Scaling Laws for Freezing Bubbles

We deposit bubbles on an icy substrate and model the dynamics of the resulting freeze front using scaling analysis. First, the substrate temperature was ranged from -10 °C to -40 °C using a Peltier stage in a room temperature environment. The freeze front was modeled as a one-dimensional Stefan problem; the latent heat of fusion was balanced by the net difference in thermal conduction across the frozen and unfrozen portions of the bubble. For most bubbles, the freeze front stopped progressing entirely at a critical height where conduction across the ice and liquid were balanced. Second, freezing bubbles were observed under isothermal conditions in a walk-in freezer set to -20 °C. With the bubble initially exhibiting a uniform temperature, the latent heat of fusion now induces a Marangoni flow going up the bubble that detaches and entrains ice particles. These flowing ice particles continue to grow, resulting in multiple freeze fronts that interlock together like hexagons on a soccer ball.