Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T19:05:51.157Z Has data issue: false hasContentIssue false
  • English
  • Français

Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 2. Interparticle forces and the quasi-stationary equilibrium hypothesis

Published online by Cambridge University Press:  20 April 2006

I. A. Valioulis ,
E. J. List  and
H. J. Pearson
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
H. J. Pearson
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

Hunt (1982) and Friedlander (1960a, b) used dimensional analysis to derive expressions for the steady-state particle-size distribution in aerosols and hydrosols. Their results were supported by the Monte Carlo simulation of a non-interacting coagulating population of suspended spherical particles developed by Pearson, Valioulis & List (1984). Here the realism of the Monte Carlo simulation is improved by accounting for the modification to the coagulation rate caused by van der Waals', electrostatic and hydrodynamic forces acting between particles. The results indicate that the major hypothesis underlying the dimensional reasoning, that is, collisions between particles of similar size are most important in determining the shape of the particle size distribution, is valid only for shear-induced coagulation. It is shown that dimensional analysis cannot, in general, be used to predict equilibrium particle-size distributions, mainly because of the strong dependence of the interparticle force on the absolute and relative size of the interacting particles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 143 , June 1984 , pp. 387 - 411
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.)

References

Adler, P. M. 1981 Heterocoagulation in shear flow. J. Coll. Interf. Sci. 83, 106–115.Google Scholar
Arp, P. A. & Mason, S. G. 1976 Orthokinetic collisions of hard spheres in simple shear flow. Can. J. Chem. 54, 3769–3774.Google Scholar
Batchelor, G. K. 1976 Brownian diffusion of particles with hydrodynamic interactions. J. Fluid Mech. 74, 1–29.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 The hydrodynamic interactions of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375–400.Google Scholar
Beyewitz, M. H., Yershalmi, J., Katz, S. & Shinnar, R. 1974 The extent of correlations in a stochastic coalescence process. J. Atmos. Sci. 31, 1604–1614.Google Scholar
Einstein, A. 1926 The Theory of the Brownian Movement. Dover.
Faisst, W. K. 1980 Characterization of particles in digested sewage sludge. In Particulates in Water: Characterization, Fate, Effects and Removal (ed. M. C. Kavanagh and J. O. Leckie). Adv. in Chem. Series 189, American Chemical Society.
Findeisen, W. 1939 Zur Frage der Regentröpfenbildung in reinem Wasserwolken. Meteor. Z. 56, 365–368.Google Scholar
Frens, G. & Overbeek, J. T. G. 1971 Repeptization and the theory of elecrostatic colloids. J. Coll. Interf. Sci. 38, 376–387.Google Scholar
Friedlander, S. K. 1960a On the particle size spectrum of atmospheric aerosols. J. Meteorol. 17, 373–374.Google Scholar
Friedlander, S. K. 1960b Similarity considerations for the particle-size spectrum of a coagulating, sedimenting aerosol. J. Meteorol. 17, 479–483.Google Scholar
Fuchs, N. A. 1964 The Mechanics of Aerosols. Pergamon.
Gillespie, D. T. 1972 The stochastic coalescence model for cloud droplet growth. J. Atmos. Sci. 29, 1496–1510.Google Scholar
Honig, E. P. & Mull, P. M. 1971 Tables and equations of the diffuse double layer repulsion at constant potential and at constant charge. J. Coll. Interf. Sci. 36, 258–272.Google Scholar
Honig, E. P., Roebersen, G. J. & Wiersema, P. H. 1971 Effect of hydrodynamic interaction on the coagulation rate of hydrophobic colloids. J. Coll. Interf. Sci. 36, 97–109.Google Scholar
Hunt, J. R. 1982 Self-similar particle-size distributions during coagulation: theory and experimental verification. J. Fluid Mech. 122, 169–185.Google Scholar
Jeffrey, D. J. 1981 Quasi-stationary approximations for the size distribution of aerosols. J. Atmos. Sci. 38, 2440–2443.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
Neiburger, M., Lee, I. Y., Lobl, E. & Rodriguez, L. 1976 Computed collision efficiencies and experimental collection efficiencies on cloud drops. In Proc. Conf. on Cloud Phys. of the Am. Meteor. Soc., Tuscon, Ariz., pp. 73–78.
Pearson, H. J., Valioulis, I. A. & List, E. J. 1984 Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 1. Brownian motion and fluid shearing. J. Fluid Mech. 143, 367–385.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
Schenkel, J. H. & Kitchener, J. A. 1960 A test of the Derjaguin—Verwey—Overbeek theory with a colloidal suspension. Trans. Faraday Soc. 56, 161–173.Google Scholar
Smoluchowski, M. 1916 Drei Vorträge über Diffusion, brownsche Bewegung und Koagulation von Kolloidteilchen. Phys. Z. 17, 557–585.Google Scholar
Smoluchowski, M. 1917 Versuch einer mathematischen Theorie der Koagulationskinetic kolloider Lösungen. Z. Phys. Chem. 92, 129.Google Scholar
Spielman, A. L. 1970 Viscous interactions in Brownian coagulation. J. Coll. Interf. Sci. 33, 562–571.Google Scholar
Stimson, M. & Jeffrey, G. B. 1926 The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. A 111, 110–116.Google Scholar
Tag, P. M. 1976 The effect of utilizing empirically derived values of coalescence efficiency in a microphysical cloud model. In Proc. Conf. on Cloud Phys. of the Am. Meteor. Soc., Tuscon, Ariz., pp. 73–78.
Valioulis, I. A. & List, E. J. 1983 Collision efficiencies of diffusing spherical particles: Hydro-dynamic, van der Waals’ and electrostatic forces. Adv. Coll. Interface Sci. (in press).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