Continuous distribution theory for Ostwald ripening: comparison with the LSW approach

A numerical solution for a general population balance equation (PBE) for Ostwald ripening is compared with the usual approach developed by Lifshitz-Slyozov-Wagner (LSW). The PBE incorporates denucleation for unstable particles smaller than the critical nucleus size and reversible growth or dissolution of stable particles. The PBE theory shows how supersaturation decays to equilibrium, and (unlike LSW) how the particle size distribution (PSD) and its moments evolve to a final monodisperse state. The LSW model is known to correctly depict time dependence of particle number concentration and average particle size, but misrepresents the PSD higher moments.

[1]  M. Zinke–Allmang,et al.  SELF-SIMILAR SPATIAL ORDERING OF CLUSTERS ON SURFACES DURING OSTWALD RIPENING , 1997 .

[2]  Venzl.  Dynamics of first-order phase transitions: Theory of coarsening (Ostwald ripening) for open systems. , 1985, Physical review. A, General physics.

[3]  B. J. McCoy,et al.  Ostwald ripening with size-dependent rates: Similarity and power-law solutions , 2002 .

[4]  L. Feldman,et al.  Clustering on surfaces , 1992 .

[5]  Carl Wagner,et al.  Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald‐Reifung) , 1961, Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaft für physikalische Chemie.

[6]  J. Bullard.  Numerical simulations of transient-stage Ostwald ripening and coalescence in two dimensions , 1997 .

[7]  I. Lifshitz,et al.  The kinetics of precipitation from supersaturated solid solutions , 1961 .

[8]  Peter W Voorhees,et al.  Ostwald Ripening of Two-Phase Mixtures , 1992 .

[9]  B. J. McCoy,et al.  Denucleation rates during Ostwald ripening: Distribution kinetics of unstable clusters , 2002 .

[10]  Benjamin J. McCoy,et al.  Distribution kinetics theory of Ostwald ripening , 2001 .

[11]  Kurt Binder,et al.  Theory for the dynamics of "clusters." II. Critical diffusion in binary systems and the kinetics of phase separation , 1977 .

[12]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[13]  E. Ruckenstein,et al.  OSTWALD RIPENING : A STOCHASTIC APPROACH , 1995 .

[14]  D. H. Napper.  Particle growth in suspensions: Edited by A. L. Smith, Soc. Chem. Ind. Monogr. No. 38, Academic Press, London, 1973. 306 pp. $16.80 (£7.00) , 1974 .

[15]  P. Voorhees,et al.  DYNAMICS OF LATE-STAGE PHASE SEPARATION : A TEST OF THEORY , 1999 .

[16]  S. Girshick.  Comment on: "Self-consistency correction to homogeneous nucleation theory" , 1991 .

[17]  A. Baldan,et al.  Review Progress in Ostwald ripening theories and their applications to nickel-base superalloys Part I: Ostwald ripening theories , 2002 .

[18]  B. J. McCoy,et al.  Transition from nucleation and growth to Ostwald ripening , 2002 .

[19]  H. Grätz.  A time constant for Ostwald ripening of precipitates and normal grain growth , 1999 .

[20]  C. H. Yang,et al.  Theory of homogeneous nucleation: A chemical kinetic view , 1986 .

[21]  J. Ross,et al.  Kinetics of phase transitions: Theory of Ostwald ripening , 1983 .

[22]  M. Slemrod,et al.  DYNAMICS OF FIRST ORDER PHASE TRANSITIONS , 1984 .

[23]  B. J. McCoy,et al.  Distribution kinetics of Ostwald ripening at large volume fraction and with coalescence. , 2003, Journal of colloid and interface science.

[24]  M. Zinke–Allmang,et al.  Rate equation approach to the late stages of cluster ripening , 1998 .

[25]  Peter W Voorhees,et al.  Phase-field simulation of 2-D Ostwald ripening in the high volume fraction regime , 2002 .