Abstract
In this paper, we present a fluid model for electrons and positrons in structured and soft-condensed matter utilizing dilute gas phase cross-sections together with a structure factor for the medium. Generalizations of the Wannier energy and Einstein (Nernst–Townsend) relations to account for coherent scattering effects present in soft-condensed matter are presented along with new expressions directly relating transport properties in the dilute gas and the structured matter phases. The theory is applied to electrons in a benchmark Percus–Yevick model and positrons in liquid argon, and the accuracy is tested against a multi-term solution of Boltzmann's equation (White and Robson 2011 Phys. Rev. E 84 031125).
Highlights
In this paper, we present a fluid model for electrons and positrons in structured and soft-condensed matter utilizing dilute gas phase cross-sections together with a structure factor for the medium
While there are many and varied techniques to close the set of moment equations and approximate the moments of the collision integral, we believe that momentum-transfer theory (MTT) represents the most transparent and internally consistent method
In light of the issues experienced using a standard MTT approach, we have developed a modified approach that utilizes the existing dilute gas phase transport coefficient literature to predict transport in the soft-condensed phase and this approach is outlined
Summary
The fundamental equation describing a swarm of light, charged particles moving through a gaseous or soft-condensed matter medium subject to an electric field, E, is the Boltzmann kinetic equation for the phase-space distribution function f ≡ f (r, v, t) [8]:. Using the explicit form of the collision operators used in [1, 27] and applying the relevant approximations from MTT, the set of moment equations (9)–(11) in the hydrodynamic regime yield for a steady-state swarm of light particles, m m0, the following hierarchy of coupled equations: qE. 2 m σA j, j (20g) represent the dilute gas phase momentum and energy transfers, soft-condensed momentum transfer and attachment collision frequencies, respectively, and are all prescribed functions of the mean energy defined in the centre of mass frame. For a further discussion on the heat flux, see [18] From this system of equations, structure-modified generalizations of well-known dilute gas phase results, such as Wannier’s energy relation [17], GER [20] and others, can be made, as detailed below
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