Nonlinear Diffusion of Ions in a Gas

Abstract

The evolution in time of an initially closely bunched group of ions in a neutral gas is examined by solving a model kinetic equation, and limits to the validity of the linear law of diffusion (Pick's law) are established. The implications of nonlinear diffusion processes for determination of ion transport coefficients in drift tube experiments are discussed.

Generalized phase-space kinetic and diffusion equations for classical and dispersive transport

“…It is clear that the effect of trapping enters equation (14) only through the operator ∂ t , while the spatial gradient terms are determined by free carrier transport. Moreover, the free carrier transport coefficients are unaltered by trapping, e.g., equation (16) provides exactly the same expressions that one obtains from the classical (non-trapping) BGK model kinetic equation [20,21]. At this point we note that we can obtain the same result in a more direct way, by simply assuming Fickʼs law for the free carriers,…”

“…corresponding to release of N (0) particles from the origin of coordinates with a Maxwellian distribution of velocities with an initial temperature T 0 , can be obtained exactly through Fourier and Laplace transformation in space and time respectively, following the same mathematical procedure as [14] and [21]. The transformed number density then follows…”

Third-order transport coefficients for localised and delocalised charged-particle transport

“…We confirm that when there are no traps present, ν trap = 0, the transport coefficients agree with those of the BGK collision model, previously found by Robson 26 : …”

“…Although this is the case in general, there are situations where the skewness can be defined using fewer than three components. Indeed, this is the case for the BGK model as studied by Robson 26 where the skewness given by Eq. ( 26 ) is defined using only the components Q 1 and Q 3 , with Q 2 = 0.…”

Turbulent dispersion in a stable layer with a quadratic exchange coefficient

“…Rapid variations in concentration lead to interesting phenomena, for example, countergradient flow in forest canopies (Denmead and Bradley, 1985) and these situations must generally be analysed by other means (Raupach, 1986). There is quite a substantial effort directed toward stochastic modelling of turbulent dispersion (van Dop et al, 1985 ;de Baas et al, 1986) in order to avoid the problems inherent in K-theory and, interestingly enough, there has also been considerable research on the corresponding problem for diffusion of non-turbulent swarms from the point of view of the kinetic theory of gases (Robson, 1975;Kumar et al, 1980;Kumar, 1984). Large-gradient effects are responsible for the phenomenon of 'diffusion cooling' in which the effective diffusion coefficient is reduced to a value below that given by the standard diffusion approximation (Robson, 1976).…”