We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Planck equations. We prove that in the diffusive limit the evolution is described by a macroscopic equation in the form of the gradient flux of the macroscopic free energy functional. Moreover, we study the sharp interface limit and find by formal Hilbert expansions that the interface motion is given in terms of a quasi-stationary problem for the chemical potentials. The velocity of the interface is the sum of two contributions: the velocity of the Mullins-Sekerka motion for the difference of the chemical potentials and the velocity of a Hele-Shaw motion for a linear combination of the two potentials. These equations are identical to the ones in Otto and E (1997 J. Chem. Phys. 107 10177-84) modelling the motion of a sharp interface for a polymer blend.

Manzi, G., Marra, R. (2006). Phase segregation and interface dynamics in kinetic systems. NONLINEARITY, 19(1), 115-147 [10.1088/0951-7715/19/1/007].

Phase segregation and interface dynamics in kinetic systems

MARRA, ROSSANA
2006-01-01

Abstract

We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Planck equations. We prove that in the diffusive limit the evolution is described by a macroscopic equation in the form of the gradient flux of the macroscopic free energy functional. Moreover, we study the sharp interface limit and find by formal Hilbert expansions that the interface motion is given in terms of a quasi-stationary problem for the chemical potentials. The velocity of the interface is the sum of two contributions: the velocity of the Mullins-Sekerka motion for the difference of the chemical potentials and the velocity of a Hele-Shaw motion for a linear combination of the two potentials. These equations are identical to the ones in Otto and E (1997 J. Chem. Phys. 107 10177-84) modelling the motion of a sharp interface for a polymer blend.
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
English
Con Impact Factor ISI
LONG-RANGE INTERACTIONS; CAHN-HILLIARD EQUATION; EXCESS FREE-ENERGY; PARTICLE-SYSTEMS; CONSERVATION LAW; ALGEBRAIC RATE; STABILITY; MODEL; DERIVATION; FRONTS
Manzi, G., Marra, R. (2006). Phase segregation and interface dynamics in kinetic systems. NONLINEARITY, 19(1), 115-147 [10.1088/0951-7715/19/1/007].
Manzi, G; Marra, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/36540
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