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Collision frequency describes the rate of collisions between two atomic or molecular species in a given volume, per unit time. In an ideal gas , assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B is: [ 1 ]
The plasma collisionality is defined as [4] [5] =, where denotes the electron-ion collision frequency, is the major radius of the plasma, is the inverse aspect-ratio, and is the safety factor. The plasma parameters m i {\displaystyle m_{\mathrm {i} }} and T i {\displaystyle T_{\mathrm {i} }} denote, respectively, the mass and temperature of the ...
This equation assumes the upper limit of a diffusive collision frequency between A and B is when the first neighbor layer starts to feel the evolution of the concentration gradient, whose reaction order is 2 + 1 / 3 instead of 2. Both the Smoluchowski equation and the JChen equation satisfy dimensional checks with SI units.
For particles in a solution, an example model to calculate the collision frequency and associated coagulation rate is the Smoluchowski coagulation equation proposed by Marian Smoluchowski in a seminal 1916 publication. [4]
The equation loses accuracy for gaps under about 10 μm in air at one atmosphere [9] and incorrectly predicts an infinite arc voltage at a gap of about 2.7 μm. Breakdown voltage can also differ from the Paschen curve prediction for very small electrode gaps, when field emission from the cathode surface becomes important.
The equation predicts that for short range interactions, the equilibrium velocity distribution will follow a Maxwell–Boltzmann distribution. To the right is a molecular dynamics (MD) simulation in which 900 hard sphere particles are constrained to move in a rectangle. They interact via perfectly elastic collisions. The system is initialized ...
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
The Spitzer resistivity is a classical model of electrical resistivity based upon electron-ion collisions and it is commonly used in plasma physics. [3] [4] [5] [6 ...