A mechanistic model for the thermal conductivity of planetary regolith: 1. The effects of particle shape, composition, cohesion, and compression at depth

Abstract This paper describes a new, analytic, and mechanistic model for calculating the effective thermal conductivity (keff) of planetary regolith, or any porous granular medium consisting of solid particles and gas (or vacuum). The model computes keff as a function of the physical properties of its components (e.g., intrinsic thermal conductivities), particle size and shape, bulk porosity, pore gas density, temperature, cohesive force, and lithostatic pressure (or depth). A simplified version of the model for the case of regolith in vacuum is also presented. Model predictions are compared to laboratory measurements from previous studies for a wide range of particle properties and temperature/pressure conditions. The model is based on the Maxwell-Eucken theoretical expressions for the upper and lower bounds for keff of heterogeneous, isotropic material. These equations provide tighter bounds than the parallel and series approximations often used to estimate keff for porous media. The effect of interparticle contact is modeled using an semi-empirical parameter fsc that represents the fractional continuity of the solid phase. An expression for this parameter is proposed with a functional dependence on the relative size and number of contacts between particles. The actual size of the contacts is estimated based on Hertzian mechanics of elastic deformation including the effects of cohesive surface forces (JKR theory). An effective contact radius is determined that also takes into account the heat transfer through the pore space in the immediate vicinity of the contact based on theoretical work by Batchelor and O’Brien (1977) , as well as lower limits due to plastic deformation. Particle shape is quantified in terms of its sphericity and roundness. The effects of sphericity are explicitly included in calculations of the Maxwell-Eucken bounds, the effective pore size and, along with roundness, the average local radius of curvature at the contacts. The effect of radiative heat transfer is included, as well as the dependence of gas conductivity on temperature and Knudsen number from kinetic theory. The only free parameters in the model are two constant coefficients in the hypothesized expressions for fsc and pore size which are empirically determined by least-squares fits to laboratory measurements of keff for glass beads over a wide range of particle size and pore gas pressure. Using these best-fit values for the coefficients, the model is then shown to predict values of keff which are in close agreement (σ ≤ 20%) with previous laboratory measurements for basalt and quartz powders, crushed kyanite, and Apollo lunar soil samples. A key finding of the model is that keff does depend on the instrinsic conductivity of the solid particles (and therefore on their composition and temperature) to a greater degree than indicated in previous studies, and is especially important for regolith on airless bodies. Finally, for cohesive particulates, a method is presented for estimating the porosity as a function of particle size, surface energy, density, and gravitational force.