Max well-Boltzmann distribution

As we are particularly interested in surface reactions and catalysis, we will calculate the rate of collisions between a gas and a surface. For a surface of area A (see Fig. 3.8) the molecules that will be able to hit this surface must have a velocity component orthogonal to the surface v. All molecules with velocity Vx, given by the Max-well-Boltzmann distribution f(v ) in Cartesian coordinates, at a distance v At orthogonal to the surface will collide with the surface. The product VxAtA = V defines a volume and the number of molecules therein with velocity Vx is J vx) V Vx)p where p is the density of molecules. By integrating over all Vx from 0 to infinity we obtain the total number of collisions in time interval At on the area A. Since we are interested in the collision number per time and per area, we calculate... 

The type of flow encountered when a highly underexpanded nozzle exhausts into a vacuum differs significantly from the random free-molecule flow characterized by the Max-well-Boltzmann distribution function, which is normally encountered in vacuum practice. The difference is illustrated in Fig. 1 and is primarily due to the large directional velocity component given to the gas molecules while still in a dense continuum flow condition in the nozzle. The velocity distribution function for the exhaust gas thus differs from that of the random flow in that it contains both the random thermal velocity components and the large directional velocity component. 

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