Kinetic, diameter energy transport

As far as the collision diameter D is concerned, the general use is to take the reaction diameter D as the average kinetic diameter between the two reacting molecules, as deduced from transport phenomena determinations.17 This choice has no sound basis, and some improvements can be made if one considers the influence of the intermolecular field. Such an analysis shows that, if the reaction needs an activation energy E, then one must use an impact diameter D,... 

To understand gas transport phenomenon it is critical to consider the interactions between the gas molecules and the pore wall. The van der Waals interactions between particles are explained well by the Lennard-Jones function containing two parameters, the kinetic diameter g (the distance where the potential energy between the particles is zero) and the well depth e (the deepest potential minimum between the particles). These parameters were used, e.g. by Freeman [52], to establish a theoretical basis for the relationship between selectivity and permeability for a range of polymers and gases (so-called first upper bonnd empirically determined by Robeson in 1991 [53] see also more recent paper by Robeson [54]). The rate of diffnsion of a gas is dependent on its kinetic diameter while its solnbility mainly depends on the condensability of the gas and consequently on the well depth for gas-gas interactions. 

Figure 5.8 Separation regimes determined by the potential energies within pores of different sizes. Potential energy el(z) for molecule A within cylindrical pores with radius R, scaled by the potential minimum i for molecule A with a single free surface and the Lennard-jones kinetic diameter parameter a a [30], Reprinted from Journal of Membrane Science, 104, R. 5. A. de Lange, K. Keizer and A. j. Burggraaf, Analysis and theory of gas transport in microporous sol-gel derived ceramic membranes, 81-100, Copyright (1995), with permission from Elsevier...

Here u is the growth rate in cm/sec, / is the fraction of sites at the interface where atoms can preferentially be added or removed, D" is the kinetic coefficient for transport across the crystal-liquid interface (having dimensions cm /sec), Qq is the molecular diameter, is the molar volume, and Gy is the free energy change per unit volume accompanying crystallization (the motivating potential). 

The equation derived by Troelstra and Kruyt is only valid for coagulating dispersions of colloids smaller than a certain maximum diameter given by the Rayleigh condition, d 0.10 A0. Equation 4 applies in cases where particles are transported solely by Brownian motion. Furthermore, the kinetic model (Equations 2 and 3) has been derived under the assumption that the collision efficiency factor does not change with time. In the case of some partially destabilized dispersions one observes a decrease in the collision efficiency factor with time which presumably results from the increase of a certain energy barrier as the size of the agglomerates becomes larger. 

Aerosol particles of dimensions comparable with the mean free path of gas molecules (about 0.06 pm) recognize their gaseous surroundings as composed of individual molecules, and every collision of a particle with a gas molecule changes its kinetic energy and direction of motion as a result, the particle moves at random through the gas (Brownian motion or diffusion). The random displacement a particle covers by this transport increases with time and with decreasing particle diameter. It is independent of the particle density. 

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