Droplet motion driven by humidity gradients during evaporation and condensation.

The motion of droplets on solid surfaces in response to an external gradient is a fundamental problem with a broad range of applications, including water harvesting, heat exchange, mixing and printing. Here we study the motion of droplets driven by a humidity gradient, i.e. a variation in concentration of their own vapour in the surrounding gas phase. Using lattice-Boltzmann simulations of a diffuse-interface hydrodynamic model to account for the liquid and gas phases, we demonstrate that the droplet migrates towards the region of higher vapour concentration. This effect holds in situations where the ambient gradient drives either the evaporation or the condensation of the droplet, or both simultaneously. We identify two main mechanisms responsible for the observed motion: a difference in surface wettability, which we measure in terms of the Young stress, and a variation in surface tension, which drives a Marangoni flow. Our results are relevant in advancing our knowledge of the interplay between gas and liquid phases out of thermodynamic equilibrium, as well as for applications involving the control of droplet motion.

Lattice Boltzmann Simulations of Multiphase Dielectric Fluids.

The dynamic effect of an electric field on dielectric liquids is called liquid dielectrophoresis. It is widely used in several industrial and scientific applications, including inkjet printing, microfabrication, and optical devices. Numerical simulations of liquid-dielectrophoresis are necessary to understand the fundamental physics of the phenomenon, but also to explore situations that might be difficult or expensive to implement experimentally. However, such modeling is challenging, as one needs to solve the electrostatic and fluid dynamics equations simultaneously. Here, we formulate a new lattice-Boltzmann method capable of modeling the dynamics of immiscible dielectric fluids coupled with electric fields within a single framework, thus eliminating the need of using separate algorithms to solve the electrostatic and fluid dynamics equations. We validate the numerical method by comparing it with analytical solutions and previously reported experimental results. Beyond the benchmarking of the method, we study the spreading of a droplet using a dielectrowetting setup and quantify the mechanism driving the variation of the apparent contact angle of the droplet with the applied voltage. Our method provides a useful tool to study liquid-dielectrophoresis and can be used to model dielectric fluids in general, such as liquid-liquid and liquid-gas systems.

Controlling the breakup of toroidal liquid films on solid surfaces.

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required. When the filament is resting on a flat solid surface which imposes wetting conditions the subtle interplay with the fluid dynamics makes the instability pathways and mode selection difficult to predict. Here, we show how controlling the static and dynamic wetting of a surface can lead to repeatable switching between a toroidal film of an electrically insulating liquid and patterns of droplets of well-defined dimensions confined to a ring geometry. Mode selection between instability pathways to these different final states is achieved by dielectrophoresis forces selectively polarising the dipoles at the solid-liquid interface and so changing both the mobility of the contact line and the partial wetting of the topologically distinct liquid domains. Our results provide insights into the wetting and stability of shaped liquid filaments in simple and complex geometries relevant to applications ranging from printing to digital microfluidic devices.

Contact-Angle Hysteresis and Contact-Line Friction on Slippery Liquid-like Surfaces.

Contact-line pinning and dynamic friction are fundamental forces that oppose the motion of droplets on solid surfaces. Everyday experience suggests that if a solid surface offers low contact-line pinning, it will also impart a relatively low dynamic friction to a moving droplet. Examples of such surfaces are superhydrophobic, slippery porous liquid-infused, and lubricant-impregnated surfaces. Here, however, we show that slippery omniphobic covalently attached liquid-like (SOCAL) surfaces have a remarkable combination of contact-angle hysteresis and contact-line friction properties, which lead to very low droplet pinning but high dynamic friction against the motion of droplets. We present experiments of the response of water droplets to changes in volume at controlled temperature and humidity conditions, which we separately compare to the predictions of a hydrodynamic model and a contact-line model based on molecular kinetic theory. Our results show that SOCAL surfaces offer very low contact-angle hysteresis, between 1 and 3°, but an unexpectedly high dynamic friction controlled by the contact line, where the typical relaxation time scale is on the order of seconds, 4 orders of magnitude larger than the prediction of the classical hydrodynamic model. Our results highlight the remarkable wettability of SOCAL surfaces and their potential application as low-pinning, slow droplet shedding surfaces.

Lattice-Boltzmann simulations of the dynamics of liquid barrels.

We study the relaxation towards equilibrium of a liquid barrel-a partially wetting droplet in a wedge geometry-using a diffuse-interface approach. We formulate a hydrodynamic model of the motion of the barrel in the framework of the Navier-Stokes and Cahn-Hilliard equations of motion. We present a lattice-Boltzmann method to integrate the diffuse-interface equations, where we introduce an algorithm to model the dynamic wetting of the liquid on smooth solid boundaries. We present simulation results of the over-damped dynamics of the liquid barrel. We find that the relaxation of the droplets is driven by capillary forces and damped by friction forces. We show that the friction is determined by the contribution of the bulk flow, the corner flow near the contact lines and the motion of the contact lines by comparing simulation results for the relaxation time of the barrel. Our results are in broad agreement with previous analytical predictions based on a sharp interface model.

