Diffusion, collision integral

Maximum intrapellet temperatures, 25 305 effect of diffusion collision integral on, 25 301-303... 

The collision integral for diffusion depends upon the choice of the intermolecular force law between colliding molecules and is a function of temperature. The characteristic length also depends upon the intermolecular force law selected. In comparison with the simple Eq. (6-2) for perfect gases, Eq. (6-3) takes into account the interactive forces between real molecules. But, while in the first case only two specific parameters are needed, the diffusion collision integral, Q0, is a complicated function of several parameters. 

The parameter the diffusion collision integral, is a function of k T/e, where is the Boltzmann constant and e is a molecular energy parameter. Values of tabulated as a function of k T/e, have been published (Hirschfelder et al., 1964 Bird et al., 1960). Neufeld et al., (1972) correlated using a simple eight parameter equation that is suitable for computer calculations (see, also, Danner and Daubert, 1983 Reid et al., 1987). Values of a and e/k (which has units of kelvin) can be found in the literature—for only a few species—or estimated from critical properties (Reid et al., 1987 Danner and Daubert, 1983). The mixture a is calculated as the arithmetic average of the pure component values. The mixture e is taken to be the geometric average of the pure component values. 

FIGURE 5.1 Plot of the Leonard-Jones reduced temperature and diffusion collision integral. 

The diffusion collision integral, = 1.3 (read from Figure5.1).Thediffusivity can then be calculated using Equation 5.2 ... 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

Our previous study (J 6) of self diffusion in compressed supercritical water compared the experimental results to the predictions of the dilute polar gas model of Monchick and Mason (39). The model, using a Stockmayer potential for the evaluation of the collision integrals and a temperature dependent hard sphere diameters, gave a good description of the temperature and pressure dependence of the diffusion. Unfortunately, a similar detailed analysis of the self diffusion of supercritical toluene is prevented by the lack of density data at supercritical conditions. Viscosities of toluene from 320°C to 470°C at constant volumes corresponding to densities from p/pQ - 0.5 to 1.8 have been reported ( 4 ). However, without PVT data, we cannot calculate the corresponding values of the pressure. 

Here Dtj incm2/s, in A, Tin K, and P in atm. The dimensionless quantity ClDij is the collision integral for diffusion, and is a function of the dimensionless temperature KrH ir The parameters (TJ and are those appearing in the Lennard-Jones potential between molecules / and j. 

The above equation expresses the diffusion of vapor A through B medium, in which, Ma and Mb ate the molecular weight (kg/kmol), Po the absolute pressure, Oab and CIq are the molecule collision diameter and the molecule collision integral which are functions of substance properties and can be determined by empirical equations... 

The three-halves power of dimensionless temperature in the expression for eA( ) is based on the temperature dependence of gas-phase ordinary molecular diffusion coefficients when the catalytic pores are larger than 1 p.m. In this pore-size regime, Knudsen diffusional resistance is negligible. The temperature dependence of the collision integral for ordinary molecular diffusion, illustrated in Bird et al. (2002, pp. 526, 866), has not been included in ea) ). The thermal energy balance given by equation (27-28), which includes conduction and interdiffu-sional fluxes, is written in dimensionless form with the aid of one additional parameter,... 

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