Diffusional film resistances

Diffusional film resistances outside the liquid membrane... 

The diffusional film resistances on the two sides of the liquid membrane, the feed side and the receiving (or strip) side, have been ignored in the preceding treatment. They can be quite important when the membrane transport rates and/or the interfacial reaction rates are high. Two examples where external mass-transfer resistances are important are briefly considered below. 

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. 

Colburn, A. P. (1939) Trans. Am Inst. Chem. Eng. 35, 211. The simplified calculation of diffusional processes, general considerations of two-film resistances. 

One final issue remains to be resolved Of the portion of the AEpi that is due to resistance, what part is caused by solution resistance and what part is caused by film resistance To explore this issue we examined the electrochemistry of a reversible redox couple (ferrocene/ferricinium) at a polished glassy carbon electrode in the electrolyte used for the TiS 2 electrochemistry. At a peak current density essentially identical to the peak current density for the thin film electrode in Fig. 27 (0.5 mV see ), this reversible redox couple showed a AEpi of 0.32 V (without application of positive feedback). Since this is a reversible couple (no contribution to the peak separation due to slow kinetics) and since there is no film on the electrode (no contribution to the peak separation due to film resistance), the largest portion of this 0.32 V is due to solution resistance. However, the reversible peak separation for a diffusional one-electron redox process is —0.06 V. This analysis indicates that we can anticipate a contribution of 0.32 V -0.06 V = 0.26 V from solution resistance in the 0.5 mV sec control TiS2 voltammogram in Fig. 27. 

A.P. Colburn, The Simplified Calculation of Diffusional Processes, General Considerations of Two Film Resistance, Trans. A.I.Ch.E, 35, 211 (1939). 

Apart from diffusion through the gas-side boundary film, adsorption kinetics are predominantly determined by the diffusion rate through the pore structure. The diffusion coefficient is governed by both the ratio of pore diameter to the radius of the molecule being adsorbed and other characteristics ofthe component being adsorbed. The rate of adsorption is governed primarily by diffusional resistance. Pollutants must first diffuse from the bulk gas stream across the gas film to the exterior surface ofthe adsorbent (gas film resistance). 

The Biot number measures the relative resistance contributed by the stagnant film surrounding the particle to the internal diffusional resistance. For most gas phase applications, this number is of the order of 10 to 100, indicating that the internal diffusional resistance is more important than the film resistance. 

Although in most gas phase applications, the Biot number is usually greater than 100, indicating that the gas film resistance is not as important as the internal diffusional resistance. In systems with fast surface diffusion, this may not be true as we shall see in this example. 

Now let us consider the same set of values but this time we assume that there is no surface diffusion. The Biot number in this case is Bi = 52. Thus we see that in the absence of surface diffusion the gas film resistance becomes negligible compared to the internal diffusional resistance. 

When the film resistance becomes negligible compared to the internal diffusional resistance, that is when Bi is very large, the fractional uptake given in eq.(9.2-33) will reduce to simpler form, tabulated in Table 9.2-3 for the three shapes of particle. 

External film resistance plus two intraparticlo diffusional resis-j tances (macropore-micropore). j ... 

It is evident that for linear systems the preci.se nature of the dispersive forces, whether external film resistance, diffusional resistance, or axial dispersion, has only a very minor effect on the shape of the transient concentration response. This observation has two practically important consequences. 

The model of Santacesaria et is an extension of the linear driving force model, with fluid side resistance, for a nonlinear multicomponent Langmuir system. It includes axial dispersion, and the combined effects of pore diffusion and external fluid film resistance are accounted for throu an overall rate coefficient. Intracrystalline diffusional resistance is neglected and equilibrium between the fluid in the macfopores and in the zeolite crystals is... 

In Figure 5.11, we described the interplay between electron transfer and mass transfer and how both are required to observe a current from a G. sulfurreducens biofilm. It is difficult to determine the role of mass transfer in biofilms simply from cyclic voltammograms usually, certain electrochemical setups are required to investigate mass transfer via electrochemical methods. In our case, we used a combination of EIS and RDEs to study electron transfer and diffusional processes in G. sulfurreducens biofilms respiring on electrodes [50]. We tested the hypothesis that the RDE can be used as an electrochemical tool that controls diffusional processes when EABs are studied. We determined the film resistance, film capacitance, interfacial resistance, interfacial capacitance, and pseudocapacitance of G. sulfurreducens biofilms as shown in Eigure 5.23. The details of the calculations and experimental procedures are given in the literature [50],... 

