Radiometer effect on an infinitely thin circular disk

Abstract

The radiometer effect is a self-thermophoretic phenomenon in which a thin body with a temperature difference between its two sides experiences a force in a rarefied gas. We numerically investigate this effect for an infinitely thin circular disk freely translating at its terminal velocity in an otherwise quiescent gas. The problem is formulated using the linearized Bhatnagar--Gross--Krook model of the Boltzmann equation with the diffuse reflection boundary condition. A major difficulty arises from the sharp disk edge, which generates discontinuities in the velocity distribution function that propagate into the gas. Accurate resolution of these discontinuities is essential for capturing the edge-localized stress associated with the radiometric force in the near-continuum regime. The discontinuities are explicitly accounted for using a characteristic-based numerical scheme, together with the appropriate far-field asymptotics for the unbounded domain. The radiometric force, the terminal velocity, and the flow and stress fields are obtained over a wide range of Knudsen numbers. The dimensionless radiometric force increases monotonically with the Knudsen number, scaling as $\mathrm{Kn}^{3/2}$ in the continuum limit and approaching a constant in the free-molecular limit. The terminal velocity exhibits a nonmonotonic dependence on the Knudsen number and slightly exceeds its free-molecular-limit value at intermediate Knudsen numbers. In the continuum limit, the magnitude of the edge-localized variation of the normal-stress difference appears to remain finite, whereas its characteristic width is of the order of the molecular mean free path. The resulting numerical data also provide reference solutions for future studies of sharp-edge kinetic problems. Finally, the computed radiometric force is independently validated using the symmetric relation for the linearized Boltzmann equation.