Collision flux

Distinguishing between 7 and 7, (introduced by Poschl et al. (2006) but not used by other authors) is meaningful because it reflects the transport from the bulk gas phase close to the particle surface (0 -> g) which might have limitations, expressed by the actual surface collision flux Fcou and the average gas kinetic flux Fcoii From equations (4.257) and (4.258) it follows that ... 

The mass accommodation process can also be defined as the fraction of the collision flux to the surface which is adsorbed no adsorption means collision where the gas molecule is reflected back to the gas phase. Therefore, it is valid that ... 

Note that the projection mt in Equations 4.16 and 4.17 vanishes because we require that the wavevector of the incident plane wave be parallel to the space-fixed quantization axis. The same choice is adopted in the conventional theory of atom-molecule collisions in the absence of fields [45]. Generally, the initial collision flux may not be parallel to the quantization axis (defined by the direction of the external field), and the differential cross-section Equation 4.13 must depend on both the orientation of the incoming flux and the direction of the outgoing flux. In this section, we restrict the discussion to the particular case of the DCS evaluated at fixed. Ri = 0 (Equation 4.17). 

If the collision flux is prepared in a single quantum channel (sm), the collision wavefunction has the form... 

To obtain this expression, we assumed that the incident collision flux is represented by a plane wave propagating in the x-direction and used the Jacobi-Anger expansion of a plane wave to express it in terms of the incident and outgoing scattering waves (Equation 4.20) ... 

Normalizing Jg with the collision flux to the surface Jcoi given by Eq. (2.82), diffusion conductance near the interface is given by... 

The final equation obtained by Becker and Doting may be written down immediately by means of the following qualitative argument. Since the flux I is taken to be the same for any size nucleus, it follows that it is related to the rate of formation of a cluster of two molecules, that is, to Z, the gas kinetic collision frequency (collisions per cubic centimeter-second). 

Figure A3.7.5. Velocity-flux contour plot for FIF product from the reaction F + para- i2 HF + F1 at a reactant collision energy of 1.84 kcal mol ...

Figure Bl.23.2. (a) Shadow cone of a stationary Pt atom in a 4 keV Ne ion beam, appearing with the overlapping of ion trajectories as a fiinction of the impact parameter. The initial position of the target atom that recoils in the collision is indicated by a solid circle, (b) Plot of the nonnalized ion flux distribution density across the shadow cone in (a). The flux density changes from 0 inside the shadow cone, to much greater than l in the focusing region, converging to 1 away from the shadow cone edge, (c) Blocking cones...

When Che diameter of the Cube is small compared with molecular mean free path lengths in che gas mixture at Che pressure and temperature of interest, molecule-wall collisions are much more frequent Chan molecule-molecule collisions, and the partial pressure gradient of each species is entirely determined by momentum transfer to Che wall by mechanism (i). As shown by Knudsen [3] it is not difficult to estimate the rate of momentum transfer in this case, and hence deduce the flux relations. 

The Stefan-Maxwell equations have been presented for the case of a gas in the absence of a porous medium. However, in a porous medium whose pores are all wide compared with mean free path lengths it is reasonable to guess that the fluxes will still satisfy relations of the Stefan-Maxwell form since intermolecular collisions still dominate molecule-wall collisions. 

Despite the fact Chat there are no analogs of void fraction or pore size in the model, by varying the proportion of dust particles dispersed among the gas molecules it is possible to move from a situation where most momentum transfer occurs in collisions between pairs of gas molecules, Co one where the principal momentum transfer is between gas molecules and the dust. Thus one might hope to obtain at least a physically reasonable form for the flux relations, over the whole range from bulk diffusion to Knudsen streaming. 

The power dissipated at two different frequencies has been calculated for all reactions and compared with the energy loss to the walls. It is shown that at 65 MHz the fraction of power lost to the boundary decreases by a large amount compared to the situation at 13.56 MHz [224]. In contrast, the power dissipated by electron impact collision increases from nearly 47% to more than 71%, of which vibrational excitation increases by a factor of 2, dissociation increases by 45%, and ionization stays approximately the same, in agreement with the product of the ionization probability per electron, the electron density, and the ion flux, as shown before. The vibrational excitation energy thresholds (0.11 and 0.27 eV) are much smaller than the dissociation (8.3 eV) and ionization (13 eV) ones, and the vibrational excitation cross sections are large too. The reaction rate of processes with a low energy threshold therefore increases more than those with a high threshold. 

In a similar spirit, Inoue et al. [120] and Hashimoto et al. [121] generalized MPC dynamics so that the collision operator reflects the species compositions in the neighborhood of a chosen cell. More specifically, consider a binary mixture of particles with different colors. The color of particle i is denoted by c,-. The color flux of particles with color c in cell E, is defined as... 

Terminal velocity, linear thermodynamics intermediate regimes and maximum flux, 25-27 regression theorem, 18-20 Test particle density, multiparticle collision dynamics, macroscopic laws and transport coefficients, 100-104 Thermodynamic variables heat flow, 58-60... 

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