Driven Brownian coagulation of polymers

Preprint, Article English OPEN
Krapivsky, P. L. ; Connaughton, Colm (2012)

We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, $a$, of the aggregates. We find that two types of long time behavior are possible. For $0\leq a < 1/2$ the size distribution reaches a stationary state with a power law distribution of cluster sizes having exponent 3/2. The amplitude of this stationary state is determined exactly as a function of $a$. For $1/2 < a \leq 1$, the cluster size distribution never reaches a stationary state. Instead a bimodal distribution is formed in which a narrow population of small clusters near the monomer scale is separated by a gap (where the cluster size distribution is effectively zero) from a population of large clusters which continue to grow for all time by absorbing small clusters. The marginal case, $a=1/2$, is difficult to analyze definitively, but we argue that the cluster size distribution becomes stationary and there is a logarithmic correction to the algebraic tail.
  • References (41)
    41 references, page 1 of 5

    1Department of Physics, Boston University, Boston, Massachusetts 02215, USA 2Mathematics Institute and Centre for Complexity Science, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK (Dated: March 20, 2012)

    [1] S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).

    [2] P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, London, 1953).

    [3] R. Drake, in Topics in Current Aerosol Research, edited by G. Hidy and J. Brock (Pergamon, New York, 1972).

    [4] S. Friedlander, Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics, 2nd ed. (Oxford University Press, Oxford, 2000).

    [5] H. Pruppacher and J. Klett, Microphysics of Clouds and Precipitation, 2nd ed. (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997).

    [6] D. J. Aldous, Bernoulli 5, 3 (1999).

    [7] F. Leyvraz, Phys. Reports 383, 95 (2003).

    [8] P. Krapivsky, S. Redner, and E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, Cambridge, 2010).

    [9] M. V. Smoluchowski, Z. Phys. Chem. 92, 129 (1917).

  • Metrics
    No metrics available
Share - Bookmark