Hostname: page-component-7dd5485656-c8zdz Total loading time: 0 Render date: 2025-10-31T07:05:50.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 1. Brownian motion and fluid shearing

Published online by Cambridge University Press:  20 April 2006

H. J. Pearson ,
I. A. Valioulis  and
E. J. List
H. J. Pearson
Affiliation:
W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California 91125
I. A. Valioulis
Affiliation:
W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California 91125
E. J. List
Affiliation:
W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California 91125
Get access Rights & Permissions [Opens in a new window]

Abstract

A method for the Monte Carlo simulation, by digital computer, of the evolution of a colliding and coagulating population of suspended particles is described. Collision mechanisms studied both separately and in combination are: Brownian motion of the particles, and laminar and isotropic turbulent shearing motions of the suspending fluid. Steady-state distributions are obtained by adding unit-size particles at a constant rate and removing all particles once they reach a preset maximum volume. The resulting size distributions are found to agree with those obtained by dimensional analysis (Hunt 1982).

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 143 , June 1984 , pp. 367 - 385
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathemtical Functions. Natl Bur. Stand.
Adler, P. M. 1981 Heterocoagulation in shear flow. J. Coll. Interface Sci. 83, 106–115.Google Scholar
Alder, B. J. & Wainwright, T. E. 1959 Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459–466.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Chandrasekhar, S. 1943 Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1–89.Google Scholar
Corrsin, S. 1963 Estimates of the relations between Eulerian and Lagrangian scale in large Reynolds number turbulence. J. Atmos. Sci. 20, 115.Google Scholar
Findheisen, W. 1939 Meteor. Z. 56, 356.
Friedlander, S. K. 1960a On the particle size spectrum of atmospheric aerosols. J. Meteor. 17, 373–374.Google Scholar
Friedlander, S. K. 1960b Similarity considerations for the particle-size spectrum of a coagulating, sedimenting aerosol. J. Meteor. 17, 479–483.Google Scholar
Gartrell, G. & Friedlander, S. K. 1975 Relating particulate pollution to sources: the 1972 California aerosol characterization study. Atmos. Environ. 9, 279–294.Google Scholar
Gelbard, F., Tambour, Y. & Seinfeld, J. H. 1980 Sectional representations for simulating aerosol dynamics. J. Coll. Interface Sci. 76, 541–556.Google Scholar
Gillespie, D. T. 1972 The stochastic coalescence model for cloud droplet growth. J. Atmos. Sci. 29, 1496–1510.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Hunt, J. R. 1982 Self-similar particle size distributions during coagulations: theory and experimental verification. J. Fluid Mech. 122, 169–185.Google Scholar
Husar, R. B. 1971 Coagulation of Knudsen aerosols. Ph.D. thesis, The University of Minnesota, Minneapolis.
Lumley, J. L. 1972 On the solution of equations describing small scale deformation. In Symposia Mathematica: Convegno sulla Teoria della Turbolenza al Instituto de Alta Matematica. Academic.
Mason, S. G. 1977 Orthokinetic phenomena in disperse systems. J. Coll. Interface Sci. 58, 275–285.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
Nowakowski, R. & Sitarski, M. 1981 Brownian coagulation of aerosol particles by Monte Carlo simulation. J. Coll Interface Sci. 83, 614–622.Google Scholar
Pruppacher, H. R. & Klett, J. D. 1978 Microphysics of Clouds and Precipitation. Reidel.
Saffman, P. G. & Turner, J. S. 1956 On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16–30.Google Scholar
Smoluchowski, M. 1916 Drei Vorträge über Diffusion brownsche Bewegung und Koagulation von Kolloidteilchen. Physik Z. 17, 557–585.Google Scholar
Smoluchowski, M. 1917 Versuch einer mathematischen Theorie der Koagulationskinetic kolloider Lösungen. Z. Phys. Chem. 92, 129.Google Scholar
Valioulis, I. A., List, E. J. & Pearson, H. J. 1984 Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 2. Interparticle forces and the quasi-stationary equilibrium hypothesis. J. Fluid Mech. 143, 387–411.Google Scholar
van de Ven, T. G. M. & Mason, S. G. 1977 The microrheology of colloidal dispersions. VIII. Effect of shear on perikinetic doublet formation. Coll. Polymer Sci. 255, 794–804.Google Scholar
Zeichner, G. R. & Schowalter, W. R. 1977 Use of trajectory analysis to study the stability of colloidal dispersions in flow fields. AIChE J. 23, 243–254.Google Scholar