  The freezing of a sessile droplet unveils fascinating physics, characterised
by the emergence of a frost halo on the underlying substrate, the progression
of the liquid-ice interface, and the formation of a cusp-like morphology at the
tip of the droplet. We investigate the freezing of a volatile sessile droplet,
focusing on the frost halo formation, which has not been theoretically
explored. The formation of the frost halo is associated with the inherent
evaporation process in the early freezing stages. We observe a negative
evaporation flux enveloping the droplet in the initial stages, which indicates
that vapour produced during freezing condenses on the substrate close to the
contact line, forming a frost halo. The condensate accumulation triggers
re-evaporation, resulting in a temporal shift of the frost halo region away
from the contact line. Eventually, it disappears due to the diffusive nature of
the water vapour far away from the droplet. We found that increasing the
relative humidity increases the lifetime of the frost halo due to a substantial
reduction in evaporation that prolonged the presence of net condensate on the
substrate. Increasing liquid volatility increases the evaporation flux, and
condensation occurs closer to the droplet, as a higher amount of vapour is in
the periphery of the droplet. We also found that decreasing the thermal
conductivity of the substrate increases the total freezing time. The slower
freezing process is accompanied by increased vaporized liquid, resulting in
condensation with its concentration reaching supersaturation.
