TY - JOUR
T1 - Phase-field model
T2 - Boundary layer, velocity of propagation, and the stability spectrum
AU - Kupferman, Raz
AU - Shochet, Ofer
AU - Ben-Jacob, Eshel
AU - Schuss, Zeev
PY - 1992
Y1 - 1992
N2 - We present a study of a phase-field model for diffusion-limited growth. A boundary-layer approximation is used to show that for sharp interface, the first approximation to the phase-field model is the free boundary model, which includes surface tension and a linear kinetic term. The velocity of propagation and the stability spectrum are calculated for a steady-state flat interface. In the case where the phase and the field have similar variation lengths, a stable growth regime is found above a critical value of driving force. We discuss the application of phase-field-like models in the description of the ensemble-average pattern.
AB - We present a study of a phase-field model for diffusion-limited growth. A boundary-layer approximation is used to show that for sharp interface, the first approximation to the phase-field model is the free boundary model, which includes surface tension and a linear kinetic term. The velocity of propagation and the stability spectrum are calculated for a steady-state flat interface. In the case where the phase and the field have similar variation lengths, a stable growth regime is found above a critical value of driving force. We discuss the application of phase-field-like models in the description of the ensemble-average pattern.
UR - http://www.scopus.com/inward/record.url?scp=0000311871&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.46.16045
DO - 10.1103/PhysRevB.46.16045
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AN - SCOPUS:0000311871
SN - 0163-1829
VL - 46
SP - 16045
EP - 16057
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
IS - 24
ER -