A Review on the Coalescence of Confined Drops with a Focus on Scaling Laws for the Growth of the Liquid Bridge.

The surface-tension-driven coalescence of drops has been extensively studied because of the omnipresence of the phenomenon and its significance in various natural and engineering systems. When two drops come into contact, a liquid bridge is formed between them and then grows in its lateral dimensions. As a result, the two drops merge to become a bigger drop. The growth dynamics of the bridge are governed by a balance between the driving force and the viscous and inertial resistances of involved liquids, and it is usually represented by power-law scaling relations on the temporal evolution of the bridge dimension. Such scaling laws have been well-characterized for the coalescence of unconfined or freely suspended drops. However, drops are often confined by solid or liquid surfaces and thus are a different shape from spheres, which affects their coalescence dynamics. As such, the coalescence of confined drops poses more complicated interfacial fluid dynamics challenges compared to that of unconfined drops. Although there have been several studies on the coalescence of confined drops, they have not been systematically reviewed in terms of the properties and geometry of the confining surface. Thus, we aim to review the current literature on the coalescence of confined drops in three categories: drop coalescence on a solid surface, drop coalescence on a deformable surface, and drop coalescence between two parallel surfaces with a small gap (i.e., Hele-Shaw cell), with a focus on power-law scaling relations, and to suggest challenges and outlooks for future research on the phenomena.