Diffusivity composition

Note that the diffusive composition fluxes are assumed to be zero on inflow boundaries. 

Equation 4.2.13 is shown in Figure 4.8 for a ternary system where it becomes clear that the limiting diffusivities are, in fact, the Maxwell-Stefan diffusion coefficients at the corners of the diffusivity-composition surface. Equation 4.2.13 should reduce to the binary Vignes... 

A study of the radiogenic isotope memory of the Earth s mantle clearly shows that the mantle is not an independent part of the Earth system, nor has it been for a long time. But rather, it records a history of the extraction and recycling of both basaltic and continental crust. Because of the relatively slow mixing rates and rates of diffusion, compositional heterogeneities within the mantle produced by these processes may be preserved for >1.0 Ga so that significant parts of the Earth s prehistory can be seen in recent mantle melts. Mantle melts from early Earth history (basalts and komatiites), therefore, have the potential to record very early mantle heterogeneities. 

The tin alloy elements must be distributed sufficiently to allow diffusion throughout the matrix. Experience with externally diffused composites dictates that the tin-rich elements must be very close to their nearest neighbors. 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

Figure C2.3.8. Self-diffusion coefficients at 45°C for AOT ( ), water ( ) and decane ( ) in ternary AOT, brine (0.6% aqueous NaCl) and decane microemulsion system as a function of composition, a. This compositional parameter, a, is tire weight fraction of decane relative to decane and brine. Reproduced by pennission from figure 3 of [46].

The starting point for developing the model is the set of diffusion equations for a gas mixture in the presence of temperature, pressure and composition gradients, and under the influence of external forces." These take the following form... 

In fact, the pressures will never settle completely to constant values until diffusion is complete and the composition is the same in both chambers, but by making the chambers sufficiently large this rate of drift of the pressures can be reduced below any desired level. 

Che Knudsen diffusion coefficient is independent of composition and pressure,... 

They then compared measured and predicted fluxes for diffusion experiments in the mixture He-N. The tests covered a range of pressures and a variety of compositions at the pellet faces but, like the model itself, they were confined to binary mixtures and isobaric conditions. Feng and Stewart [49] compared their models with isobaric flux measurements in binary mixtures and with some non-isobaric measurements in mixtures of helium and nitrogen, using data from a variety of sources. Unfortunately the information on experimental conditions provided in their paper is very sparse, so it is difficult to assess how broadly based are the conclusions they reached about the relative merits oi their different models. 

In general, tests have tended to concentrate attention on the ability of a flux model to interpolate through the intermediate pressure range between Knudsen diffusion control and bulk diffusion control. What is also important, but seldom known at present, is whether a model predicts a composition dependence consistent with experiment for the matrix elements in equation (10.2). In multicomponent mixtures an enormous amount of experimental work would be needed to investigate this thoroughly, but it should be possible to supplement a systematic investigation of a flux model applied to binary systems with some limited experiments on particular multicomponent mixtures, as in the work of Hesse and Koder, and Remick and Geankoplia. Interpretation of such tests would be simplest and most direct if they were to be carried out with only small differences in composition between the two sides of the porous medium. Diffusion would then occur in a system of essentially uniform composition, so that flux measurements would provide values for the matrix elements in (10.2) at well-defined compositions. 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

Liquid Junction Potentials A liquid junction potential develops at the interface between any two ionic solutions that differ in composition and for which the mobility of the ions differs. Consider, for example, solutions of 0.1 M ITCl and 0.01 M ITCl separated by a porous membrane (Figure 11.6a). Since the concentration of ITCl on the left side of the membrane is greater than that on the right side of the membrane, there is a net diffusion of IT " and Ck in the direction of the arrows. The mobility of IT ", however, is greater than that for Ck, as shown by the difference in the... 

Potentiometric electrodes also can be designed to respond to molecules by incorporating a reaction producing an ion whose concentration can be determined using a traditional ion-selective electrode. Gas-sensing electrodes, for example, include a gas-permeable membrane that isolates the ion-selective electrode from the solution containing the analyte. Diffusion of a dissolved gas across the membrane alters the composition of the inner solution in a manner that can be followed with an ion-selective electrode. Enzyme electrodes operate in the same way. 

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

Cotton linters or wood pulp are nitrated using mixed acid followed by treatment with hot acidified water, pulping, neutralization, and washing. The finished product is blended for uniformity to a required nitrogen content. The controlling factors in the nitration process are the rates of diffusion of the acid into the fibers and of water out of the fibers, the composition of mixed acid, and the temperature (see Cellulose esters, inorganic esters). 

The Beckstead-Derr-Price model (Fig. 1) considers both the gas-phase and condensed-phase reactions. It assumes heat release from the condensed phase, an oxidizer flame, a primary diffusion flame between the fuel and oxidizer decomposition products, and a final diffusion flame between the fuel decomposition products and the products of the oxidizer flame. Examination of the physical phenomena reveals an irregular surface on top of the unheated bulk of the propellant that consists of the binder undergoing pyrolysis, decomposing oxidizer particles, and an agglomeration of metallic particles. The oxidizer and fuel decomposition products mix and react exothermically in the three-dimensional zone above the surface for a distance that depends on the propellant composition, its microstmcture, and the ambient pressure and gas velocity. If aluminum is present, additional heat is subsequently produced at a comparatively large distance from the surface. Only small aluminum particles ignite and bum close enough to the surface to influence the propellant bum rate. The temperature of the surface is ca 500 to 1000°C compared to ca 300°C for double-base propellants. 

Fig. 1. The postulated flame stmcture for an AP composite propellant, showing A, the primary flame, where gases are from AP decomposition and fuel pyrolysis, the temperature is presumably the propellant flame temperature, and heat transfer is three-dimensional followed by B, the final diffusion flame, where gases are O2 from the AP flame reacting with products from fuel pyrolysis, the temperature is the propellant flame temperature, and heat transfer is three-dimensional and C, the AP monopropellant flame where gases are products from the AP surface decomposition, the temperature is the adiabatic flame temperature for pure AP, and heat transfer is approximately one-dimensional. AP = ammonium perchlorate.

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