Diffusion partial pressure

If tire diffusion coefficient is independent of tire concentration, equation (C2.1.22) reduces to tire usual fonn of Pick s second law. Analytical solutions to diffusion equations for several types of boundary conditions have been derived [M]- In tlie particular situation of a steady state, tire flux is constant. Using Henry s law (c = kp) to relate tire concentration on both sides of tire membrane to tire partial pressure, tire constant flux can be written as... 

Ac Che limic of Knudsen screaming Che flux relacions (5.25) determine Che fluxes explicitly in terms of partial pressure gradients, but the general flux relacions (5.4) are implicic in Che fluxes and cheir solution does not have an algebraically simple explicit form for an arbitrary number of components. It is therefore important to identify the few cases in which reasonably compact explicit solutions can be obtained. For a binary mixture, simultaneous solution of the two flux equations (5.4) is straightforward, and the result is important because most experimental work on flow and diffusion in porous media has been confined to pure substances or binary mixtures. The flux vectors are found to be given by... 

In practice it would not be reasonable to solve the balances at the limit of Knudsen diffusion control by considering the n simultaneous boundary value problems (11.7). All the partial pressures can be expressed in terms of by integrating equations (11,25), with the result... 

Hite s treatment is based on equations (5.18) and (5.19) which describe the dusty gas model at the limit of bulk diffusion control and high permeability. Since temperature Is assumed constant, partial pressures are proportional to concentrations, and it is convenient to replace p by cRT, when the flux equations become... 

A molecule colliding with the pore wall is reflected in a specular manner so that the direction of the molecule leaving the surface has no correlation with that of the incident molecule. This leads to a Fickian mechanism, known as Knudsen diffusion, in which the flux is proportional to the gradient of concentration of partial pressure. The Knudsen diffusivity is independent of pressure and varies only weaMy with temperature ... 

Although microporous membranes are a topic of research interest, all current commercial gas separations are based on the fourth type of mechanism shown in Figure 36, namely diffusion through dense polymer films. Gas transport through dense polymer membranes is governed by equation 8 where is the flux of component /,andare the partial pressure of the component i on either side of the membrane, /is the membrane thickness, and is a constant called the membrane permeability, which is a measure of the membrane s ability to permeate gas. The ability of a membrane to separate two gases, i and is the ratio of their permeabilities,a, called the membrane selectivity (eq. 9). 

The Permeation Process Barrier polymers limit movement of substances, hereafter called permeants. The movement can be through the polymer or, ia some cases, merely iato the polymer. The overall movement of permeants through a polymer is called permeation, which is a multistep process. First, the permeant molecule coUides with the polymer. Then, it must adsorb to the polymer surface and dissolve iato the polymer bulk. In the polymer, the permeant "hops" or diffuses randomly as its own thermal kinetic energy keeps it moving from vacancy to vacancy while the polymer chains move. The random diffusion yields a net movement from the side of the barrier polymer that is ia contact with a high concentration or partial pressure of the permeant to the side that is ia contact with a low concentration of permeant. After crossing the barrier polymer, the permeant moves to the polymer surface, desorbs, and moves away. 

Eor a food container, the amount of sorption could be estimated in the following way. Eor simple diffusion the concentration in the polymer at the food surface could be estimated with equation 3. This would require a knowledge of the partial pressure of the flavor in the food. This is not always available, but methods exist for estimating this when the food matrix is water-dorninated. The concentration in the polymer at the depth of penetration is zero. Hence the average concentration C is as from equation 9. 

Fig. 3. The diffusion coefficients of several single-crystal and polycrystaUine ceramic materials as a function of temperature where Pq represents the partial pressure of oxygen. The activation energy is obtained from the slope and the insert eg, for O diffusion in CaQ 86 186 2 Tl4 cation % Ca,...

Plasticization Gas solubility in the membrane is one of the factors governing its permeation, but the other factor, diffusivity, is not always independent of solubility. If the solubility of a gas in a polymer is too high, plasticization and swelhng result, and the critical structure that controls diffusion selectivity is disrupted. These effects are particularly troublesome with condensable gases, and are most often noticed when the partial pressure of CO9 or H9S is high. H9 and He do not show this effect This problem is well known, but its manifestation is not always immediate. 

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. 

The tlrermodynamic activity of nickel in the nickel oxide layer varies from unity in contact with tire metal phase, to 10 in contact with the gaseous atmosphere at 950 K. The sulphur partial pressure as S2(g) is of the order of 10 ° in the gas phase, and about 10 in nickel sulphide in contact with nickel. It therefore appears that the process involves tire uphill pumping of sulphur across this potential gradient. This cannot occur by the counter-migration of oxygen and sulphur since the mobile species in tire oxide is the nickel ion, and the diffusion coefficient aird solubility of sulphur in the oxide are both vety low. 

Temperature rc) Humidity kg HjO/kg dry air) Water vapor partial pressure (kPa) Water v K>r partial density (kg/m ) Water vaporization heat M/kg) Mixture enthalpy (kj/kg dry air) Dry air partial density (lKinematic viscosity (I0< mJ/s) Specific heat (kJ/K kg) Heat conductivity (W/m K) Diffusion factor water air (1 O mJ/s) Temperature rc)... 

The sulphide usually forms an interconnected network of particles within a matrix of oxide and thus provides paths for rapid diffusion of nickel to the interface with the gas. At high temperatures, when the liquid Ni-S phase is stable, a duplex scale forms with an inner region of sulphide and an outer porous NiO layer. The temperature dependence of the reaction is complex and is a function of gas pressure as indicated in Fig. 7.40 . A strong dependence on gas pressure is observed and, at the higher partial pressures, a maximum in the rate occurs at about 600°C corresponding to the point at which NiS04 becomes unstable. Further increases in temperature lead to the exclusive formation of NiO and a large decrease in the rate of the reaction, due to the fact that NijSj becomes unstable above about 806°C. 

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