Interfacial transfer transport coefficients

Interfacial transfer of chemicals provides an interesting twist to our chemical fate and transport investigations. Even though the flow is generally turbulent in both phases, there is no turbulence across the interface in the diffusive sublayer, and the problem becomes one of the rate of diffusion. In addition, temporal mean turbulence quantities, such as eddy diffusion coefficient, are less helpful to us now. The unsteady character of turbulence near the diffusive sublayer is crucial to understanding and characterizing interfacial transport processes. 

Dungan et al. [186] have measured the interfacial mass transfer coefficients for the transfer of proteins (a-chymotrypsin and cytochrome C) between a bulk aqueous phase and a reverse micellar phase using a stirred diffusion cell and showed that charge interactions play a dominant role in the interfacial forward transport kinetics. The flux of protein across the bulk interface separating an aqueous buffered solution and a reverse micellar phase was measured for the purpose. Kinetic parameters for the transfer of proteins to or from a reverse micellar solution were determined at a given salt concentration, pH, and stirring... 

From the above outline, the mass-transport problem is seen to consist of coupled boundary value problems (in gas and aqueous phase) with an interfacial boundary condition. Cloud droplets are sufficiently sparse (typical separation is of order 100 drop radii) that drops may be treated as independent. For cloud droplets (diameter 5 ym to 40 pm) both gas- and aqueous-phase mass-transport are dominated by molecular diffusion. The flux across the interface is given by the molecular collision rate times an accommodation coefficient (a 1) that represents the fraction of collisions leading to transfer of material across the interface. Magnitudes of mass-accommodation coefficients are not well known generally and this holds especially in the case of solute gases upon aqueous solutions. For this reason a is treated as an adjustable parameter, and we examine the values of a for which interfacial mass-transport limitation is significant. Values of a in the range 10 6 to 1 have been assumed in recent studies (e.g.,... 

Once the equations have been solved to obtain the composition and temperature profiles, the diffusion fluxes can be calculated and the interfacial transfer rates determined. It is customary to determine, on the basis of the chosen hydrodynamic model, mass transfer coefficients that reflect the overall transfer facility (molecular and turbulent transport) of the phase under consideration. 

Stemling and Scriven wrote the interfacial boundary conditions on nonsteady flows with free boundary and they analyzed the conditions for hydrodynamic instability when some surface-active solute transfer occurs across the interface. In particular, they predicted that oscillatory instability demands suitable conditions cmcially dependent on the ratio of viscous and other (heat or mass) transport coefficients at adjacent phases. This was the starting point of numerous theoretical and experimental studies on interfacial hydrodynamics (see Reference 4, and references therein). Instability of the interfacial motion is decided by the value of the Marangoni number, Ma, defined as the ratio of the interfacial convective mass flux and the total mass flux from the bulk phases evaluated at the interface. When diffusion is the limiting step to the solute interfacial transfer, it is given by... 

In the rate-based models, the mass and energy balances around each equilibrium stage are each replaced by separate balances for each phase around a stage, which can be a tray, a collection of trays, or a segment of a packed section. Rate-based models use the same m-value and enthalpy correlations as the equilibrium-based models. However, the m-values apply only at the equilibrium interphase between the vapor and liquid phases. The accuracy of enthalpies and, particularly, m-values is crucial to equilibrium-based models. For rate-based models, accurate predictions of heat-transfer rates and, particularly, mass-transfer rates are also required. These rates depend upon transport coefficients, interfacial area, and driving forces. It... 

The mass transfer coefficient km for gas-phase plus interfacial mass transport has units s 1. The rate / aq in (12.1 IS) is in equivalent gas-phase concentration units, but the conversion to aqueous-phase units is straightforward multiplying by H h. The mass transfer coefficient as a function of the accommodation coefficient cc and the droplet radius is shown in Figure 12.13. For values of a > 0.1 the mass transfer rate is not sensitive to the exact value of a. However, for a < 0.01, surface accommodation starts limiting the mass transfer rate to the drop, and km, decreases with decreasing a for all droplet sizes. 

Table 4.17 Expressions for gas-particle mass transfer n , g, Mq and Haq molecule density of the same substance far from the particle, close to the particle, at particle surface and within the particle (droplet) p — gas partial pressure far from the droplet, c g - aqueous-phase concentration, k - mass transfer coefficient (recalculable into spjecific rate constant) g - gas-phase, aq - aqueous-phase, het - interfadal layer (chemistry), in - interfacial layer (transport), coll - collision, ads — adsorption (surface striking), sol - dissolution, diff -diffusion in gas-phase, des - desorption.

