Mass diffusional

Although they are termed homogeneous, most industrial gas-phase reactions take place in contact with solids, either the vessel wall or particles as heat carriers or catalysts. With catalysts, mass diffusional resistances are present with inert solids, the only complication is with heat transfer. A few of the reactions in Table 23-1 are gas-phase type, mostly catalytic. Usually a system of industrial interest is liquefiea to take advantage of the higher rates of liquid reactions, or to utihze liquid homogeneous cat ysts, or simply to keep equipment size down. In this section, some important noncatalytic gas reactions are described. 

We will limit ourselves to a discussion of systems where the reference velocity for the determination of the mass diffusional flux disappears, cf. (1.153). As a... 

Carberry, J.J. Heat and mass diffusional intrusions in catalytic reactor behavior. Catal. Rev. 1969, 3 (1), 61-91. 

The Rouse-Bueche theory is useful especially below 1% concentration. However, only poor agreement is obtained on studies of the bulk melt. The theory describes the relaxation of deformed polymer chains, leading to advances in creep and stress relaxation. While it does not speak about the center-of-mass diffusional motions of the polymer chains, the theory is important because it serves as a precursor to the de Gennes reptation theory, described next. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Diffusion and Mass Transfer During Leaching. Rates of extraction from individual particles are difficult to assess because it is impossible to define the shapes of the pores or channels through which mass transfer (qv) has to take place. However, the nature of the diffusional process in a porous soHd could be illustrated by considering the diffusion of solute through a pore. This is described mathematically by the diffusion equation, the solutions of which indicate that the concentration in the pore would be expected to decrease according to an exponential decay function. 

Below about 0.5 K, the interactions between He and He in the superfluid Hquid phase becomes very small, and in many ways the He component behaves as a mechanical vacuum to the diffusional motion of He atoms. If He is added to the normal phase or removed from the superfluid phase, equiHbrium is restored by the transfer of He from a concentrated phase to a dilute phase. The effective He density is thereby decreased producing a heat-absorbing expansion analogous to the evaporation of He. The He density in the superfluid phase, and hence its mass-transfer rate, is much greater than that in He vapor at these low temperatures. Thus, the pseudoevaporative cooling effect can be sustained at practical rates down to very low temperatures in heHum-dilution refrigerators (72). 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Siegel, Sparrow, and Hallman, Appl. Sd. Res. Sec. A., 7, 386 (1958). SissomandPitts, Elements of Transpoit Phenomena, McGraw-HiU, 1972. Skelland, Diffusional Mass Transfer, Wiley (1974). 

The phenomenological aspects of diffusional mass transfer in adsorption systems can be described in terms of Fick s law ... 

For an adsorbate which is homogeneous within the patches of reconstructed and unreconstructed surface only the diffusional exchange of mass between these two types contributes to the time evolution. The equations of motion read... 

To evaluate the average diffusional flux, the total mass-transfer rate from the entire surface of the bubble must be divided by that entire surface ... 

Since the total mass transfer rate of B is zero, there must be a bulk flow of the system towards the liquid surface exactly to counterbalance the diffusional flux away from the surface, as shown in Figure 10.1, where ... 

Whatever the physical constraints placed on the system, the diffusional process causes the two components to be transferred at equal and opposite rates and the values of the diffusional velocities uDA and uDB given in Section 10.2.5 are always applicable. It is the bulk How velocity uF which changes with imposed conditions and which gives rise to differences in overall mass transfer rates. In equimolecular counterdiffusion. uF is zero. In the absorption of a soluble gas A from a mixture the bulk velocity must be equal and opposite to the diffusional velocity of B as this latter component undergoes no net transfer. 

Thus, the diffusional process does not give rise to equal and opposite mass fluxes. 

Thus, the diffusional process in a liquid gives rise to a situation where the components are being transferred at approximately equal and opposite mass (rather than molar) rates. 

The effectiveness factor accounts for the diffusional resistances in the liquid-filled catalyst pores. It does not account for the mass transfer resistance between the liquid and gas phases. This is the job of the ki and kg terms. 

Confined flows typically exhibit laminar-flow regimes, i.e. rely on a diffusion mixing mechanism, and consequently are only slowly mixed when the diffusion distance is set too large. For this reason, in view of the potential of microfabrication, many authors pointed to the enhancement of mass transfer that can be achieved on further decreasing the diffusional length scales. By simple correlations based on Fick s law, it is evident that short liquid mixing times in the order of milliseconds should result on decreasing the diffusion distance to a few micrometers. 

During electrolysis there is no change in composition of an individual melt close to the electrode surfaces only its quantity (volume) will change. The resulting void space is filled again by flow of the entire liquid melt mass. This flow replaces the diffusional transport of ions customarily associated with aqueous solutions. This has particular consequences for the method used to measure ionic transport numbers ... 

There is a need for rigorous analysis of such systems. The thickness of the water film may be less than or comparable to the diffusional film thickness and this has particular relevance to reactions that have mass-transfer limitations. The effect of local pH has to be assessed properly. The mechanism of uptake of the substrate also needs elucidation. 

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