Coagulation equations with gelation

Journal Article · Wed Jun 01 04:00:00 EDT 1983 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01019497· OSTI ID:5589438

Hendriks, E M; Ernst, M H; Ziff, R M

Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel K/sub i/j models the bonding mechanism. For different classes of kernels we derive criteria for the occurrences of gelation, and obtain critical exponents in the pre- and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation t/sub c/, and give an exact postgelation solution for the model K/sub i/j = (ij)/sup ..omega../ (..omega..>1/2) and K/sub i/j = ..cap alpha../sup i/+j (..cap alpha..>1). For the model K/sub i/j = i/sup ..omega../+j/sup ..omega../ (..omega..<1, without gelation) initial solutions are given. It is argued that the kernel K/sub i/japprox. (ij)/sup ..omega../ with ..omega..approx. =1-1/d (d is dimensionality) effectively models the sol-gel transformation is polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer (..omega.. = 1). For all ..omega.. the exponents, tau = ..omega..+3/2 and sigma = ..omega..-1/2, ..gamma.. = (3/2-..omega..)/(..omega..-1/2) and ..beta.. = 1, characterize the size distribution, at the slightly below the gel point, under the assumption that scaling is valid.

• Research Organization: Institut voor Theoretische Fysica, Fijksuniversiteit Utrecht, The Netherlands
• OSTI ID: 5589438
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 31:3; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics &amp; Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COLLOIDS
DISPERSIONS
FLOCCULATION
GELATION
GELS
KERNELS
KINETICS
PRECIPITATION
SCALING LAWS
SEPARATION PROCESSES