Related Experiment Video
Updated: Jul 7, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
New coarse-grained derivation of a phase field model for precipitation
Q Bronchart1, Y Le Bouar, A Finel
1Laboratoire d'Etude des Microstructures, ONERA-CNRS 29, avenue de la Division Leclerc BP 72, 92322 Chatillon Cedex, France.
Abstract:
We present the first derivation of the phase field equations using a coarse-graining procedure on a microscopic master equation. The procedure leads to a mesoscopic nonlinear Fokker-Planck equation equivalent to a Cahn-Hilliard equation supplemented with a noise, but with specific prescriptions for the mobilities and the noise term. All the ingredients (chemical potentials, mobilities, stiffness coefficient) depend on the coarse-graining size. Finally, we show the ability of the phase field equations to describe a precipitation kinetics involving a nucleation and growth mechanism.
Related Concept Videos
Precipitation Processes
Precipitate Formation and Particle Size Control
The obtained precipitate should be either a pure substance of known composition or easily converted to one by a simple process, such as ignition or drying. In addition, the precipitate should be insoluble and easily filterable. In general, filterability...
Precipitation and Co-precipitation
Precipitation Gravimetry
In determining nickel by gravimetric analysis, a precipitant of ethanolic dimethylglyoxime is added to a hot nickel salt solution. This is quickly followed by the dropwise addition of dilute ammonia solution until precipitation occurs. A...
Precipitation of Ions
The equation that describes the equilibrium between solid calcium carbonate and its solvated ions is:
Types of Coprecipitation
Sometimes, ions in a crystal lattice can undergo isomorphous replacement by inclusions of similar charge and size. For...
