Flows in a freezing soap foam

The manufacture of a solid foam, widely used for its mechanical, thermal, or acoustic properties, always begins with the solidification of a liquid foam. By placing a model aqueous foam in contact with a cold surface, we observe that, as it freezes, the foam undergoes a drastic change in volume, revealing important water and air migration in the foam. We start by looking at the freezing dynamics and show that the ice front always begins by following a self-similar diffusive dynamics. We propose a 1D diffusion model, using a new expression for the foam conductivity, that enables to predict this dynamics. Based on this model, we highlight a cryosuction phenomenon, where water flows towards the solidification front, and propose a prediction of the vertical profile of the solid fraction in the solid foam. Next, we present scaling laws for the collapse velocity of the foam and for its final volume, which depend on the size of the liquid films and the substrate temperature. Finally, based on these results and the observation of bubbles behaviour at the solidification front, we discuss mechanisms to explain the gas and liquid flows. These results improve our understanding of the mechanisms involved in foam solidification, in particular the flows generated by the presence of a solidification front. More generally, they shed new light on the cryosuction phenomena that occur in many contexts, from soil solidification to the cryopreservation of living organisms.