Heat transfer in granular media consisting of particles in humid air at low confining pressure

I study the heat transfer in systems of weakly interacting particles at low confining pressure in the normal atmosphere. The particles have surface roughness with self-affine fractal properties, as expected for mineral particles produced by fracture, e.g., by crunching brittle materials in a mortar. I show that for small particles (say <10μm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<10 \ \mathrm{\mu m}$$\end{document}) with hydrophilic surfaces, at large humidity water capillary bridges dominate the heat transfer, while for big particles heat transfer via the air dominates. This differs from vacuum conditions where the propagating electromagnetic (EM) waves give the dominant heat transfer for large particles, while for small particles both the evanescent EM-waves and the phononic contribution from the area of real contact are most important.