TY - JOUR

T1 - Transient nucleation with a monotonically changing barrier

AU - Shneidman, Vitaly A.

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/9/10

Y1 - 2010/9/10

N2 - Nucleation is considered for nonzero rate of change of the dimensionless barrier B, which is characterized by a finite, slowly varying "nonstationary index" N- (dB/dt). In the standard adiabatic approximation it is assumed that after the start of nucleation an N -independent nucleation flux is established instantaneously, with a quasi-steady-state (QSS) value determined by the current barrier B (t). Those assumptions, however, can be justified only in the strict limit N→0, and otherwise both transient nucleation at small times, and subsequent deviations from QSS are essential. Earlier results for the non-QSS transient flux are refined and generalized to account for arbitrary relations between the rates of the change of the barrier and of the critical size, and for a variable N (t). The N -dependent transient distributions of growing nuclei and their numbers also are obtained. The treatment is mostly based on matched asymptotic (singular perturbation) analysis of the Becker-Döring equation (BDE), and involves comparison with exact numerics. General results are specified within the continuous Zeldovich-Frenkel approximation to BDE, with a large fixed critical size and a barrier which either increases (N<0) or decays (N>0) with time. In such cases growth can be described exactly, allowing to extend the nucleation solution to arbitrary sizes without additional approximations. Resulting distributions f (r,t) are monotonic in size r for N0, with a diverging total number of particles ρ as t→. For N<0 distributions acquire an asymmetric bell shape with a finite ρ, which is exponentially small compared to ρQSS.

AB - Nucleation is considered for nonzero rate of change of the dimensionless barrier B, which is characterized by a finite, slowly varying "nonstationary index" N- (dB/dt). In the standard adiabatic approximation it is assumed that after the start of nucleation an N -independent nucleation flux is established instantaneously, with a quasi-steady-state (QSS) value determined by the current barrier B (t). Those assumptions, however, can be justified only in the strict limit N→0, and otherwise both transient nucleation at small times, and subsequent deviations from QSS are essential. Earlier results for the non-QSS transient flux are refined and generalized to account for arbitrary relations between the rates of the change of the barrier and of the critical size, and for a variable N (t). The N -dependent transient distributions of growing nuclei and their numbers also are obtained. The treatment is mostly based on matched asymptotic (singular perturbation) analysis of the Becker-Döring equation (BDE), and involves comparison with exact numerics. General results are specified within the continuous Zeldovich-Frenkel approximation to BDE, with a large fixed critical size and a barrier which either increases (N<0) or decays (N>0) with time. In such cases growth can be described exactly, allowing to extend the nucleation solution to arbitrary sizes without additional approximations. Resulting distributions f (r,t) are monotonic in size r for N0, with a diverging total number of particles ρ as t→. For N<0 distributions acquire an asymmetric bell shape with a finite ρ, which is exponentially small compared to ρQSS.

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U2 - 10.1103/PhysRevE.82.031603

DO - 10.1103/PhysRevE.82.031603

M3 - Article

AN - SCOPUS:77957253247

VL - 82

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

M1 - 031603

ER -