Evolution to similarity solutions for fragmentation and aggregation

Abstract The theory of binary fragmentation and aggregation is of interest in numerous engineering applications, including polymer decomposition and addition. Particles can randomly aggregate and simultaneously fragment to smaller sizes that may be distributed randomly or nonrandomly. When the initial particle-size distribution (PSD) is represented as a generalized γ distribution, the time evolution of its parameters can be determined. We assume the fragmentation rate coefficient depends on particle size,x, asxλ, and the aggregation rate coefficient is independent of particle size. The type of fission (e.g., random or midpoint) is governed by the stoichiometric coefficient. Numerical solutions show the time evolution for general cases of fragmentation and aggregation. We show that the PSD approaches similarity solutions for special cases of fragmentation–aggregation stoichiometry and of λ.

[1]  Benjamin J. McCoy,et al.  Time evolution to similarity solutions for polymer degradation , 1998 .

[2]  B. J. McCoy,et al.  Distribution kinetics of radical mechanisms: Reversible polymer decomposition , 1997 .

[3]  J. Smith,et al.  Molecular Weight Effect on the Dynamics of Polystyrene Degradation , 1997 .

[4]  B. J. McCoy,et al.  Degradation kinetics of polymers in solution : Dynamics of molecular weight distributions , 1997 .

[5]  J. Smith,et al.  Degradation of poly(methyl methacrylate) in solution , 1996 .

[6]  J. Smith,et al.  Thermal degradation of poly(a-methylstyrene) in solution , 1996 .

[7]  Patrick T. Spicer,et al.  Coagulation and fragmentation: Universal steady‐state particle‐size distribution , 1996 .

[8]  Neil A. Dotson,et al.  Polymerization Process Modeling , 1995 .

[9]  J. Smith,et al.  Continuous kinetics for thermal degradation of polymer in solution , 1995 .

[10]  B. J. McCoy,et al.  Continuous-mixture fragmentation kinetics: particle size reduction and molecular cracking , 1994 .

[11]  Ruben D. Cohen.  The self-similar cluster size distribution in random coagulation and breakup , 1992 .

[12]  Robert M. Ziff,et al.  New solutions to the fragmentation equation , 1991 .

[13]  R. Ziff,et al.  Analytical solutions to fragmentation equations with flow , 1988 .

[14]  Robert M. Ziff,et al.  Kinetics of polymer degradation , 1986 .

[15]  Meakin,et al.  Kinetics of coagulation with fragmentation: Scaling behavior and fluctuations. , 1986, Physical review letters.

[16]  Robert M. Ziff,et al.  The kinetics of cluster fragmentation and depolymerisation , 1985 .

[17]  Michael Aizenman,et al.  Convergence to equilibrium in a system of reacting polymers , 1979 .

[18]  Doraiswami Ramkrishna,et al.  A population balance model for mass transfer in lean liquid—liquid dispersions , 1973 .

[19]  David Mautner Himmelblau,et al.  Process Analysis and Simulation. Deterministic Systems , 1968 .

[20]  S. Friedlander,et al.  The self-preserving particle size distribution for coagulation by brownian motion☆ , 1966 .

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

[22]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[23]  M. Inokuti.  Weight‐Average and z‐Average Degree of Polymerization for Polymers Undergoing Random Scission , 1963 .

[24]  C. Sleicher.  Maximum stable drop size in turbulent flow , 1962 .

[25]  O. Saito.  On the Effect of High Energy Radiation to Polymers I. Cross-linking and Degradation , 1958 .

[26]  P. J. Blatz,et al.  Note on the Kinetics of Systems Manifesting Simultaneous Polymerization-Depolymerization Phenomena , 1945 .

[27]  D. Browarzik,et al.  Continuous kinetics of reversible reactions in polydisperse mixtures , 1997 .

[28]  I. Chin,et al.  Degradation of microbial polyesters : A theoretical prediction of molecular weight and polydispersity , 1996 .

[29]  G. Price,et al.  Ultrasonic degradation of polymer solutions. 1. Polystyrene revisited , 1991 .

[30]  Thomas W. Peterson,et al.  Similarity Solutions for the Population Balance Equation Describing Particle Fragmentation , 1986 .

[31]  S. A. Liebman,et al.  Pyrolysis and GC in polymer analysis , 1985 .

[32]  D. Ramkrishna.  The Status of Population Balances , 1985 .

[33]  P. Flory.  Principles of polymer chemistry , 1953 .