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

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Abstract
The theoretical expression for the drag force on a spherical particle moving with low Reynolds number in a gas is customarily written by multiplying the Stokes' law expression by a slip correction factor of the form C x = 1 +Kn[γ1 + γ2 exp(-γ3/Kn)], where Kn is the particle Knudsen number and γ1, γ2, and γ3 are empirical constants. We have measured the drag forces on spherical polystyrene latex particles suspended in dry air using the modulated dynamic light scattering technique which is fundamentally different from the Millikan cell approach. Data are time autocorrelation functions of the intensity of light scattered by single test particles from the intersection volume of two coherent laser beams. The data provide detailed information about test particle Brownian motion including the value of the particle diffusion coefficient. Each test particle was held in air suspension by an electrostatic trap to permit measurements to be made on the same particle at air pressures ranging from 760 to 0.2 torr. Data for a set of pressures provide values for the particle diffusion coefficient as a function of Kn allowing the particle diameter and the slip correction factor at each pressure to be calculated. Measurements were made on 72 solid spherical particles with diameters ranging from 1.0 to 2.2 μm. Collected data provide 1586 distinct experimental values of the slip correction factor with Kn ranging from 0.06 to 500. Analysis of these data gives the values γ1 = 1.2310 ± 0.0022 S.E., γ2 = 0.4695±0.0037 S.E., and γ3 = 1.1783 ± 0.0091 S.E., where the mean free path of air molecules and the viscosity dry air are taken to be 6.73 × 10 −8 m and 1.8325 × 10 −5 Pas, respectively, at 760 torr and 296.15 K. Results from this work for the ratio of the drag force at arbitrary Kn to the drag force in the free molecule flow regime (Kn >> 1) differ from kinetic theory results by as much as 8% in the slip regime (0.09 ≤ Kn ≤ 18).