Flow of a Rarefied Gas past an Axisymmetric Body. II. Case of a Sphere

Abstract

The drag exerted by the flow on a sphere is explicitly calculated by using the relation between the drag and a certain functional. A comparison of the results with the experimental data of Millikan gives excellent agreement.

Comparison between Navier-Stokes and DSMC Calculations for Low Reynolds Number Slip Flow Past a Confined Microsphere

“…We compare the normalized total drag coefficient on the microsphere, C D Re/12 [1] versus the Knudsen number for three separate blockage ratios, B=2.0, B=5.0 and B=13.0 (DSMC) and B=40.0 (NS). For the largest value of B, the normalized drag coefficient was also compared against the analytical formula presented by Beresnev et al [4], which is in good agreement with other theoretical and numerical results (see for example [6,7]). For complete diffusive reflection on the surface of the sphere, the normalized analytical drag coefficient [4] can be written as follows: …”

“…For the most difficult computational case (Kn=0.04, B=13.0), a pipe domain with dimensions (L,R)=(64×20) µm was employed and the radius of the spherical particle was taken as R p =1.55 µm. The total number of simulated molecules in the pipe volume was approximately 20×10 6 . In this case, the computational domain was covered by a grid with 2400×800 basic cells.…”

Slip Correction Measurements for Solid Spherical Particles by Modulated Dynamic Light Scattering

“…Plots of drag force ratio D, versus Knudsen number from (1) the kinetic theory results of Cercignani et al (1968), (2) reevaluation of Millikan's oil droplet data (Allen and Raabe, 1982), (3) measurements on solid particles in this work, and (4) measurements on solid particles by Allen and Raabe (1985). the kinetic theory and oil droplet D, values fall below those for solid particles over the full range of the 20 value list (0.09 5 Kn I 18) given by Cercignani et al (1968), with differences as much as 8%. This indicates that the drag force ratio varies significantly with test particle type and that drag force measurements provide a means for study of molecule-surface interactions.…”

“…Cercignani et al (1968) Loyalka (1992) has given an accurate description of the motion of a sphere in a gas based on the linearized Boltzmann equation.…”

“…Quantity $J is a dimensionless kinetic theory parameter relating gas viscosity, molecular mean free path, and mean molecular speed, to which Raabe (1982,1985) assigned the value 0.491. Cercignani et al (1968) defined the molecular mean free path s, as s, = ( q /~) (~k~/ 2 r n ) ' " , (23) and parameter R as R = ~"~d / ( 4 s~ ).…”