Area-related collision rate

Wall flux density (area-related collision rate). A measure of the rate of flow of matter from one part of a system to another is given by the flux (flow rate per unit area). For the transportation of matter, this is given by ... 

The kinetic theory of gases was briefly discussed. It enables the mean or thermal velocity (c) of gas molecules at a given temperature to be obtained and gas flux to be calculated. From the latter, effusion rates, area-related condensation rates and conductances under molecular flow can be determined (see Examples 1.5 and 1.7-1.10). Calculation of collision frequency (obtained from c, n and the collision cross-section of molecules), enables the mean free path (f) of particles to be determined. The easily obtained expression for Ip is a convenient way of stating the variation of / withp (Examples 1.11-1.15). 

Pumping speed. So far, the maximum area-related pumping speed (collision rate, SA) has been used in calculations. For a cryopanel built into a chamber with Acryo < Achdmber, the pumping speed is given by ... 

The evaluation of pre.scnts a closure problem because the term /4 ,ph, which is a function of time, is not known over the path of the system. However, i4 pb is closety related to the minimum surface area of the aero.sol—(hat is, the surface area that would be attained if each individual agglomerate particle became spherical. Indeed, the two would be equal if the aerosol were monodi.sperse with size v. When the rate of coalescence is fast compared with the collision rate, the minimum surface area can be approximated by the self-preserving size distribution for coalescing spheres (Chapter 7). 

The basic mechanism for transition from bubble to slug flow appears to be the same as in vertical pipe flow. That is, as the gas flow rate is increased for a given liquid flow rate, the bubble density increases, many collisions occur and cell-type Taylor bubbles are formed, and the transition to slug flow takes place. As shown in the case of vertical pipe upflow, Taitel et al. (1980) assumed that this transition takes place when ac = 0.25. This criterion is also applicable here. However, because of the preferable geometry in the rod bundle, where the bubbles are observed to exist, instead of in the space between any two rods, this void fraction of 0.25 applies to the local preferable area only, a.L. The local voids, aL, can be related to the average void by (Venkateswararao et al., 1982)... 

In dynamic equilibrium, the rate of desorption equals Nr" because r" Is the probability that an adsorbed molecule will desorb in one second. The rate of adsorption is determined by the available empty area a Ng- N), the pressure (i.e. by the number of molecules in the gas phase per unit volume) and by the rate at which they move. The result Is a p N N]/[2nmkT) molecules per second. The factor (27tmfcT) stems from the kinetic theory of gases and Is related to the collision frequency. Equating the two rates gives, after some rearrangements, the Langmuir equation with... 

A related matter concerns the physical mechanism by which radicals (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Garden (1968) and subsequently developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then a should be proportional to r, where r is the radius of the locus. A second possibility (Fitch, I973) is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximatdy proportional to r rather than to r. A fairly extensive literature now exists concerning this matter (see, e.g., Ugelstad and Hansen, 1976, 1978. 1979a, b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not. however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus constancy of a therefore implies that the size of the locus does not change much as a consequence of polymerization. 

Pressure due to a classical or quantum gas is physically expressed by collisions between the gas particles and the gas boundary - thus it is directly related to the kinetic energy of the particles. Consider a box of dimension D containing N particles, each having velocity v and momentum p = mv. Assuming that collisions with the boundaries are elastic, each collision imparts momentum 2pz, and occurs at a rate vz/2D. The rate of transfer of momentum to unit area is then pzvzJ D2, and averaging over all particles,... 

This is the problem of the rate of evaporation of a liquid into a vacuum, first considered by Hertz (1882). Consider a liquid, such as mercury, in equilibrium with its vapor in a container kept at an absolute temperature T. At equilibrium (Fig. 2.3.1a) the number of vapor molecules striking unit liquid surface per unit time and condensing upon it (i.e., the rate of condensation r is equal to the number of molecules leaving the liquid-vapor interface, per unit time and per unit area (i.e., the rate of evaporation r,). If a molecule striking the liquid from the vapor condenses on the surface with a probability a, the rate of condensation can be related to the rate of collision of vapor molecules with the surface tooii through this condensation coefficient a ... 

Boundary layers next to the two sides of the membrane can substantially contribute to the overall mass transfer resistance molecular diffusion across the boundary layer is often the rate-limiting step. Resistance to mass transfer within the pores of the membrane results from the transfer of momentum, or from the collision of diffusing molecules with other molecules (molecular resistance) or with the membrane itself (Knudsen resistance). In the same figure, resistance related to surface diffusion is also shown in MD this mechanism is present but generally its influence is negligible because the surface diffusion area is small in comparison to the pore area. Surface diffusion resistance may however be important in the development of hydrophilic membranes. 

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