Slippery when wet: mobility regimes of confined drops in electrowetting.

The motion of confined droplets in immiscible liquid-liquid systems strongly depends on the intrinsic relative wettability of the liquids on the confining solid material and on the typical speed, which can induce the formation of a lubricating layer of the continuous phase. In electrowetting, which routinely makes use of aqueous drops in ambient non-polar fluids that wet the wall material, electric stresses enter the force balance in addition to capillary and viscous forces and confinement effects. Here, we study the mobility of droplets upon electrowetting actuation in a wedge-shaped channel, and the subsequent relaxation when the electrowetting actuation is removed. We find that the droplets display two different mobility regimes: a fast regime, corresponding to gliding on a thin film of the ambient fluid, and a slow regime, where the film is replaced by direct contact between the droplet and the channel walls. Using a combination of experiments and numerical simulations, we show that the cross-over between these regimes arises from the interplay between the small-scale dynamics of the thin film of ambient fluid and the large-scale motion of the droplet. Our results shed light on the complex dynamics of droplets in non-uniform channels driven by electric actuation, and can thus help the rational design of devices based on electrowetting-driven droplet transport.

Lattice-Boltzmann Simulations of Electrowetting Phenomena.

When a voltage difference is applied between a conducting liquid and a conducting (solid) electrode, the liquid is observed to spread on the solid. This phenomenon, generally referred to as electrowetting, underpins a number of interfacial phenomena of interest in applications that range from droplet microfluidics to optics. Here, we present a lattice-Boltzmann method that can simulate the coupled hydrodynamics and electrostatics equations of motion of a two-phase fluid as a means to model the electrowetting phenomena. Our method has the advantage of modeling the electrostatic fields within the lattice-Boltzmann algorithm itself, eliminating the need for a hybrid method. We validate our method by reproducing the static equilibrium configuration of a droplet subject to an applied voltage and show that the apparent contact angle of the drop depends on the voltage following the Young-Lippmann equation up to contact angles of ≈50°. At higher voltages, we observe a saturation of the contact angle caused by the competition between electric and capillary stresses, similar to previous experimental observations. We also study the stability of a dielectric film trapped between a conducting fluid and a solid electrode and find a good agreement with analytical predictions based on lubrication theory. Finally, we investigate the film dynamics at long times and report observations of film breakup and entrapment similar to previously reported experimental results.

Snap evaporation of droplets on smooth topographies.

Droplet evaporation on solid surfaces is important in many applications including printing, micro-patterning and cooling. While seemingly simple, the configuration of evaporating droplets on solids is difficult to predict and control. This is because evaporation typically proceeds as a "stick-slip" sequence-a combination of pinning and de-pinning events dominated by static friction or "pinning", caused by microscopic surface roughness. Here we show how smooth, pinning-free, solid surfaces of non-planar topography promote a different process called snap evaporation. During snap evaporation a droplet follows a reproducible sequence of configurations, consisting of a quasi-static phase-change controlled by mass diffusion interrupted by out-of-equilibrium snaps. Snaps are triggered by bifurcations of the equilibrium droplet shape mediated by the underlying non-planar solid. Because the evolution of droplets during snap evaporation is controlled by a smooth topography, and not by surface roughness, our ideas can inspire programmable surfaces that manage liquids in heat- and mass-transfer applications.

Energy Invariance in Capillary Systems.

We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary surfaces in contact with solid boundaries of arbitrary shape and examine the implications of dynamic frictional forces upon a reconfiguration of the boundaries. Experimentally, we realize our ideas by manipulating the position of a droplet in a wedge geometry using lubricant-impregnated solid surfaces, which eliminate the contact-angle hysteresis and provide a test bed for quantifying dissipative losses out of equilibrium. Our experiments show that dissipative energy losses for an otherwise energy-invariant reconfiguration are relatively small, provided that the actuation time scale is longer than the typical relaxation time scale of the capillary surface. We discuss the wider applicability of our ideas as a pathway for liquid manipulation at no potential energy cost in low-pinning, low-friction situations.

Drop transport and positioning on lubricant-impregnated surfaces.

We demonstrate the transport and positioning of water droplets on macro-patterned lubricant-impregnated surfaces. The macro-patterning produces menisci features in the impregnating liquid layer which interact with a droplet via a capillary mechanism similar to the Cheerios effect. These interactions control the droplet motion and positioning on an otherwise completely slippery surface. We present experimental results using a V-shape channel geometry as a model system. The interaction between deformations on the lubricant layer induced by the droplet and the underlying V-shape geometry leads to both local and global equilibrium positions for the droplet within the channel. We present a mathematical model to quantify the transition from local equilibrium states to the global equilibrium state and show that the latter can be described on the basis of a force balance along the apparent contact line of the droplet. We highlight possible applications where lubricated macro-patterned surfaces can be used to control the motion and localisation of droplets.