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

A sublimation heat engine

Heat engines are based on the physical realization of a thermodynamic cycle, most famously the liquid–vapour Rankine cycle used for steam engines. Here we present a sublimation heat engine, which can convert temperature differences into mechanical work via the Leidenfrost effect. Through controlled experiments, quantified by a hydrodynamic model, we show that levitating dry-ice blocks rotate on hot turbine-like surfaces at a rate controlled by the turbine geometry, temperature difference and solid material properties. The rotational motion of the dry-ice loads is converted into electric power by coupling to a magnetic coil system. We extend our concept to liquid loads, generalizing the realization of the new engine to both sublimation and the instantaneous vapourization of liquids. Our results support the feasibility of low-friction in situ energy harvesting from both liquids and ices. Our concept is potentially relevant in challenging situations such as deep drilling, outer space exploration or micro-mechanical manipulation

Statics and dynamics of liquid barrels in wedge geometries

We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle , confined in a solid wedge geometry of opening angle . We focus on a mostly non-wetting regime, given by the condition , where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales

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

Not spreading in reverse: the dewetting of a liquid film into a single droplet

Wetting and dewetting are both fundamental modes of motion of liquids on solid surfaces. They are critically important for processes in biology, chemistry and engineering, such as drying, coating and lubrication. However, recent progress in wetting, which has led to new fields such as superhydrophobicity and liquid marbles, has not been matched by dewetting. A significant problem has been the inability to study the model system of a uniform film dewetting from a non-wetting surface to a single macroscopic droplet – a barrier which does not exist for the reverse wetting process of a droplet spreading into a film. Here, we report the dewetting of a dielectrophoresis-induced film into a single equilibrium droplet. The emergent picture of the full dewetting dynamics is of an initial regime, where a liquid rim recedes at constant speed and constant dynamic contact angle, followed by a relatively short exponential relaxation of a spherical-cap shape. This sharply contrasts with the reverse wetting process, where a spreading droplet follows a smooth sequence of spherical-cap shapes. Complementary numerical simulations and a hydrodynamic model reveal a local dewetting mechanism driven by the equilibrium contact angle, where contact-line slip dominates the dewetting dynamics. Our conclusions can be used to understand a wide variety of processes involving liquid dewetting, such as drop rebound, condensation and evaporation. In overcoming the barrier to studying single film-to-droplet dewetting our results provide new ways of fluid manipulation and use of dewetting, such as inducing films of prescribed initial shapes and slip-controlled liquid retraction

Beyond Leidenfrost levitation: A thin-film boiling engine for controlled power generation

Overcoming friction between moving components is important for reducing energy losses and component wear. Hydrodynamic lubrication via thin-film boiling provides an opportunity for reduced friction energy and mass transport. A common example of such lubrication is the Leidenfrost effect, where a liquid droplet levitates on a cushion of its own vapor on a surface heated to temperatures above the liquid's boiling point. An asymmetry in this vapor flow, self-propels the droplet on the surface due to viscous drag, converting thermal energy to mechanical motion, like a heat engine. Although levitation significantly reduces friction, the induced self-propulsion depends on substrate geometry and material properties, which limits dynamic propulsion control. Therefore, the ability to control the power output is a significant challenge in realizing operational mm and sub-mm scale virtually frictionless engines. Here, we present a thin-film boiling engine where we control the power output mechanically. The rotor, which comprises of a working liquid coupled to a non volatile solid, is manually positioned over a heated turbine-inspired stator in a thin-film boiling state. We show that by controlling the position of the rotor over the substrate the power output from the rotation can be controlled above and below the Leidenfrost temperature (~250°C). We explain these experimental observations using a hydrodynamic analytical model. Additionally, we achieve propulsion outputs almost 4 times higher than levitation-based propulsion systems. The ability to control the rotation characteristics of such virtually frictionless engines allows potential applications in extreme environments such as at microscales or for space and planetary exploration

Capillary imbibition in lubricant coated channels

Capillary imbibition underpins many processes of fundamental and applied relevance in fluid mechanics. A limitation to the flow is the coupling to the confining solid, which induces friction forces. Here we study the effect of coating the solid with a liquid lubricant layer. Using a theoretical framework, we show that for sufficiently small lubricant viscosity dissipation entirely occurs in the lubricant layer, resulting in a linear growth of the advancing front. We extend our study to forced imbibition, where the same mechanism gives rise to an exponential front growth. This new ability to control multiphase flows in confinement opens new opportunities for flow control in micro- and nano-fluidic devices

Control of droplet evaporation on smooth chemical patterns

We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the equilibrium properties of the droplet as its size is changed, observing the emergence of a hierarchy of bifurcations that strongly depends on the particular underlying chemical pattern. Symmetric and periodic patterns lead to a sequence of pitchfork and saddle-node bifurcations that make stable solutions to become saddle nodes. Under dynamic conditions, this change in stability suggests that any perturbation in the system can make the droplet to shift laterally while relaxing to the nearest stable point, as is confirmed by numerical computations of the Cahn-Hilliard and Navier-Stokes system of equations. We also consider patterns with an amplitude gradient that creates a set of disconnected stable branches in the solution space, leading to a continuous change of the droplet's location upon evaporation