  The transverse force exerted on a rotating sphere immersed in an otherwise
uniform flow of a rarefied gas is investigated based on the
Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation assuming the
Maxwell boundary condition on the sphere. In several existing studies, it has
been shown that the transverse force acting on the sphere, also known as the
Magnus force, has opposite signs in the free molecular and continuum flows. The
present study intends to clarify the force's transition in terms of the Knudsen
number (i.e., the reciprocal ratio of the sphere radius to the molecular mean
free path) with a particular interest in the impact of the sphere's surface
accommodation. It is found that the threshold of the Knudsen number, at which
the transverse force changes the sign, depends only weakly on the accommodation
coefficient, suggesting certain robustness in the threshold. The present study
is an extension of the previous work [S. Taguchi and T. Tsuji, J. Fluid. Mech.
933, A37 (2022)], in which the case of complete accommodation (diffuse
reflection) is exclusively considered.
