This presentation describes a new, analytic, and mechanistic model [Wood, 2020] for calculating the effective thermal conductivity (keff) of planetary regolith 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). The model is based on the Maxwell-Eucken theoretical expressions for the upper and lower bounds for keff of heterogeneous, isotropic material - equivalent to the Hashin-Shtrikman bounds. The effect of interparticle contact is modeled using a parameter fsc that represents the fractional continuity of the solid phase, which depends 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. 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, as well as lower limits due to plastic deformation. Particle shape is quantified in terms of its sphericity and roundness. 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 predicts values of keff which are in close agreement with previous laboratory measurements for basalt and quartz powders, crushed kyanite, and Apollo lunar soil samples.
An important application of such models is the physical interpretation of thermal inertia values derived from remote-sensing observations of surface temperature variations. Of particular interest is the regolith particle size, which has long been related to thermal inertia values on Mars and, more recently, on airless bodies. Results based on the new model will be presented showing the sensitivity of the relationship between thermal inertia and particle size to temperature and to uncertainties in other parameters including bulk porosity, particle shape, and composition.
Wood, S. E. (2020), DOI:10.1016/j.icarus.2020.113964