By A. M. Howatson (Auth.)

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E, is the Hall parameter and Deli is simply a manifestation of the Hall effect. By inserting in eqn. e, it can be shown that mobility is affected in a precisely analogous way to diffusion. H ~ DJße and which is inversely proportional to B2. 2). In practice, drift across the field is often found to vary as \jB rather than \/B2, an effect known as Böhm diffusion which can be explained in terms of small-scale instabilities. The diffusion of positive ions is affected in the same way as that of electrons; but we should note that for concentration gradients in the same direction Hall diffusion occurs in opposite directions, while Hall drift in a field E occurs in the same direction for the two species.

Ions of number density n{ diffuse with a velocity given, for one-dimensional flow, by nx n{ Pi ox ox where pi is the partial pressure of ions, assumed to be at uniform temperature T. But dpjdx is the total force acting on the ions in unit volume; the electric field E which would exercise the same force is such that Eenv = dp-Jdx, or enx dx This field would then produce the same drift velocity ux by virtue of mobility only. 24) in which k is Boltzmann's constant, using the perfect gas law. The ratio of diffusion coefficient to mobility is therefore proportional to the mean random energy \kT.

In the same way, two initially separate gases become uniformly mixed. The process by which the condition of equilibrium is reached is diffusion. 1. The Diffusion Process Consider the concentration n of a simple gas in a container to vary, for any reason, in the x-direction only at some instant; there is then a net transfer of particles across any plane normal to x. It is to be expected that the net number of particles crossing unit area of such a plane per second is proportional to the on concentration gradient — ; the constant of proportionality is ox called the diffusion coefficient D for particles in their own gas, or the coefficient of self-diffusion.

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