Collision momentum

The fundamental postulate is that as a dilute gas is compressed two novel effects become important because the molecules have finite volumes. First, it is expected that during a molecular collision momentum and energy are transferred over a distance equal to the separation of the molecules. In the particular case of rigid spherical molecules this collisional transfer of momentum and energy takes place instantaneously and results in a transfer over the distance between their centers. Second, the collision frequency may be altered. One possible mechanism is that the collision frequency is increased... 

VISCOSITY AND MOMENTUM FLUX. Although Eq. (3.3) serves to define the viscosity of a fluid, it can also be interpreted in terms of momentum flux. The moving fluid just above plane C in Fig. 3.1 has slightly more momentum in the X direction than the fluid just below this plane. By molecular collisions momentum is transferred from one layer to the other, tending to speed up the slower moving layer and to slow down the faster moving one. Thus, momentum passes across plane C to the fluid in the layer below this layer transfers momentum to the next lower layer, and so on. Hence x-direction momentum is transferred in the y direction all the way to the wall bounding the fluid, where = 0, and is delivered to the wall as wall shear. Shear stress at the wall is denoted by t ,. 

Impulsanderung beim Stofi, collisive momentum 458, 462, 491, 510, 532. Impulsiibertragungsreaktion, impulsive reaction 454. 

This phenomenon is termed free diffusion. Statistical considerations indicate the possibility of calculating the concentration of the diffusing particles with a given initial situation as a function of space and time. Assume that no force effects exist between the suspended particles and the molecules of the solvent, but only that occasional transmissions of collision momentum occur, and further, that the particles do not interfere with each other s movements and are very small in comparison with the dimensions of the vessel in a unidimensional diffusion process, we obtain, for the probability dW that at a time t a particle will be encountered in the plane between x and x + dx, the relation... 

I he existence of attraction forces among the molecules leads to a certain decrea.se in the real gas pressure on the vessel walls (P < Pm). Assuming that the attraction forces cause a decrease both in the number of molecule collisions with the walls and in the collision momentum as well, and that each of the.se effects is proportional to the gas den.sity ( /Va/V), we obtain... 

In the frame of the method proposed in Kustova Nagnibeda (1998) Nagnibeda Kustova (2009) for the solution of Eqs. (2), the distribution functions are expanded in a power series of the small parameter e. The peculiarity of the modified Chapman-Enskog method is that the distribution functions and macroscopic parameters are determined by the collision invariants of the most frequent collisions. Under condition (1), the set of collision invariants contains the invariants of any collision (momentum and total energy) and the additional invariants of rapid processes. In our case, these additional invariants are any variables indepiendent of the velocity and internal energy and depending arbitrary on chemical species c because chemical reactions are supposed to be frozen in rapid processes This set of collision invariants provides the following set of macroscopic parameters for a closed flow description number densities of species Tic r,t) (c = 1,..., L), gas velocity v(r, f) and temperature T(r,f). 

Tjn denotes the mean time between subsequent collisions (momentum relaxation time). The electrons move with a constant drift velocity which is proportional to the applied electric field strength, E, such that... 

Knock-on sputtering proceeds via a sequence of individual elastic collisions (momentum transfer) occurring between atoms and/or ions as they come into close proximity to each other. How close they approach depends on the energies involved. At and below 100 keV, the distance of closest approach can be defined via the Coulombic potential as ... 

In fact (98) is model independent to order u, since only the linear term in u c, contributes. To close the hydrodynamic equations for the mass and momentum densities [(74) and (75)] we need expressions for the pre-collision and post-collision momentum fluxes, and n . From (76) we can obtain an expression for in terms of the velocity gradient. 

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