Momentum in collisions

Operation. In a diffusion pump, the pump fluid is heated so that a vapour pressure of 1-10 mbar is established in the boiler. The vapour rises in the jet assembly where it is expanded through nozzles and enters the space between the nozzle and the cooled wall of the pump at high supersonic velocity. Pumping action is based on the transfer of momentum in collisions between the high speed (several times the speed of sound) pump fluid vapour molecules and particles that have entered the vapour jet. 

The thermal diffusion factor a is proportional to the mass difference, (mi — mo)/(mi + m2). The thermal diffusion process depends on the transport of momentum in collisions between unlike molecules. The momentum transport vanishes for Maxwellian molecules, particles which repel one another with a force which falls off as the inverse fifth power of the distance between them. If the repulsive force between the molecules falls off more rapidly than the fifth power of the distance, then the light molecule will concentrate in the high temperature region of the space, while the heavy molecule concentrates in the cold temperature region. When the force law falls off less rapidly than the fifth power of the distance, then the thermal diffusion separation occurs in the opposite sense. The theory of the thermal diffusion factor a is as yet incomplete even for classical molecules. A summary of the theory has been given by Jones and Furry 15) and by Hirschfelder, Curtiss, and Bird 14), Since the thermal diffusion factor a for isotope mixtures is small, of the order of 10", it remained for Clusius and Dickel (8) to develop an elegant countercurrent system which could multiply the elementary effect. 

Anrade s theory. This states that viscosity is the result of transportation of momentum in collisions of molecules. 

Many of the larger diameter particles will lose momentum In collisions with the wall at the bend and become deposited on the tube wall. The smaller particles will remain suspended In the gas with minimal disturbance due to the bend. On the other hand, this effect may also be caused by a segregation of particle diameters In the bulk stream, with particles having a larger diameter migrating away from the center of the stream. Particles with... 

E.E.B. Campbell, H. Schmidt, I.V. Hertel, Symmetry and angular momentum in collisions with laser excited polarized atoms. Adv. Chem. Phys. 72, 37 (1988)... 

Campbell, E. E. B. and R. D. Levine (2000). Delayed ionization and fragmentation en route to thermionic emission statistics and dynamics. Ann. Rev. Phys. Chem. 51, 65. Campbell, E. E. B., H. Schmidt, et al. (1988). Symmetry and angular momentum in collisions with laser excited polarised atoms. ylrfu Chem. Phys. 72, 37. 

Equations 4.48 through 4.50 specify the volume fraction and the stress ratio as functions of the inertial parameter, the coefficient of restitution, and the parameter c. These relations are equivalent to those proposed hy GDR Midi (2004) over the range of volume fractions and coefficients of restitution for which exchanges of momentum in collisions dominate the momentum transfer and before force chains span the system. That is, as v increases for a given e, the chain length I given hy (4.46) will approach the system size. When it does, there is an additional mechanism for the transfer of momentum in the flow that we do not consider (e.g., Hatano et al. 2007)—ephemeral chains of particles that transfer force across the flow and are responsible for the development of a yield stress. The model of GDR Midi continues to apply above this volume fraction and includes the rate-independent mechanism of momentum transfer, but the model described here does not. 

Differences in the nature of the energy transfer have been pointed out by Thompson. In cases like (iii), the initial orbital momentum in collisions is much larger than in (ii), because of the greater reduced mass, /x. There is consequently less constraint imposed by the requirement to conserve total... 

Now encounters between molecules, or between a molecule and the wall are accompanied by momentuin transfer. Thus if the wall acts as a diffuse reflector, molecules colliding wlch it lose all their axial momentum on average, so such encounters directly change the axial momentum of each species. In an intermolecuLar collision there is a lateral transfer of momentum to a different location in the cross-section, but there is also a net change in total momentum for species r if the molecule encountered belongs to a different species. Furthermore, chough the total momentum of a particular species is conserved in collisions between pairs of molecules of this same species, the successive lateral transfers of momentum associated with a sequence of collisions may terminate in momentum transfer to the wall. Thus there are three mechanisms by which a given species may lose momentum in the axial direction ... 

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. 

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

In collisions between two bodies the contact force and the duration of contact are usually unknown. However, the duration of contact is the same for both bodies, and the force on the first body is the negative of the force on the second body. Thus the net change in momentum is zero. This is called the principle of conservation of momentum. 

In collisions, angular momentum, like linear momentum, is conserved. 

Equation 9.72 shows that HPP collisions give rise to three conservation laws (i) total number of particles 0), (ii) momentum in the a -direction Ci — C3 =... 

Since /S Tj0) = , its integral over the collision term is zero (conservation of momentum in a collision). Thus the result of multiplying the Boltzmann equation by and integrating is ... 

Relations (2.46) and (2.47) are equivalent formulations of the fact that, in a dense medium, increase in frequency of collisions retards molecular reorientation. As this fact was established by Hubbard within Langevin phenomenology [30] it is compatible with any sort of molecule-neighbourhood interaction (binary or collective) that results in diffusion of angular momentum. In the gas phase it is related to weak collisions only. On the other hand, the perturbation theory derivation of the Hubbard relation shows that it is valid for dense media but only for collisions of arbitrary strength. Hence the Hubbard relation has a more general and universal character than that originally accredited to it. 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

In the second step the angular momentum of the Rydberg molecule may be randomized in collisions with ambient electrons (/-mixing and possibly m-mixing),... 

The dipole oscillator strength is the dominant factor in dipole-allowed transitions, as in photoabsorption. Bethe (1930) showed that for charged-particle impact, the transition probability is proportional to the matrix elements of the operator exp(ik r), where ftk is the momentum transfer. Thus, in collision with fast charged particles where k r is small, the process is again controlled by dipole oscillator strength (see Sects. 2.3.4 and 4.5). 

At long times the excess temperature, (T) - T, decays exponentially, as can be shown from the preceding equation. The relaxation rate has independent, additive contributions from momentum transfer collisions (as in the case of rare gases) and from each pair of states connected by inelastic collision. Thus the net relaxation rate is given by... 

Symbols m, momentum transfer collision v, vibrational collision (0<- l) J (0 through 6) means rotational collision (JoJ + 2). Other processes make negligible contribution in this temperature range. 

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