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Updated: Jun 29, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Unified moving-boundary model with fluctuations for unstable diffusive growth
Matteo Nicoli1, Mario Castro, Rodolfo Cuerno
1Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
This study models interface growth in thin films, revealing how attachment speed affects surface evolution. Slow attachment leads to Kuramoto-Sivashinsky dynamics, while fast attachment results in Kardar-Parisi-Zhang scaling, explaining experimental challenges.
Area of Science:
- Materials Science
- Physics
- Chemical Engineering
Background:
- Interface growth is crucial in thin-film deposition techniques like chemical vapor deposition and electrochemical deposition.
- Understanding the interplay between matter transport and interface kinetics is key to controlling film morphology.
- Fluctuations in diffusive and attachment processes significantly influence interface dynamics.
Purpose of the Study:
- To develop and analyze a moving-boundary model for nonconserved interface growth.
- To investigate the impact of attachment kinetics on interface evolution.
- To explain experimental difficulties in observing scaling laws like Kardar-Parisi-Zhang (KPZ).
Main Methods:
- Formulation of a moving-boundary model incorporating diffusive transport and aggregation kinetics.
- Application of a small-slope approximation to derive effective interface evolution equations (IEEs).
- Mathematical analysis of IEEs and numerical simulations for different kinetic regimes.
Main Results:
- The model predicts distinct interface evolution behaviors based on attachment kinetics.
- Slow attachment kinetics lead to dynamics described by the Kuramoto-Sivashinsky equation, transitioning to Kardar-Parisi-Zhang (KPZ) roughening.
- Instantaneous attachment kinetics result in IEEs combining Mullins-Sekerka dispersion with KPZ nonlinearity, with observed dynamics influenced by long preasymptotic transients.
Conclusions:
- The derived effective interface evolution equations capture essential physics of nonconserved interface growth.
- Preasymptotic transient behavior can obscure the observation of universal scaling laws in experiments.
- The model provides a framework for understanding and potentially controlling thin-film morphology in deposition processes.
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