Diffusional resistance

Designing metals and ceramics to resist diffusional flow... 

All three elements can scarcely be identified from impedance spectra of systems with adsorption for example, in many cases the adsorption resistance is masked by the diffusional element. In addition, whenever electrodes of inhomogeneous surfaces (e.g., poly crystalline electrodes) are measured, the resistance-diffusional element - capacitance terms of the adsorption impedance are smeared out yielding a CPE-like impedance. 

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. 

For a non-reactive system, the transport rate in the basic HFCLM technique is determined by five resistances in series feed fluid phase boimdary layer resistance, diffusional resistance through the fluid in the feed fiber pores, CLM resistance in the shell side, diffusional resistance in the fluid in the strip fiber pores, and strip fluid... 

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 ... 

As a consequence of this, i enever bulk dlffusional resistance domin ates Knudsen diffusional resistance, so that 1, it follows that fi 1 also, and hence viscous flow dominates Knudsen streaming. Thus when we physically approach the limit of bulk diffusion control, by increasing the pore sizes or the pressure, we must simultaneously approach the limit of viscous flow. This justifies a statement made in Chapter 5. 

The mesopores make some contribution to the adsorptive capacity, but thek main role is as conduits to provide access to the smaller micropores. Diffusion ia the mesopores may occur by several different mechanisms, as discussed below. The macropores make very Htde contribution to the adsorptive capacity, but they commonly provide a major contribution to the kinetics. Thek role is thus analogous to that of a super highway, aHowkig the adsorbate molecules to diffuse far kito a particle with a minimum of diffusional resistance. 

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...

A further problem is possible if the reinforcements are very small. Coarsening of the particles or whiskers may occur driven by Ostwald ripening, in which large particles grow through diffusional transport at the expense of smaller ones. This can be minimized by choosing matrices in which the reinforcement elements have very low solid solubilities and diffusion coefficients. Platelets, however, have been shown to be more resistant to coarsening than particles or whiskers. 

For catalytic investigations, the rotating basket or fixed basket with internal recirciilation are the standard devices nowadays, usually more convenient and less expensive than equipment with external recirculation. In the fixed basket type, an internal recirculation rate of 10 to 15 or so times the feed rate effectively eliminates external diffusional resistance, and temperature gradients. A unit holding 50 cm (3.05 in ) of catalyst can operate up to 800 K (1440 R) and 50 bar (725 psi). 

Use of Operating Curve Frequently, it is not possible to assume that = 0 as in Example 2, owing to diffusional resistance in the liquid phase or to the accumulation of solute in the hquid stream. When the back pressure cannot be neglected, it is necessary to supplement the equations with a material balance representing the operating line or curve. In view of the countercurrent flows into and from the differential section of packing shown in Fig. 14-3, a steady-state material balance leads to the fohowing equivalent relations ... 

Overall Rate Equations with Diffusional Resistances. 23-52... 

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. 

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. 

The critical properties of water are 374°C (705°F) and 218 atm (3,205 psi). Above this condition a heterogeneous mixture of water, organic-compounds, and oxygen may become homogeneous. Then the rate of oxidation may be considerably accelerated because of (1) elimination of diffusional resistances, (2) increase of oxygen concentration by rea-... 

OVERALL RATE EQUATIONS WITH DIFFUSIONAL RESISTANCES... 

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

When the product layer is porous the reaction will continue but at decreasing rate as the diffusional resistance increases with increasing conversion. Then,... 

Diffusional flow is important when grains are small (as they often are in ceramics) and when the component is subject to high temperatures at low loads. To select a material which resists it, you should... 

Metallic alloys are usually designed to resist power-law creep diffusional flow is only rarely considered. One major exception is the range of directionally solidified ( DS ) alloys described in the Case Study of Chapter 20 here special techniques are used to obtain very large grains. 

Ceramics, on the other hand, often deform predominantly by diffusional flow (because their grains are small, and the high lattice resistance already suppresses power-law creep). Special heat treatments to increase the grain size can make them more creep-resistant. 

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... 

Thus, two factors may be pointed out that determine the possibility of obtaining high yields of crystalline polyethylene on a solid catalyst with no diffusional restriction (1) the splitting up of the catalyst into small particles (< 1000 A), possible when using supports with low resistance to breaking (2) the formation of polymer grains with polydispersed porosity. 

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... 

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. 

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

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

---