Séminaire

Mardi 8 Octobre 2024 à 14h00.

Freezing of capillary objects

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We investigate how the freezing of capillary objects leads to original shapes. The freezing of drops and bubbles reveal pecularities due to differences between the melt and the solid phase. In this regard as in many other, water is the most peculiar substance: liquid water is denser than ice; there is a finite contact angle of water on ice; water is a good solvent but ice is not.

A good example is the shape of the air bubbles trapped in ice, that one can easily observe in an ice cube out of the freezer. Water usually contains dissolved gases. When it freezes, these gases are expelled and form bubbles which eventually are trapped in ice. These bubbles are never spherical; in fact they come in a range of shapes evoking eggs or pears, elongated and asymetric. Some of these bubbles are "ice worms", micrometer-thick and centimeter-long. The peculiar shape of air bubbles trapped in ice results of a delicate balance between heat and mass transfer, freezing and surface tension. We show that these intertwined mechanisms can be modeled by a single ordinary differential equation, strongly non-linear. Its analysis explains several features of the bubble shape, such as their flat top, and provides a bifurcation diagram for the ice worms. This mathematical model is confirmed by our experiments. By matching the solutions of the differential equation to the empirical bubble shapes, we are able to estimate the gas supersaturation in the melt and the nucleation radius of the bubble at the freezing front. Our work could find applications in glaciology, but also in designing porous materials made through freezing-casting.

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