Size- and structure-independence of the thermophoretic transport of an aerosol particle for specular boundary conditions in the free molecule regime

Early conjectures and recent numerical simulations indicate that the motion of aerosol particles, including multispherule fractal aggregates, established as the result of temperature inhomogeneities in the prevailing gas are, to within a few percent, insensitive to particle size and morphology, especially in the free-molecule limit. Extending these results, we show here that in the limiting case of specular boundary conditions and free-molecular flow, particle thermophoretic velocity is exactly independent of size and structure (shape), and equal to the well-known analytical expression of Waldmann for an isolated, spherical particle in the same local environment. Our result, which applies to particles of any morphology, constitutes perhaps the only available analytical solution of a free molecular transport property for particles which can be locally concave and, more importantly, provides additional rational justification for the principal assumption underlying the widely used technique of thermophoretic sampling. Beyond the theoretical interest of the result as the limiting behavior of Maxwell's model of partial diffusive-specular scattering, our finding is of practical relevance for particles smaller than a few nanometers, for which there is now conclusive evidence that specular scattering adequately describes gas molecules-particle interactions. The result additionally provides a good test case to validate numerical algorithms dealing with complex geometries.