Diffusivity for gases

Dk Knudson diffusivity for gases in small pores mvs or cmvs ft /h... 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Lee-Thodos presented a generahzed treatment of self-diffusivity for gases (and liquids). These correlations have been tested for more than 500 data points each. The average deviation of the first is 0.51 percent, and that of the second is 17.2 percent. 8 = PyVr, s/cm and where G = (X - X)/(X - 1), X = p,/T h and X = p /T evaluated at the solid melting point. 

PRANDTL NUMBER. A dimensionless number equal to the ratio of llie kinematic viscosity to the tlienuoiiielric conductivity (or thermal diffusivity), For gases, it is rather under one and is nearly independent of pressure and temperature, but for liquids the variation is rapid, Its significance is as a measure of the relative rates of diffusion of momentum and heat m a flow and it is important m the study of compressible flow and heat convection. See also Heat Transfer. 

The effective diffusivity for gases, which is incorporated in expression 8.8 for 02 can be approximated by the equation (see Equation 3.27)... 

Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal, AIChE J. 30, 641 (1984), Ertf and Dullien, AIChE J. 19,1215 (1973), and Vadovic and Colver, AIChE J. 18,1264 (1972)]. 

In a somewhat similar paper, diffusion through a 2D porous solid modeled by a regular array of hard disks was evaluated [65] using non-equilibrium molecular dynamics. It was found that Pick s law is not obeyed in this system unless one takes different diffusion constants for different regions in the flow system. Other non-equilibrium molecular dynamics simulations of diffusion for gases within a membrane have been presented [66]. The membrane was modeled as a randomly... 

Before closing this brief discussion on mass transfer fundamentals, further mention should be made of the diffusion coefficient. Equations for predicting gas diffusivities are given by Fuller and are also given in Perry s Handbook. The orders of magnitude of the diffusivities for gases, liquids, and... 

To explain the temperature behavior of thermal conductivity, we note that by analogy with v cl the thermal diffusivity for gases is given by... 

For low wind speeds, one might ask, at what characteristic depth or distance from the interface is the rate of advective transfer of normal dissolved gases away from the interface equal to diffusive transfer To answer this question, we can use the dimensionless Peclet number, (dV/D), which expresses the relative importance of mass transfer by advection to transfer by diffusion. In the Peclet number, d can be taken as the thickness of the diffusive layer, V the velocity and D as the gas diffusivity in the water phase. If we take V as the piston velocity with an appropriately low value of about 1 cm h, and a typical diffusivity for gases in water of about 10" cm s the thickness of the boundary layer can be determined for a Peclet number, Pe= 1, i.e. at a distance from the interface where advective and diffusive transport are comparable. Under these conditions, d is... 

Table 15-1. Binary Fickian diffusivities for gases at 1.0 atm. For example, the diffusivity of air and ammonia at 273 K is 0.198 x 10 m /s = 0.198 cm /s. For each gas pair at low pressures and a given tenperature, pj t D g = constant. (Cussler. 2009 DemireL 2007 Geankoplis, 2003 Poling et al..

In 1832 the Scottish chemist Thomas Graham found that under the same conditions of temperature and pressure, rates of diffusion for gases are inversely proportional to the square roots of their molar masses. This statement, now known as Graham s law of diffusion, is expressed mathanatically as... 

Prediction of diffusivity for gases. The diffusivity of a binary gas mixture in the dilute gas region, i.e., at low pressures near atmospheric, can be predicted using the kinetic theory of gases. The gas is assumed to consist of rigid spherical particles that are completely elastic on collision with another molecule, which implies that momentum is conserved. 

Equimolar counter diffusion for gases. For the special case of equimolar counterdiffus-ion of gases at constant pressure and no reaction, c = constant, = 0, D g = constant, R = 0, and Eq. (7.5-15) becomes... 

The rates of effusion and diffusion for gases depend on the velocities of their molecules. 

Phases I and II are skipped if < MINGRHO + po — MINGRHO)(lTjj). MINGRHO has a value of 0.5 and is a minimum density at which the calculation will proceed. This is for handling free surfaces and to eliminate false diffusion. For gases at free surfaces Wf-j is replaced by one. 

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