Kinetic Theory of Hydrodynamic Flows, III. The Torque on a Rotating Sphere or Cylinder 1

In two earlier papers, (1'2) referred to here as I and II, respectively, we showed how to calculate the drag force on a macroscopic sphere or cylinder moving through a dilute gas by using an extended Boltzmann equation. This equation differs from the usual Boltzmann equation in that it treats the effect of collisions between.gas molecules and the macroscopic object as a term in the Boltzmann equation itself rather than by means of a boundary condition to be satisfied by the distribution function at the surface of the object. This equation, although equivalent to the Boltzmann equation plus boundary conditions, (3) enabled us to describe the gas flow in both the rarefied and hydrodynamic regions and to compute the drag force directly in terms of the collisions between the gas molecules and the object.