The physics of icing drops under complex conditions

Icing of water droplets is a ubiquitous phenomenon with significant implications across natural systems and industrial applications. Despite extensive research, the intricate interplay among heat transfer, mass transport, and phase change during droplet freezing remains incompletely understood, particularly in the context of multiscale dynamics and environmental dependencies. This review critically examines recent advances in uncovering the fundamental mechanisms of droplet icing through experimental, theoretical, and computational approaches. We begin by revisiting the classical tip singularity problem in the freezing of pure water droplets, analyzing its mathematical formulation and physical significance. Subsequent sections explore how environmental boundary conditions and multicomponent effects influence freezing kinetics, solute redistribution, and ice morphology. Furthermore, we evaluate emerging hybrid numerical frameworks that resolve coupled multiphase physics during solidification processes. Finally, we identify key challenges and open questions that require further investigation in this field.