Einzel, Panzer, and Liu ͓Phys. Rev. Lett. 64, 2269 ͑1990͔͒ suggest that the slip boundary condition for a fluid moving near a wall is modified by the radius of curvature of the surface. Using particle simulations of a microscopic flow between concentric cylinders we qualitatively confirm their prediction and point out that the effect is seen in a limiting case derived by Maxwell ͓Nature ͑London͒ 16, 244 ͑1877͔͒.
͓S1063-651X͑97͒00208-0͔PACS number͑s͒: 47.45. Gx, 47.27.Lx, 51.10.ϩy, 47.10.ϩg In conventional hydrodynamics, one assumes the no-slip boundary condition for a fluid moving past a solid wall, that is, the velocity of the fluid at the surface is assumed to equal the wall's velocity. As was originally pointed out by Maxwell ͓1,2͔, this boundary condition is not accurate at microscopic scales since gradients normal to the surface cause particles approaching the wall to have a different velocity distribution from those leaving the wall. For a fluid moving past a stationary wall, this ''slip'' phenomenon is expressed by the boundary condition, v ʈ ϭn •ٌv ʈ , where v ʈ is the component of fluid velocity parallel to the surface, n is a unit vector normal to the surface, and is the slip length. The velocity profile extrapolates to zero at a distance inside the wall. For a dilute gas moving over a plane, the slip length is ͓3͔, 0 ϭa(2Ϫ␣/␣), where is the mean free path and aϷ1.15. The accommodation coefficient ␣ is the fraction of molecules whose velocity is thermalized at the surface and (1Ϫ␣) is the fraction that scatters elastically. In a planar channel ͑flow between parallel planes͒, the slip length at one wall is affected by the presence of the other wall when the width of the channel is less than about 10 ͓4,5͔.Einzel, Panzer, and Liu ͑EPL͒ ͓6,7͔ have suggested a more general form for the slip length, ϭ(1/ 0 Ϫ1/) Ϫ1 , where is the radius of curvature of the surface (Ͼ0 for a concave surface͒. As an example, EPL predict the angular speed for a fluid between concentric cylinders ͑radii R 1 and R 2 , R 1 ϽR 2 ) to beand is angular frequency of the inner cylinder; the outer cylinder is stationary. When 0 is large, EPL point out that the velocity field extrapolates to zero in the fluid and not, as usual, behind the outer wall ͓7͔.We performed simulations of a hard sphere dilute gas between concentric cylinders in order to test these predictions. Because of its computational efficiency, the direct simulation Monte Carlo ͑DSMC͒ method was employed ͓8,9͔. As in molecular dynamics ͑MD͒, the DSMC algorithm evolves the positions and velocities of the gas particles. Unlike MD, the individual collision trajectories are not calculated, instead collisions are stochastically selected and evaluated using the rates and probabilities given by kinetic theory. Previous studies have demonstrated DSMC to be in excellent agreement with laboratory experiments ͓10͔ and MD simulations ͓11͔, including predictions of slip in planar geometries ͓5͔.A number of DSMC simulations were performed, but here we present only the results from va...
