Transient nucleation with a monotonically changing barrier.

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 N≥0, 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 ρ(QSS).