.)...

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

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. 

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... 

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... 

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. 

Jean-Claude Charpentier, Mass-Transfer Rates in Gas-Liquid Absorbers and Reactors Dee H. Barker and C. R. Mitra, The Indian Chemical Industry-lts Development and Needs Lawrence L. Tavlarides and Michael Stamatoudis, The Analysis of Interphase Reactions and Mass Transfer in Liquid-Liquid Dispersions... 

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. 

In heterogeneous reactions, phase boundaries exist between phases and transport processes the intrinsic rate of reaction should be taken into account simultaneously in reactor design. The combination of mass transfer rates and reaction rates leads to the so-called overall rate. The goal is to express the global rate in terms of the bulk properties of the phases, eliminating the interphase properties. 

The reason for the disparity in performance of such devices in the two services has been clearly outlined by Hachmuth (HI). Bubble-tray towers for distillation, for example, use as the source of energy for dispersion of the gas and for developing the desirable turbulent flow conditions both the expansion of the vapor as it experiences a pressure drop in flowing through the tray, and the liquid head available between trays. In liquid extraction only the liquid head is available. When it is considered that the difference in densities of the contacted phases in distillation may be of the order of 50 to 60 lb./cu. ft., whereas in extraction it is more likely to be of the order of 5 or less, it is easy to understand that in the latter case there is simply insufficient energy available from this source to provide for adequate dispersion and interphase movement. Interfacial area between phases remains small, turbulences developed are of a low order, and mass transfer rates are disappointingly small. 

When heterogeneous mixtures are involved, the conversion rate often is limited by the rate of interphase mass transfer, so that a large interfacial surface is desirable. Thus, solid reactants or... 

When two phases are mixed together (gas-liquid, immiscible liquid-liquid), a fine dispersion of bubbles or drops and a high specific interfacial area are produced because of the intensive turbulence and shear. For this reason, resistance to interphase mass transfer is considerably smaller than in conventional equipment. In addition, a wide range of gas-liquid flow ratios can be handled, whereas in stirred tanks the gas-flow rate is often limited by the onset of flooding. Mass transfer coefficients (kLa) can be 10-100 times higher than in a stirred tank. 

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