James E. Sprittles

How Coalescing Droplets Jump

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.

Coalescence of liquid drops: Different models versus experiment

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.

The dynamics of liquid drops and their interaction with solids of varying wettabilities

Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation free-surface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquiddrops. Our codes ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed.

Capillary Breakup of a Liquid Bridge: Identifying Regimes and Transitions

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

Dynamic measurements and simulations of airborne picolitre-droplet coalescence in holographic optical tweezers

Oh

A parametric study of the coalescence of liquid drops in a viscous gas

. 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-

Viscous flow over a chemically patterned surface

Oh

Anomalous dynamics of capillary rise in porous media

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.

Wetting front dynamics in an isotropic porous medium

We report studies of the coalescence of pairs of picolitre aerosol droplets manipulated with holographic optical tweezers, probing the shape relaxation dynamics following coalescence by simultaneously monitoring the intensity of elastic backscattered light (EBL) from the trapping laser beam (time resolution on the order of 100 ns) while recording high frame rate camera images (time resolution <10 μs). The goals of this work are to: resolve the dynamics of droplet coalescence in holographic optical traps; assign the origin of key features in the time-dependent EBL intensity; and validate the use of the EBL alone to precisely determine droplet surface tension and viscosity. For low viscosity droplets, two sequential processes are evident: binary coalescence first results from the overlap of the optical traps on the time scale of microseconds followed by the recapture of the composite droplet in an optical trap on the time scale of milliseconds. As droplet viscosity increases, the relaxation in droplet shape eventually occurs on the same time scale as recapture, resulting in a convoluted evolution of the EBL intensity that inhibits quantitative determination of the relaxation time scale. Droplet coalescence was simulated using a computational framework to validate both experimental approaches. The results indicate that time-dependent monitoring of droplet shape from the EBL intensity allows for robust determination of properties such as surface tension and viscosity. Finally, the potential of high frame rate imaging to examine the coalescence of dissimilar viscosity droplets is discussed.

A continuum model for the flow of thin liquid films over intermittently chemically patterned surfaces

The coalescence of two liquid drops surrounded by a viscous gas is considered in the framework of the conventional model. The problem is solved numerically with particular attention paid to resolving the very initial stage of the process which only recently has become accessible both experimentally and computationally. A systematic study of the parameter space of practical interest allows the influence of the governing parameters in the system to be identified and the role of viscous gas to be determined. In particular, it is shown that the viscosity of the gas suppresses the formation of toroidal bubbles predicted in some cases by early computations where the gas’ dynamics was neglected. Focusing computations on the very initial stages of coalescence and considering the large parameter space allows us to examine the accuracy and limits of applicability of various ‘scaling laws’ proposed for different ‘regimes’ and, in doing so, reveal certain inconsistencies in recent works. A comparison with experimental data shows that the conventional model is able to reproduce many qualitative features of the initial stages of coalescence, such as a collapse of calculations onto a ‘master curve’ but, quantitatively, overpredicts the observed speed of coalescence and there are no free parameters to improve the fit. Finally, a phase diagram of parameter space, differing from previously published ones, is used to illustrate the key findings.