We study the freezing of water drops on a copper substrate for temperatures ranging from $-9$ to $-79{}^{\circ }\mathrm{C}$. We propose a thermal and geometrical analytical model for the freezing front dynamics. It assumes a propagation of the front at the center described by the three-phase (liquid, ice, substrate) Stefan model in one dimension. The growth is characterized by an effective diffusion coefficient that increases as the substrate temperature decreases. We also consider a spherical front that meets the edges of the drop perpendicularly. Our model captures well our experimental data between $-9$ and $-40{}^{\circ }\mathrm{C}$ and highlights the importance of the heat diffusion in the liquid for the freezing process. Beyond these temperatures, the adhesion of the drops to the copper decreases and the substrate temperature must be considered equal to $-41{}^{\circ }\mathrm{C}$ to rationalize the experimental findings.

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• Liquid-solid phase transition
• Drops & bubbles