Slip Correction Measurements of Spherical Solid Aerosol Particles in an Improved Millikan Apparatus

Abstract

A slip correction factor is used to correct Stokes' law for the fact that the no-slip boundary condition is violated for small aerosol particles moving with respect to the gaseous medium. The Knudsen-Weber form of the slip correction is given by C(Kn)= 1 + Kn[α + β exp(—γ/Kn)]. The parameters α, β, and γ are customarily those based upon the experiments reported in 1917 and 1923 by R. A. Millikan for aerosol droplets of oil. Because of differences in molecular interactions with the surfaces of solid particles and oil drops, different parameters should be appropriate for solid particles.

In this study an improved version of the Millikan apparatus was designed, built, and used to measure the slip correction factors for 90 solid, spherical particles in air. Measurements were made on 11 polystyrene latex-divinylbenzene particles, 25 polyvinyltoluene particles, and 54 polystyrene latex particles, spanning a Knudsen number range from 0.03 to 7.2. The fitted nonlinear least squares values of α, β, and γ are 1.142 (±0.0024 SE), 0.558 (± 0.0024 SE), and 0.999 (±0.0212 SE), respectively, for the assumed mean free path of 0.0673 μm for air at sea level and 23°C with viscosity of 183.245 micropoise. This value of α agrees very closely with Millikan's result (adjusted to the same mean free path). The sum of α + β = 1.700 (applicable in the free molecular regime) was 4.45% higher than Millikan's value for oil droplets; this observation is consistent with the expectation that a higher percentage of molecules undergo specular reflections from the surface of a solid particle than from the surface of an oil droplet.