A moment methodology for coagulation and breakage problems: Part 3—generalized daughter distribution functions

Abstract Population balances for simultaneous coagulation and breakage (and their analogs, e.g., polymerization and depolymerization) are employed in describing many systems including aerosols, powders and polymers, and many unit operations including reactors, crystallizers, and size reduction/enlargement equipment. The birth term for the breakage process is usually formulated in terms of a distribution of breakage products known as the daughter distribution. There are many daughter distribution forms proposed in the literature in part because these distributions are notoriously difficult to determine experimentally. Here, a generalization of these forms is developed for multi-particle breakup which has the flexibility to represent a wide variety of distribution shapes. The simplicity of the generalized expression renders the population balance equations for simultaneous coagulation and breakage accessible to analytical attack, leading to an analytical expression for the fine end of the steady-state product size distribution. This expression has potential utility in both design and analysis of experiments aimed at measuring daughter distribution parameters.

[1]  J. H. Olson,et al.  A moment methodology for coagulation and breakage problems: Part 1—analytical solution of the steady-state population balance , 2002 .

[2]  Margaritis Kostoglou,et al.  On the steady-state size distribution of dispersions in breakage processes , 1997 .

[3]  Robert P. Hesketh,et al.  Experimental observations of bubble breakage in turbulent flow , 1991 .

[4]  Ka Ming Ng,et al.  New discretization procedure for the breakage equation , 1995 .

[5]  Leonard G. Austin,et al.  Some Results on the Description of Size Reduction as a Rate Process in Various Mills , 1976 .

[6]  H. Svendsen,et al.  Theoretical model for drop and bubble breakup in turbulent dispersions , 1996 .

[7]  Robert M. Ziff,et al.  On the stability of coagulation--fragmentation population balances , 1989 .

[8]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[9]  L. Tavlarides,et al.  Simulation analysis of drop breakage, coalescence and micromixing in liquid-liquid stirred tanks , 1983 .

[10]  Doraiswami Ramkrishna,et al.  Droplet breakage in stirred dispersions. Breakage functions from experimental drop-size distributions , 1996 .

[11]  A. W. Etchells,et al.  Bubble breakage in pipeline flow , 1991 .

[12]  K. S. Gandhi,et al.  A new model for the breakage frequency of drops in turbulent stirred dispersions , 1992 .

[13]  Costas Tsouris,et al.  Breakage and coalescence models for drops in turbulent dispersions , 1994 .

[14]  Ka Ming Ng,et al.  Statistics of multiple particle breakage , 1996 .

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

[16]  R. Diemer,et al.  A moment methodology for coagulation and breakage problems: Part 2 Moment models and distribution reconstruction , 2002 .

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