Surface engineering at the nanoscale is a rapidly developing field that promises to impact a range of applications including energy production, water desalination, self-cleaning and anti-icing surfaces, thermal management of electronics, microfluidic platforms, and environmental pollution control. As the area advances, more detailed insights of dynamic wetting interactions on these surfaces are needed. In particular, the coalescence of two or more droplets on ultra-low adhesion surfaces leads to droplet jumping. Here we show, through detailed measurements of jumping droplets during water condensation coupled with numerical simulations of binary droplet coalescence, that this process is fundamentally inefficient with only a small fraction of the available excess surface energy (≲ 6%) convertible into translational kinetic energy. These findings clarify the role of internal fluid dynamics during the jumping droplet coalescence process and underpin the development of systems that can harness jumping droplets for a wide range of applications.

The process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the 'conventional' one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this 'internal interface' that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product of our research, the range of validity of different 'scaling laws' advanced as approximate solutions to the problem formulated using the conventional model is established.

SUMMARYThe finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the solid, is considered. For this class of flows, different finite element method (FEM) implementations have been used in the literature, and in some cases, these produced apparently contradictory results. In the present paper, a robust framework for the FEM simulation of dynamic wetting flows is developed, which, by consistently adhering to the FEM methodology, leaves no room for ad hoc 'optional' variations in the numerical handling of these flows. The developed approach makes it possible to conduct a convergence study, assess the spatial resolution required to achieve a preset accuracy and provide the corresponding benchmark calculations. This analysis allows one to identify numerical artefacts, which had previously been interpreted as physical effects, and demonstrates that suppressing numerical errors using a 'strong' implementation of a boundary condition creates bigger and less detectable errors elsewhere in the computational domain. We provide practical recommendations on the spatial resolution required by a numerical scheme for a given set of non-dimensional similarity parameters and give a user-friendly step-by-step guide specifying the entire implementation, which allows the reader to easily reproduce all presented results including the benchmark calculations. It is also shown how the developed framework accommodates generalizations of the mathematical model accounting for additional physical effects, such as gradients in surface tensions.

Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous-inertial balances, that is, different limits of the Ohnesorge number Oh. To accurately establish the transitions between regimes, the minimum bridge radius is resolved through four orders of magnitude using a purpose-built multiscale finite element method. This allows us to construct a quantitative phase diagram for the breakup phenomenon which includes the appearance of a recently discovered low-Oh viscous regime. The method used to quantify the accuracy of the similarity solutions allows us to identify a number of previously unobserved features of the breakup, most notably an oscillatory convergence towards the viscous-inertial similarity solution. Finally, we discuss how the new findings open up a number of challenges for both theoretical and experimental analysis.