While the lower order models described in Section 6.3 are useful for the quick prediction of the overall performance of a reactor, these models often rely on simplified flow approximations and often fail to account for change in the local fluid dynamics or transport processes during the presence of internal hardware or changes in flow regimes. Moreover, these models are also based on empirical knowledge (as discussed in Section 6.4) of several parameters such as interfacial area, dispersion coefficients, and mass transfer coefficients. Some of these limitations may be avoided by using CFD models for simulations of gas-liquid-solid flows in three-phase slurry and fluidized bed. 

It was further shown that individual transport coefficients could be combined into overall mass transfer coefficients to represent transport across adjacent interfacial layers. The underlying concept is referred to as two-film theory. Chapter 1 has been confined to simple applications of the mass transfer coefficient which is either assumed to be known, or is otherwise evaluated numerically in simple fashion. 

Appropriate boundary conditions arise from the actual process or the problem statement. They essentially are given, or, more often, must be deduced from, physical principles associated with the problem. These physical principles are usually mathematical statements that show that the dependent variable at the boundary is at equilibrium, or, if some transport is taking place, that the flux is conserved at the boimdary. Another type of boundary condition uses interfacial transport coefficients (e g. heat Iransfer or mass transfer coefficients) that express the flux as the product of the interphase transport coefficient and some kind of driving force. 

Recall the mathematical classification of boundary conditions summarized in Table 3.5. For example, in energy transport, the first type corresponds to the specified temperature at the boundary the second type corresponds to the specified heat flux at the boundary and the third type corresponds to the interfacial heat transport governed by a heat transfer coefficient. 

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

After phase separation, two sets of equations such as those in Table A-1 describe the polymerization but now the interphase transport terms I, must be included which couples the two sets of equations. We assume that an equilibrium partitioning of the monomers is always maintained. Under these conditions, it is possible, following some work of Kilkson (17) on a simpler interfacial nylon polymerization, to express the transfer rates I in terms of the monomer partition coefficients, and the iJolume fraction X. We assume that no interphase transport of any polymer occurs. Thus, from this coupled set of eighteen equations, we can compute the overall conversions in each phase vs. time. We can then go back to the statistical derived equations in Table 1 and predict the average values of the distribution. The overall average values are the sums of those in each phase. 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

Requirements regarding laboratory liquid-liquid reactors are very similar to those for gas-liquid reactors. To interpret laboratory data properly, knowledge of the interfacial area, mass-transfer coefficients, effect of contaminants on mass-transport processes, ionic characteristics of the system, etc. is needed. Commonly used liquid-liquid reactors have been discussed by Doraiswamy and Sharma (1984). 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

Due to the ionic nature of cephalosporin molecules, the interfacial chemical reaction may in general be assumed to be much faster than the mass transfer rate in the carrier facilitated transport process. Furthermore, the rate controlling mass transfer steps can be assumed to be the transfer of cephalosporin anion or its complex, but not that of the carrier. The distribution of the solute anion at the F/M and M/R interfaces can provide the equilibrium relationship [36, 69]. The equilibrium may be presumably expressed by the distribution coefficients, mf and m at the F/M and M/R interfaces, respectively and these are defined as... 

Eqns. (3.4-1) to (3.4-3) are practical for describing interfacial transport in combination with transfer coefficients. The use of transfer coefficients is a simplification that involves the linearization of gradients over the boundary layer. Let us assume that a solid dissolves from a non-porous plate into a flowing fluid that sweeps the surface. According to the boundary layer theory, there is a smooth transition between the immobile fluid located on the plane up to the bulk of the fluid that moves with a uniform velocity. In this layer, the three transfer processes... 

Interfacial mass transfer is an important consideration in many dynamic processes involving the transport of a gaseous species across a gas-liquid interface. In particular the rate of trace gas incorporation into aqueous drops in the atmosphere has recently received much attention because of its relevance to acid precipitation (1,2). In the present paper, mass accommodation coefficient measurements are reported for O3 and SO2 on water surfaces, using an UV absorption-stop flow technique. The results are incorporated into a simple model considering the coupled interfacial mass transfer and aqueous chemistry in aqueous drops. Some implications of the measured accommodation coefficients on the oxidation of SO2 by O3 in cloud water are discussed. 

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