Example models with two resistances include external fluid film resistance plus intraparticle diffusion or two internal diffusional resistances such as macropore and micropore. A complex three-resistance model might include the external film resistance plus two intraparticle resistances. Such a... 

One procedure makes use of a box on whose silk screen bottom powdered desiccant has been placed, usually lithium chloride. The box is positioned 1-2 mm above the surface, and the rate of gain in weight is measured for the film-free and the film-covered surface. The rate of water uptake is reported as u = m/fA, or in g/sec cm. This is taken to be proportional to - Cd)/R, where Ch, and Cd are the concentrations of water vapor in equilibrium with water and with the desiccant, respectively, and R is the diffusional resistance across the gap between the surface and the screen. Qualitatively, R can be regarded as actually being the sum of a series of resistances corresponding to the various diffusion gradients present ... 

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...

The partial pressures in the rate equations are those in the vicinity of the catalyst surface. In the presence of diffusional resistance, in the steady state the rate of diffusion through the stagnant film equals the rate of chemical reaction. For the reaction A -1- B C -1-. . . , with rate of diffusion of A limited. 

Overall coefficients cannot be predicted directly from the physical properties and flow rates of a system but must be derived from the individual film coefficients. It is important therefore to be able to relate overall and film coefficients. This can be done if it is realized that the coefficients are in effect conductances. The diffusional resistance of the two films are equal to the reciprocals of the film coefficients, and... 

A simple rectifying column consists of a tube arranged vertically and supplied at the bottom with a mixture of benzene and toluene as vapour. At the top a condenser returns some of the product as a reflux which flows in a thin film down the inner wall of the tube. The tube is insulated and heat losses can be neglected. At one point in the column the vapour contains 70 mol% benzene and the adjacent liquid reflux contains 59 moi% benzene. The temperature at this point is 365 K. Assuming the diffusional resistance to vaponr transfer to be equivalent to the diffusional resistance of a stagnant vapour layer 0.2 mm thick, calculate the rate of interchange of benzene and toluene between vapour and liquid. The molar latent heats of the two materials can be taken as equal. The vapour pressure of toluene at 365 K is 54.0 kN/nt2 and the diffusivity of the vapours is 0.051 cm2/s... 

Gas-liquid reactors. Gas-liquid reactors are quite common. Gas-phase components will normally have a small molar mass. Consider the interface between a gas and a liquid that is assumed to have a flow pattern giving a stagnant film in the liquid and the gas on each side of the interface, as illustrated in Figure 7.2. The bulk of the gas and the liquid are assumed to have a uniform concentration. It will be assumed here that Reactant A must transfer from the gas to the liquid for the reaction to occur. There is diffusional resistance in the gas film and the liquid film. 

The design of fixed-bed ion exchangers shares a common theory with fixed-bed adsorbers, which are discussed in Chapter 17. In addition, Thomas(14) has developed a theory of fixed-bed ion exchange based on equation 18.21. It assumed that diffusional resistances are negligible. Though this is now known to be unlikely, the general form of the solutions proposed by Thomas may be used for film- and pellet-diffusion control. 

Since reactant A must move from gas to liquid for reaction to occur, diffusional resistances enter the rate. Here we will develop everything in terms of the two-film theory. Other theories can and have been used however, they give essentially the same result, but with more impressive mathematics. 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

The resistance in each phase is made up of two parts the diffusional resistance in the laminar film and the resistance in the bulk fluid. All current theories on mass transfer, i. e. film, penetration, and surface renewal assume that the resistance in the bulk fluid is negligible and the major resistance occurs in the laminar films on either side of the interface (Figure 3-2). Fick s law of diffusion forms the basis for these theories proposed to describe mass transfer through this laminar film to the phase boundary. 

There are three distinct mass-transfer resistances (1) the external resistance of the fluid film surrounding the pellet, (2) the diffusional resistance of the macropores of the pellet, and (3) the diffusional resistance of the zeolite crystals. The external mass-transfer resistance may be estimated from well-established correlations (4, 5) and is generally negligible for molecular sieve adsorbers so that, under practical operating conditions, the rate of mass transfer is controlled by either macropore diffusion or zeolitic diffusion. In the present analysis we consider only systems in which one or other of these resistances is dominant. If both resistances are of comparable importance the analysis becomes more difficult. 

Many investigations have been conducted of the mass transfer coefficient at the external surfaces of particles and of other diffusional mechanisms. Some of the correlations are discussed in Chapters 13 and 17. A model developed by Rosen [Ind. Eng. Chem. 46, 1590 (1954)] takes into account both external film and pore diffusional resistance to mass transfer together with a linear isotherm. A numerical example is worked out by Hines and Maddox (1985, p. 485). 

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