Freezing in a drop impacting a cold substrate: Where dendrites can't penetrate?

Ice accretion on cold solid surfaces, often resulting from the impact and freezing of supercooled water drops (SLD), poses critical challenges in aviation, energy systems, and infrastructure. In practice, some drops freeze with dendritic structures-forming a solid-liquid mixture (mushy region) that may cause refreezing downstream (runback ice)-while others freeze without dendrites. We hypothesize this depends on the relative thicknesses of the propagating ice layer and the supercooled liquid layer.

Water drops, both room-temperature and supercooled, were studied after impacting cold substrates using high-speed imaging. For room-temperature drops, freezing was triggered by cooling the substrate down to as low as -35^∘C, with impact velocity adjusted by varying the syringe height. For supercooled drops, both the drop and the substrate were maintained at -10^∘C. To achieve freezing under these conditions, a wind tunnel was employed to increase the impact velocity via airflow in a cold chamber.

Three freezing regimes were identified: (i) dendrite cloud propagation, (ii) thin ice layer expansion without dendrites, and (iii) a reverse freezing sequence where an ice layer forms after initial dendrite growth. To explain these regimes, a one-dimensional heat conduction model was developed, accounting for temperature-dependent thermal properties of water and predicting contact temperature and the evolution of a supercooled liquid layer. A threshold condition was established: dendrites form only if the supercooled liquid layer is thicker than the thin ice layer. Theoretical predictions align well with experimental observations. These results offer insight into freezing dynamics and implications for ice prediction in aerospace applications.