  Induction time, a measure of how long one will wait for nucleation to occur,
is an important parameter in quantifying nucleation kinetics and its underlying
mechanisms. Due to the stochastic nature of nucleation, efficient methods for
measuring large number of independent induction times are needed to ensure
statistical reproducibility. In this work, we present a novel approach for
measuring and analyzing induction times in sessile arrays of microdroplets via
deliquescence/recrystallization cycling. With the help of a recently developed
image analysis protocol, we show that the interfering diffusion-mediated
interactions between microdroplets can be eliminated by controlling the
relative humidity, thereby ensuring independent nucleation events. Moreover,
possible influence of heterogeneities, impurities, and memory effect appear
negligible as suggested by our 2-cycle experiment. Further statistical analysis
(k-sample Anderson-Darling test) reveals that upon identifying possible
outliers, the dimensionless induction times obtained from different datasets
(microdroplet lines) obey the same distribution and thus can be pooled together
to form a much larger dataset. The pooled dataset showed an excellent fit with
the Weibull function, giving a mean supersaturation at nucleation of 1.61 and
1.85 for the 60pL and 4pL microdroplet respectively. This confirms the effect
of confinement where smaller systems require higher supersaturations to
nucleate. Both the experimental method and the data-treatment procedure
presented herein offer promising routes in the study of fundamental aspects of
nucleation kinetics, particularly confinement effects, and are adaptable to
other salts, pharmaceuticals, or biological crystals of interest.
