Estimation of primary nucleation rates from nucleation time distribution data

Abstract

Nucleation (or induction) time, the time elapsed from the instance of creation of supercooling a solution to the instance of detection of a first nucleation event, differs widely in a stochastic manner when samples are small like droplets. The nucleation time distributions P_r(t) are closely related to primary nucleation rates. Many attempts have been made to estimate primary nucleation rates from P_r(t). When the plot of ln P_r(t) vs. t is not linear, primary nucleation rates have never been estimated successfully, although these non-linear plots are frequently encountered in reality. This paper proposes a new method for estimating primary nucleation rates from non-linear P_r(t) distribution data. Primary nucleation rates were extracted by analyzing literature data of P_r(t) distributions. The extracted nucleation rates were heterogeneous ones. The relevance of mononuclear-mode nucleation in small samples to polynuclear-mode nucleation in large industrial-scale crystallizers is discussed theoretically.