Citation
Wang, Chiusen (1966) A mathematical study of the particle size distribution of coagulating disperse systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd09232002110824
Abstract
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The behavior of the particle size distribution of coagulating dispersions is studied theoretically. If the collision frequency factor is a homogeneous function of particle volume, the partial integrodifferential equation describing the coagulation kinetics can be transformed into an ordinary integrodifferential equation by a similarity transformation originally proposed by Friedlander. The solution to the resulting equation, called the selfpreserving spectrum, is determined for three different collision mechanisms: (1) constant collision frequency factor, (2) Brownian motion, and (3) simultaneous Brownian motion and shear flow, in which the shear rate decreases with time in a particular way. The results of this study indicate that the shape of the selfpreserving spectrum is greatly influenced by the collision mechanism.
If a slip correction for the particle drag is taken into consideration, the coagulation equation for Brownian motion cannot be reduced to an ordinary integrodifferential equation. However, the coagulation equation can be written in terms of a reduced size spectrum, By assuming that the reduced size spectrum varies slowly with time, a family of "quasiselfpreserving" spectra are obtained for various values of a parameter [?] which is a function of the mean free path of the fluid, the total volume concentration and the total number concentration of particles.
The selfpreserving hypothesis concerning the particle size distribution is proved to be true for the case of constant collision frequency factor. For Brownian coagulation, arguments are presented to support the hypothesis.
In the cases which are worked out, it is assumed that the particles are uncharged and spherical in shape and that their density is conserved in the coagulation process.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Chemistry and Chemical Engineering 
Major Option:  Chemical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  10 May 1966 
Record Number:  CaltechETD:etd09232002110824 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd09232002110824 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3706 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  24 Sep 2002 
Last Modified:  26 Dec 2012 03:02 
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