From polycrystalline materials to beer head : Discovering kinetic relation describing capillarity-driven transformation rate

Capillarity-driven transformation is observed in a wide range of materials, from polycrystalline alloys to foams, and it noticeably influences their behaviour. During this transformation, the temporal change in the size of individual entities (grains or foams) is often claimed to be dictated by several factors, including topological and geometrical features of the evolving unit, its neighbours, and the entire system. Despite extensive theoretical and experimental investigations, a convincing understanding is yet to be gained on the significance of these factors in the evolution of the entities. In this work, going beyond conventional data analysis, the role of the different geometrical and topological features of the entities, neighbours, and entire system in dictating the capillarity-driven evolution is definitively realised. More importantly, a kinetic relation, applicable to a wide range of curvature-driven evolution, that describes and predicts the quantitative temporal evolution of individual units is discovered. The resulting kinetic relation unravels that the temporal change in the size of individual entities, during capillarity-driven transformation, can be convincingly described by the interplay of the size and number of sides of the evolving unit alone. In other words, this study decisively affirms the marginal significance of neighbouring entities in the capillarity-driven transformation of individual units. Additionally, the coherence of the present data-driven kinetic law with the existing understanding of curvature-driven evolution is briefly discussed.