Smoluchowski coagulation equation
E52850
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
integro-differential equation
ⓘ
kinetic equation ⓘ model in statistical physics ⓘ |
| appliesTo |
aerosols
ⓘ
cloud microphysics ⓘ colloidal suspensions ⓘ gelation phenomena ⓘ planetary formation models ⓘ polymerization processes ⓘ |
| assumes |
mean-field approximation
ⓘ
pairwise particle collisions ⓘ spatial homogeneity ⓘ |
| canExhibit | gelation transition ⓘ |
| describes |
binary collisions between particles
ⓘ
cluster aggregation ⓘ particle coagulation ⓘ time evolution of cluster size distribution ⓘ |
| feature |
gain term due to aggregation
ⓘ
loss term due to aggregation ⓘ nonlinear integral term ⓘ |
| field |
applied mathematics
ⓘ
physical chemistry ⓘ soft matter physics ⓘ statistical physics ⓘ |
| hasSolutionType |
scaling solutions
ⓘ
self-similar solutions ⓘ |
| hasSpecialCase |
additive kernel coagulation model
ⓘ
constant kernel coagulation model ⓘ multiplicative kernel coagulation model ⓘ |
| hasVariable |
cluster size distribution
ⓘ
particle concentration as a function of size and time ⓘ |
| influenced | modern coagulation-fragmentation theory ⓘ |
| involves | collision rate between particles ⓘ |
| mathematicalForm | integro-differential equation in time and cluster size ⓘ |
| namedAfter | Marian Smoluchowski ⓘ |
| originatedIn | early 20th century ⓘ |
| relatedTo |
Boltzmann equation
ⓘ
Fokker–Planck equation ⓘ
surface form:
Smoluchowski diffusion equation
fragmentation equations ⓘ population balance equations ⓘ |
| requires | initial cluster size distribution ⓘ |
| studiedIn |
non-equilibrium statistical mechanics
ⓘ
probability theory ⓘ stochastic processes ⓘ |
| usedFor |
analyzing aggregation kinetics
ⓘ
modeling cluster growth ⓘ predicting particle size distributions ⓘ |
| uses | coagulation kernel ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.