Drag force, diffusion coefficient, and electric mobility of small particles. II. Application.

We propose a generalized treatment of the drag force of a spherical particle due to its motion in a laminar fluid media. The theory is equally applicable to analysis of particle diffusion and electric mobility. The focus of the current analysis is on the motion of spherical particles in low-density gases with Knudsen number Kn>>1. The treatment is based on the gas-kinetic theory analysis of drag force in the specular and diffuse scattering limits obtained in a preceding paper [Z. Li and H. Wang, Phys. Rev. E., 68, 061206 (2003)]. Our analysis considers the influence of van der Waals interactions on the momentum transfer upon collision of a gas molecule with the particle and expresses this influence in terms of an effective, reduced collision integral. This influence is shown to be significant for nanosized particles. In the present paper, the reduced collision integral values are obtained for specular and diffuse scattering, using a Lennard-Jones-type potential energy function suitable for the interactions of a gas molecule with a particle. An empirical formula for the momentum accommodation function, used to determine the effective, reduced collision integral, is obtained from available experimental data. The resulting treatment is shown to be accurate for interpreting the mobility experiments for particles as small as approximately 1 nm in radius. The treatment is subsequently extended to the entire range of the Knudsen number, following a semiempirical, gas-kinetic theory analysis. We demonstrate that the proposed formula predicts very well Millikan's oil-droplet experiments [R. A. Millikan, Philos. Mag. 34, 1 (1917); Phys. Rev. 22, 1 (1923)]. The rigorous theoretical foundation of the proposed formula in the Kn>>1 limit makes the current theory far more general than the semiempirical Stokes-Cunningham formula in terms of the particle size and condition of the fluid and, therefore, more attractive than the Stokes-Cunningham formula.

[1]  H. G. Scheibel,et al.  Generation of monodisperse Ag- and NaCl-aerosols with particle diameters between 2 and 300 nm , 1983 .

[2]  V. Vítek,et al.  Twin boundaries and incoherent steps on twin boundaries in body-centered-cubic metals , 1976 .

[3]  R A Millikan,et al.  THE ISOLATION OF AN ION, A PRECISION MEASUREMENT OF ITS CHARGE, AND THE CORRECTION OF STOKES'S LAW. , 1910, Science.

[4]  Y. Kuga,et al.  Classification Performance of a Low Pressure Differential Mobility Analyzer for Nanometer-sized Particles , 2001 .

[5]  S. Garofalini,et al.  Silver clustering in sodium silicate glasses: a molecular dynamics study , 1997 .

[6]  E. A. Mason,et al.  Equilibrium and Transport Properties of Eleven Polyatomic Gases At Low Density , 1987 .

[7]  Hai Wang,et al.  Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  V. Rudyak,et al.  Kinetic description of nanoparticle diffusion in rarefied gas , 2001 .

[9]  C. Farina,et al.  A simple way of understanding the nonadditivity of van der Waals dispersion forces , 1999 .

[10]  A. Schmidt-ott,et al.  Mass and size determination of nanometer particles by means of mobility analysis and focused impaction , 2003 .

[11]  M. Stowell.  The solid-liquid interfacial free energy of lead from supercooling data , 1970 .

[12]  Hannes Tammet,et al.  Size and mobility of nanometer particles, clusters and ions , 1995 .

[13]  S. Kaufman,et al.  Macromolecule analysis based on electrophoretic mobility in air:  globular proteins. , 1996, Analytical chemistry.

[14]  R. Millikan.  I. A new determination of e, N, and related constants , 1917 .

[15]  Edward A. Mason,et al.  Gaseous Diffusion Coefficients , 1972 .

[16]  P. S. Epstein,et al.  On the Resistance Experienced by Spheres in their Motion through Gases , 1924 .

[17]  Methods of measuring the diffusion coefficient and sizes of nanoparticles in a rarefied gas , 2002 .

[18]  O. Raabe,et al.  Re-evaluation of millikan's oil drop data for the motion of small particles in air , 1982 .