The kinetic boundary layer around an absorbing sphere and the growth of small droplets
Abstract
Deviations from the classical Smoluchowski expression for the growth rate of a droplet in a supersaturated vapor can be expected when the droplet radius is not large compared to the mean free path of a vapor molecule. The growth rate then depends significantly on the structure of the kinetic boundary layer around a sphere. The authors consider this kinetic boundary layer for a dilute system of Brownian particles. For this system a large class of boundary layer problems for a planar wall have been solved. They show how the spherical boundary layer can be treated by a perturbation expansion in the reciprocal droplet radius. In each order one has to solve a finite number of planar boundary layer problems. The first two corrections to the planar problem are calculated explicitly. For radii down to about two velocity persistence lengths (the analog of the mean free path for a Brownian particle) the successive approximations for the growth rate agree to within a few percent. A reasonable estimate of the growth rate for all radii can be obtained by extrapolating toward the exactly known value at zero radius. Kinetic boundary layer effects increase the time needed for growth from 0 to 10more »
 Authors:
 (Johannes Kepler Universitaet Linz (Austria))
 Publication Date:
 OSTI Identifier:
 5504889
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Statistical Physics; (USA); Journal Volume: 55:56
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DROPLETS; BOUNDARY LAYERS; GASES; SUPERSATURATION; VAPOR CONDENSATION; PERTURBATION THEORY; ABSORPTION; ALGORITHMS; BOUNDARYVALUE PROBLEMS; BROWNIAN MOVEMENT; CONVERGENCE; EIGENFUNCTIONS; KINETIC EQUATIONS; LIQUIDS; MEAN FREE PATH; MILNE PROBLEM; MOLECULES; RESONANCE; SERIES EXPANSION; STATISTICAL MECHANICS; THERMODYNAMICS; TRANSPORT THEORY; TWOPHASE FLOW; VAPORS; EQUATIONS; FLUID FLOW; FLUIDS; FUNCTIONS; LAYERS; MATHEMATICAL LOGIC; MECHANICS; PARTICLES; SATURATION; 656002*  Condensed Matter Physics General Techniques in Condensed Matter (1987); 657002  Theoretical & Mathematical Physics Classical & Quantum Mechanics
Citation Formats
Widder, M.E., and Titulaer, U.M. The kinetic boundary layer around an absorbing sphere and the growth of small droplets. United States: N. p., 1989.
Web. doi:10.1007/BF01041081.
Widder, M.E., & Titulaer, U.M. The kinetic boundary layer around an absorbing sphere and the growth of small droplets. United States. doi:10.1007/BF01041081.
Widder, M.E., and Titulaer, U.M. 1989.
"The kinetic boundary layer around an absorbing sphere and the growth of small droplets". United States.
doi:10.1007/BF01041081.
@article{osti_5504889,
title = {The kinetic boundary layer around an absorbing sphere and the growth of small droplets},
author = {Widder, M.E. and Titulaer, U.M.},
abstractNote = {Deviations from the classical Smoluchowski expression for the growth rate of a droplet in a supersaturated vapor can be expected when the droplet radius is not large compared to the mean free path of a vapor molecule. The growth rate then depends significantly on the structure of the kinetic boundary layer around a sphere. The authors consider this kinetic boundary layer for a dilute system of Brownian particles. For this system a large class of boundary layer problems for a planar wall have been solved. They show how the spherical boundary layer can be treated by a perturbation expansion in the reciprocal droplet radius. In each order one has to solve a finite number of planar boundary layer problems. The first two corrections to the planar problem are calculated explicitly. For radii down to about two velocity persistence lengths (the analog of the mean free path for a Brownian particle) the successive approximations for the growth rate agree to within a few percent. A reasonable estimate of the growth rate for all radii can be obtained by extrapolating toward the exactly known value at zero radius. Kinetic boundary layer effects increase the time needed for growth from 0 to 10 (or 2{1/2}) velocity persistence lengths by roughly 35% (or 175%).},
doi = {10.1007/BF01041081},
journal = {Journal of Statistical Physics; (USA)},
number = ,
volume = 55:56,
place = {United States},
year = 1989,
month = 6
}

The structure of the plasma disturbance near a spherical charged body is analyzed with allowance for the boundedness of the region of finite particle motion. The significance of the outer radius of the spherical region in which trapped particles can exist is demonstrated. The radius of the trapping sphere is determined by the boundary condition imposed on Poisson's equation. The important role played by the boundary of the trapping region in the general analysis and solution of the problem is illustrated by simple examples.

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