1063-7761/05/10106- $26.00 © 2005 Pleiades Publishing, Inc. 1147 Journal of Experimental and Theoretical Physics, Vol. 101, No. 6, 2005, pp. 1147–1152. Translated from Zhurnal Éksperimental’noœ i Teoreticheskoœ Fiziki, Vol. 128, No. 6, 2005, pp. 1307–1313. Original Russian Text Copyright © 2005 by Shandakov, Nasibulin, Polygalov, Samchinskiœ, Kauppinen. 1. INTRODUCTION The last decade has seen rapid progress in nanotech- nologies (e.g., see [1–3]). The need to develop methods for synthesis and assembly of nanostructures stimulates theoretical prediction of their characteristics based on available experimental data, which obviously include characteristics of motion of nanoparticles and nanopar- ticle aggregates in gases [4–9]. Even though the kinetic theory of gases can be considered complete [10, 11], intermolecular interaction between polyatomic gas molecules or atoms and a particle or an ion remains an issue [10–14]. Moreover, expressions (e.g., for particle or ion drag force or mobility) obtained in the free- molecular and hydrodynamic limits of the theory are mutually inconsistent [11]. One simple method for determining the characteristics particle motion in the intermediate regime relies on the use of formal averag- ing procedures or correction factors involving empiri- cal parameters. In particular, the coagulation rate in the intermediate regime has been successfully determined by using the harmonic-mean approximation [15, 16]. In the most accurate calculations of the particle drag force, a correction factor is introduced into the Stokes law [17, 18]. Despite numerous attempts to match the expressions for the drag force obtained for limit regimes, in particular, by correcting boundary condi- tions or introducing empirical parameters, the problem remains unsolved [11]. Generally, it is assumed that an external force field does not accelerate the motion of a particle or an ion in both free-molecular and hydrodynamic limits. In the free-molecular limit, when the gas is not perturbed by particle motion, the drag force on a particle or an ion moving in a gas with a mass-average velocity V p is related to the binary diffusion coefficient by the Stokes–Einstein formula [12] (1) where k B is Boltzmann’s constant and T is temperature. Note that this relation is exact only in the limit of van- ishing external field [12]. The subscript “diff” in (1) refers to the free-molecular limit interpreted as the regime of diffusive particle motion (when forces are negligible). The subscript “hydr” used below refers to the hydrodynamic limit, in which the particle velocity is constant, the force acting on it is finite, and diffusion is negligible. In both limits, particle acceleration is neglected and diffusion due to the difference in acceler- ation between particles and molecules moving in a force field is ignored accordingly. In the intermediate regime, the acceleration of particles or ions by a force field becomes increasingly important as the particle– molecule collision frequency decreases with particle size. In this paper, we analyze particle motion in both F diff k B T D 12 -------- V p , – = Effect of Acceleration by Internal and External Force Fields on Particle Motion in Intermediate Regimes between the Hydrodynamic and Free-Molecular Limits S. D. Shandakov a, *, A. G. Nasibulin b , Yu. I. Polygalov a , E. Yu. Samchinskiœ a , and E. I. Kauppinen b,c a Kemerovo State University, Kemerovo, 650043 Russia b Center for New Materials and Department of Engineering Physics and Mathematics, Helsinki University of Technology, P.O. Box 1602, FIN-02044 VTT, Espoo, Finland c VTT Processes, Aerosol Technology Group, P.O. Box 1602, FIN-02044 VTT, Espoo, Finland *e-mail: cphys@kemsu.ru, Sergey.Shandakov@hut.fi Received June 20, 2005 Abstract—The kinetic theory of gases is applied to analyze slow translational motion of low-concentration particles driven by an external force in a homogeneous gas. The analysis takes into account the diffusion due to the difference in acceleration between particles and molecules in internal and external force fields. A general expression is derived for the particle drag force in hydrodynamic, free-molecular, and intermediate regimes. This expression reduces to a simple relation between the drag force and its values in the hydrodynamic and free- molecular limits and the force of intermolecular interaction between particles and gas molecules. In the case of spherically symmetric potential of interaction between the particle and molecules, the drag force is the har- monic mean of its limit values. © 2005 Pleiades Publishing, Inc. STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS