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Updated: May 31, 2026
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Published on: February 4, 2021
Aggregation according to classical kinetics: from nucleation to coarsening.
1G. Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, Madrid, Spain. yfarjoun@ing.uc3m.es
Summary
This study analyzes cluster size distributions during material formation. It confirms a discontinuous distribution persists through coarsening, resolving intermediate stages and defining key scaling parameters.
Area of Science:
- Physics
- Materials Science
- Chemical Engineering
Background:
- A prior kinetic model predicted a discontinuous cluster size distribution after initial creation.
- Lifshitz-Slyozov coarsening is known to preserve this discontinuity, contradicting earlier theories.
Purpose of the Study:
- To analytically and numerically solve Lifshitz-Slyozov equations starting from a discontinuous distribution.
- To investigate the intermediate stages of cluster evolution and coarsening.
- To identify characteristic time and size scales for the onset of coarsening.
Main Methods:
- Analytic-numerical solution of Lifshitz-Slyozov equations.
- Simulation of cluster dynamics from a discontinuous initial state.
Main Results:
- The discontinuous cluster size distribution is confirmed to persist during late-stage coarsening.
- Intermediate stages of cluster evolution were resolved.
- Specific time and cluster size scales characterizing the onset of coarsening were determined.
Conclusions:
- The Lifshitz-Slyozov model, when initiated with a discontinuous distribution, leads to a persistent discontinuity in late-stage coarsening.
- This study provides a detailed understanding of the transition from initial cluster formation to late-stage coarsening.
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