Mass diffusivities

For pressures up to about 1 MPa (or perhaps even higher), the diffusion coefficient for a binary mixture of gases A and B may be estimated from the Fuller, Schettler, and Giddings relationship 

The calculation of the mass diffusivity with Equation 3.36 is illustrated in Example 9.5 in Chapter 9. 

In the absence of a rigorous theory for diffusion in liquids, a number of empirical relationships have been proposed, one of which we mention briefly. For a binary mixture of solute A in solvent B, the diffusion coefficient D°AB (cm2 s1) of A diffusing in an infinitely diluted solution of A in B can be found with the Wilke-Chang correlation  

This equation is good only for dilute solutions of nondissociating solutes. In engineering work D is assumed to be a representative diffusion coefficient even for concentrations of A up to 5 -10 mol % Note that Equation 3.37 is not dimensionally consistent the variables must be employed with the specified units (see Example 9.6). 

Thus generally, for liquids D°AB D°BA. Different techniques with which to estimate the infinite dilution diffusion coefficient are described by Reid et al. [31]. Various correlation s (valid for an arbitrary composition of a binary mixture and for electrolytes) are also given. In the Wilke-Chang correlation for D°AB the effect of temperature has been accounted for by assuming D°AB — T. Although this approximation may be valid over small temperature ranges, it is usually preferable to assume that 

---

A closer look at the Lewis relation requires an examination of the heat- and mass-transfer mechanisms active in the entire path from the hquid—vapor interface into the bulk of the vapor phase. Such an examination yields the conclusion that, in order for the Lewis relation to hold, eddy diffusivities for heat- and mass-transfer must be equal, as must the thermal and mass diffusivities themselves. This equahty may be expected for simple monatomic and diatomic gases and vapors. Air having small concentrations of water vapor fits these criteria closely. 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient. 5-46... 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

Analysis of neutron data in terms of models that include lipid center-of-mass diffusion in a cylinder has led to estimates of the amplitudes of the lateral and out-of-plane motion and their corresponding diffusion constants. It is important to keep in mind that these diffusion constants are not derived from a Brownian dynamics model and are therefore not comparable to diffusion constants computed from simulations via the Einstein relation. Our comparison in the previous section of the Lorentzian line widths from simulation and neutron data has provided a direct, model-independent assessment of the integrity of the time scales of the dynamic processes predicted by the simulation. We estimate the amplimdes within the cylindrical diffusion model, i.e., the length (twice the out-of-plane amplitude) L and the radius (in-plane amplitude) R of the cylinder, respectively, as follows ... 

D Mass diffusivity Used in mass transfer applications involving aerosols. 

In Fig. 20 we show the MSQ of a system of GM [66] with different mean chain lengths (depending on 7, cf. Eq. (12)) for three values of LO=l, 0.1, 0. 01. Since the individual chains have only transient identity, it is meaningless to discuss their center of mass diffusion. It is evident from Fig. 20 that the MSQ of the segments, g t) = ([x( ) - x(O)j ), follows an intermediate sub-diffusive regime, g(t) oc which is later replaced by conventional diffusion at some characteristic crossover time which grows... 

N. C. Bartelt, T. L. Einstein, E. D. Williams. Measuring surface mass diffusion coefficients by observing step fluctuation. Surf Sci 572 411, 1994. 

Temperature gradients within the porous catalyst could not be very large, due to the low concentration of combustibles in the exhaust gas. Assuming a concentration of 5% CO, a diffusion coefficient in the porous structure of 0.01 cms/sec, and a thermal conductivity of 4 X 10-4 caI/sec°C cm, one can calculate a Prater temperature of 1.0°C—the maximum possible temperature gradient in the porous structure (107). The simultaneous heat and mass diffusion is not likely to lead to multiple steady states and instability, since the value of the 0 parameter in the Weisz and Hicks theory would be much less than 0.02 (108). 

Most in depth studies of termination deal only with the low conversion regime. Logic dictates that simple center of mass diffusion and overall chain movement by reptation or many other mechanisms will be chain length dependent. At any instant, the overall rate coefficient for termination can be expressed as a weighted average of individual chain length dependent rate coefficients (eq. 20) 39... 

