Diffusivity pseudo binary

For naphthalene in air the ordinary molecular diffusivity may be evaluated using a pseudo binary approach and the methods outlined in Reid and Sherwood (10). For an inlet temperature of 630 °K and an inlet pressure of 25 psia, the result is... 

Am pseudo-binary diffusivity of species A in a multicomponent gas mixture... 

This method provides the exact solutions for ideal systems at constant temperature and pressure. It is successful in describing diffusion flow in (i) nearly ideal mixtures, (ii) equimolar counter diffusion where the total flux is zero (Nt = 0), (iii) diffusion of one component through a mixture of n — 1 inert components, and (iv) pseudo-binary case and the diffusion of two very similar components in a third. 

In reactive flow analysis the Pick s law for binary systems (2.285) is frequently used as an extremely simple attempt to approximate the multicomponent molecular mass fluxes. This method is based on the hypothesis that the pseudo-binary mass flux approximations are fairly accurate for solute gas species in the particular cases when one of the species in the gas is in excess and acts as a solvent. However, this approach is generally not recommend-able for chemical reactor analysis because reactive mixtures are normally not sufficiently dilute. Nevertheless, many industrial reactor systems can be characterized as convection dominated reactive flows thus the Pickian diffusion model predictions might still look acceptable at first, but this interpretation is usually false because in reality the diffusive fluxes are then neglectable compared to the convective fluxes. 

ORDINARY MOLECULAR DIFFUSION IN BINARY AND PSEUDO-BINARY MIXTURES... 

If an n-component gas mixture (i.e., n >2) can be treated as a pseudo-binary mixture, and the ordinary molecular diffusivity a. mix of component A is desired, then the formalism described above is applicable under the following conditions ... 

This resistance is larger when convective mass transfer is negligible relative to diffusion, and V is insignificant. Under these conditions, and the mass transfer resistance simplifies to 1/23ab- If convective mass transfer is important in a nonreactive mixture of n components which can be treated as a pseudo-binary, then ... 

Finally, one estimates the total mass transfer resistance for methane due to convection and ordinary molecular diffusion in this pseudo-binary mixture as follows, when ymethane = Tl = 0.20 ... 

Mutual differential diffusion coefficients of binary (e.g. [6-8]) and pseudo binary systems (such as, e.g., cobalt chloride in aqueous solutions of sucrose [9]), have been measured using a conductometric cell and an automatic apparatus to follow diffusion. This cell uses an open-ended capillary method and a conductometric technique is used to follow the diffusion process by measuring the resistance of the solution inside the capillaries, at recorded times. Figure 1 shows a schematic representation of the open-ended capillary cell. 

Mutual diEFerential diffusion coefficients of several electrolytes 1 1, 2 2, and 2 1, in different media (considering these systems as binary or pseudo binary systems, depending on the circumstances) have been measured using a conductometric cell [1]. The already published mutual differential diffusion coefficients data are average results of, at least, three independent measurements. The imprecision of such average results is, with few exceptions, lower than 1%. 

In fact, comparing the estimated diffusion coefficients of Pb(N03)3, with the related experimental values [5], an increase in the experimental D values is found in lead (II) nitrate concentrations below 0.025M. This can be explained not only by the initial Pb(N03)2 gradient, but also by a further HjO flux. Consequently, as H3O+ diffuses more rapidly than NO3" or Pb , the lead(II) nitrate gradient generates its own HNO3 flux. Thus, the PbfNOjtj/water mixture should be considered a ternary system. However, in the present experimental conditions we may consider the system as pseudo-binary, mainly for c. OIM, and consequently, take the meastrred parameter, D, as the main diffusion coefficient, D. ... 

By a derivation based on Maxwell-Stefan diffusion, we were able to obtain an advanced formulation, which overcomes this problem and is applicable to any diffusion mechanism, Maxwell-Stefan as well as (pseudo-)binary Fickian diffusion. Contrarily to the old approach, higher moments diffusion is a function of the diffusive polymer flux (a complete derivation is yet to be published) ... 

The net diffusive mass flux for each phase still vanishes for binary systems as s- k s using Pick s law, whereas for dilute pseudo-binary systems the latter relationship is only approximate. 

If we compare Eqs. 5.1.14 with the conservation equation (Eq. 5.1.2) for a binary system and the pseudo-Fick s law Eq. 5.1.15, with Eq. 3.1.1 then we can see that from the mathematical point of view these pseudomole fractions and pseudofluxes behave as though they were the corresponding variables of a real binary mixture with diffusion coefficient D-. The fact that the are real, positive, and invariant under changes of reference velocity strengthens the analogy. If the initial and boundary conditions can also be transformed to pseudocompositions and fluxes by the same similarity transformation, the uncoupled equations represent a set of independent binary-type problems, n - 1 in number. Solutions to binary diffusion problems are common in the literature (see, e.g.. Bird et al., 1960 Slattery, 1981 Crank, 1975). Thus, the solution to the corresponding multicomponent problem can be written down immediately in terms of the pseudomole fractions and fluxes. Specifically, if... 

The Stokes-Einstein equation for binary molecular diffusion coefficients of dilute pseudo-spherical molecules subject to creeping flow through an incompressible Newtonian fluid is (see equation 25-98) ... 

The model geometry is described in two dimensions. In x-direction the flux of ions and electrons accounts for charge transport perpendicular to the cell layers. The influence of ohmic drops within the current collectors is assumed to be zero, thus only three domains are taken into account. These are the anode (graphite), a porous separator and the cathode (LiFeP04). The solid diffusion within the electrode s active material particles is calculated in an additional pseudo-dimension in spherical coordinates. So at every point x within an electrode domain a second dimension r is used to describe this flux directed to or away from the particle s centre. The dimensions are coupled at the particle s surface. A binary electrolyte (one salt in one solvent) is assumed, whereas only the cation flux is described, since the anions do not contribute to the electrochemical reaction of the cell. The subscript + indicates the aforementioned cationic species (LE). 

The qualitative nature of the departure from the pseudo-stationary state can be explained on the basis of very simple considerations. Let us treat our hypothetical chain system and simplify the multi-component diffusion equations by assuming that the free radical B diffuses through the mixture of other components (regarded as a single species) with an effective binary diffusion coefficient, Then, combining the equation of continuity with the equation for diffusion of the free radical. 

The calculations of Klein, and Campbell, Hirschfelder, and Schalit on the ABC flame provide an excellent example of the deviations from the pseudo-steady state. The reaction scheme for the ABC flame is that given in our h5qx)thetical example, Eqs. (130), (131), and (132). To simplify the calculations the specific heats at constant pressure of A, B, and C are taken equal to 5R (where R is the gas constant) the three binary diffusion coefficients, be> ae taken to be equal and have values such that the corresponding Lewis numbers dab. bc ae 3 ch equal to unity. The rate constants are taken to be... 

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