Mahabadi and O Driscolm considered that segmental motion and center of mass diffusion should be the dominant mechanisms at low conversion. They analyzed data for various polymerizations and proposed that k, J should be dependent on chain length such that the overall rale constant obeys the expression ... 

Parametric studies showed that mass diffusion in the gas phase could be neglected under most conditions. The calculations also show that the selection of the hypergolic combination (i.e., the gaseous oxidizer and the propellant system) fixes all of the parameters except the initial temperature and the oxidizer concentration. A general solution of the model shows that the ignition-delay time is approximately rated to the gaseous oxidizer concentration by the relation... 

Applied Pressure Equilibrium Mass Diffusion Coefficient D... 

A number of theoretical (5), (19-23). experimental (24-28) and computational (2), (23), (29-32). studies of premixed flames in a stagnation point flow have appeared recently in the literature. In many of these papers it was found that the Lewis number of the deficient reactant played an important role in the behavior of the flames near extinction. In particular, in the absence of downstream heat loss, it was shown that extinction of strained premixed laminar flames can be accomplished via one of the following two mechanisms. If the Lewis number (the ratio of the thermal diffusivity to the mass diffusivity) of the deficient reactant is greater than a critical value, Lee > 1 then extinction can be achieved by flame stretch alone. In such flames (e.g., rich methane-air and lean propane-air flames) extinction occurs at a finite distance from the plane of symmetry. However, if the Lewis number of the deficient reactant is less than this value (e.g., lean hydrogen-air and lean methane-air flames), then extinction occurs from a combination of flame stretch and incomplete chemical reaction. Based upon these results we anticipate that the Lewis number of hydrogen will play an important role in the extinction process. 

The EMA method is similar to the volume-averaging technique in the sense that an effective transport coefficient is determined. However, it is less empirical and more general, an assessment that will become clear in a moment. Taking mass diffusion as an example, the fundamental equation to solve is... 

The concentration gradient may have to be approximated in finite difference terms (finite differencing techniques are described in more detail in Secs. 4.2 to 4.4). Calculating the mass diffusion rate requires a knowledge of the area, through which the diffusive transfer occurs, since... 

The dynamical properties of polymer molecules in solution have been investigated using MPC dynamics [75-77]. Polymer transport properties are strongly influenced by hydrodynamic interactions. These effects manifest themselves in both the center-of-mass diffusion coefficients and the dynamic structure factors of polymer molecules in solution. For example, if hydrodynamic interactions are neglected, the diffusion coefficient scales with the number of monomers as D Dq /Nb, where Do is the diffusion coefficient of a polymer bead and N), is the number of beads in the polymer. If hydrodynamic interactions are included, the diffusion coefficient adopts a Stokes-Einstein formD kltT/cnr NlJ2, where c is a factor that depends on the polymer chain model. This scaling has been confirmed in MPC simulations of the polymer dynamics [75]. 

Summary of experimental data Film boiling correlations have been quite successfully developed with ordinary liquids. Since the thermal properties of metal vapors are not markedly different from those of ordinary liquids, it can be expected that the accepted correlations are applicable to liquid metals with a possible change of proportionality constants. In addition, film boiling data for liquid metals generally show considerably higher heat transfer coefficients than is predicted by the available theoretical correlations for hc. Radiant heat contribution obviously contributes to some of the difference (Fig. 2.40). There is a third mode of heat transfer that does not exist with ordinary liquids, namely, heat transport by the combined process of chemical dimerization and mass diffusion (Eq. 2-162). 

For small angles (QRe 1), the second and third terms in (24) are negligibly small and S(Q,t) describes the center-of-mass diffusion of the coil... 

In fact, the diffusion constant in solutions has the form of an Einstein diffusion of hard spheres with radius Re. For a diffusing chain the solvent within the coil is apparently also set in motion and does not contribute to the friction. Thus, the long-range hydrodynamic interactions lead, in comparison to the Rouse model, to qualitatively different results for both the center-of-mass diffusion—which is not proportional to the number of monomers exerting friction - as well as for the segment diffusion - which is considerably accelerated and follows a modified time law t2/3 instead of t1/2. 

---