Electric energy generation from falling droplets has seen a hundred-fold rise in efficiency over the past year. However, even these newest devices can only extract a small portion of the droplet energy. In this paper, we theoretically investigate the contributions of hydrodynamic and electric losses in limiting the efficiency of droplet electricity generators (DEG). Noting that the electro-mechanical energy conversion occurs during the recoil that immediately follows droplet impact, we identify three limits on existing droplet electric generators: (i) the impingement velocity is limited in order to maintain the droplet integrity; (ii) much of droplet mechanical energy is squandered in overcoming viscous shear force with the substrate; (iii) insufficient electrical charge of the substrate. Of all these effects, we found that up to 83% of the total energy available was lost by viscous dissipation during spreading. Minimizing this loss by using cascaded DEG devices to reduce the droplet kinetic energy may increase future devices efficiency beyond 10%.
The study reports the aspects of postimpact hydrodynamics of ferrofluid droplets on superhydrophobic SH surfaces in the presence of a horizontal magnetic field. A wide gamut of dynamics was observed by varying the impact Weber number We, the Hartmann number Ha and the magnetic field strength manifested through the magnetic Bond number Bom. For a fixed We 60, we observed that at moderately low Bom 300, droplet rebound off the SH surface is suppressed. The noted We is chosen to observe various impact outcomes and to reveal the consequent ferrohydrodynamic mechanisms. We also show that ferrohydro…
Here, we trap and control the position of droplets to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented Stokes trap by incorporating a drop-on-demand system to generate droplets at a T-junction geometry on the same microfluidic chip. We then study confined droplet dynamics in response to perturbation by applying a millisecond-pressure pulse to deform trapped droplets. Droplet shape relaxation after cessation of the pressure pulse follows an exponential decay. The characteristic droplet shape relaxation…
Post impingement morphology and dynamics of water droplets on convex cylindrical surfaces has been explored experimentally. Droplet impact and post-impact feature studies have been conducted on hydrophillic and superhydrophobic cylindrical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio have been studied. The post-impact hydrodynamics have been quantified using the wetting fraction, the spreading factor and nondimensional film thickness at the north pole of the target. The observations reveal that the wetting fraction and spread factor increases with an increase …
The overall traffic of droplets in a network of microfluidic channels is strongly influenced by the liquid properties of the moving droplets. In particular, the effective hydrodynamic resistance of individual droplets plays a key role in their global behavior. We here propose two simple and low-cost experimental methods for measuring this parameter by analyzing the dynamics of a regular sequence of droplets injected into an "asymmetric loop" network. The choice of a droplet taking either route through the loop is influenced by the presence of previous droplets which modulate the hydrodynamic r…
Water droplets coalesce into larger ones in atmospheric clouds to form rain. But droplets on collision courses do not always coalesce due to the cushioning effects of the air between them. The extent to which these so-called hydrodynamic interactions reduce coalescence rates is embodied in the collision efficiency, which is often small and is not generally known. In order to characterize the mechanisms that determine the collision efficiency, we exploited new time-resolved three-dimensional droplet tracking techniques to measure the positions of cloud droplet pairs settling through quiescent a…
Understanding the influence of hydrodynamic stresses and colloidal interactions between droplets and membranes will inform better engineered membrane surfaces and process conditions. Using a long-wave hydrodynamic description that incorporates wettability and electrostatic repulsion, we numerically investigate the influence of droplet shapes and membrane characteristics on the overall repulsion-attraction towards the membrane surface. A stability phase diagram classifies stable-unstable drop shapes and investigate whether there is reversible deposition of droplets onto the membrane.
Modification and control over the vaporization kinetics of microfluidic droplets may have strong utilitarian implications in several scientific and technological applications. The article reports the control over the vaporization kinetics of pendent droplets under the influence of competing internal electrohydrodynamic and ferrohydrodynamic advection. Experimental and theoretical studies are performed and the morphing of vaporization kinetics of electrically conducting and paramagnetic fluid droplets using orthogonal electric and magnetic stimuli is established. Analysis of the observations re…
The hydrodynamics of droplets is significant in wide-ranging applications involving immiscible fluids and emulsions in food and pharmaceutical. The control and manipulation of droplets are primarily a function of flow governing and geometrical parameters. The finite element and level set approaches are used in this work to explore the influences of capillary number (Ca) and flow rate ratio (Qr) of dispersed and continuous phases on hydrodynamics of droplet generation in two-phase flow through T-junction cross-flow microfluidic device. A mathematical model based on a mass continuity, Navier-Sto…
We provide a basic method of Smoothed Particle Hydrodynamics (SPH) to simulate liquid droplet with surface tension in three dimensions. Liquid droplet is a simple case for surface tension modeling. Surface tension works only on fluid surface. In SPH method, we simply apply the surface tension on the boundary particles of liquid. The particle on the 3D boundary was detected dynamically using Free-Surface Detection algorithm. The normal vector and curvature of the boundary surface were calculated simultaneously with 3D boundary surface reconstruction using Moving Least-Squares (MLS) method. Befo…
Droplets abound in nature and technology. In general, they are multicomponent, and, when out of equilibrium, with gradients in concentration, implying flow and mass transport. Moreover, phase transitions can occur, with either evaporation, solidification, dissolution, or nucleation of a new phase. The droplets and their surrounding liquid can be binary, ternary, or contain even more components, and with several even in different phases. In the last two decades the rapid advances in experimental and numerical fluid dynamical techniques has enabled major progress in our understanding of the phys…
A fluid droplet may exhibit self-propelled motion by modifying the wetting properties of the substrate. We propose a novel model for droplet propagation upon a terraced landscape of ordered layers formed as a result of surface freezing driven by the contact angle dependence on the terrace thickness. Simultaneous melting or freezing of the terrace edge results in a joint droplet-terrace motion. The model is tested numerically and compared to experimental observations on long-chain alkane system in the vicinity of the surface melting point.
We reported an electro-hydrodynamic shooting phenomenon of liquid metal stream. A small voltage direct current electric field would induce ejection of liquid metal inside capillary tube and then shooting into sodium hydroxide solution to form discrete droplets. The shooting velocity has positive relationship with the applied voltage while the droplet size is dominated by the aperture diameter of the capillary nozzle. Further, the motion of the liquid metal droplets can be flexibly manipulated by the electrodes. This effect suggests an easy going way to generate metal droplets in large quantity…
Coalescence of micrometer-scale droplets is impacted by several parameters, including droplet size, viscosities of the two phases, droplet velocity and angle of approach, as well as interfacial tension and surfactant coverage. The dynamics and thinning of films between coalescing droplets can be particularly complex in the presence of surfactants, due to the generation of Marangoni stresses and reduced film mobility. In this work, a microfluidic hydrodynamic Stokes trap is used to gently steer and trap surfactant-laden micrometer-sized droplets at the center of a cross-slot. Incoming droplets …
We study the phenomenon of the "walking droplet", by means of numerical fluid dynamics simulations using the Smoothed Particle Hydrodynamics numerical method. This phenomenon occurs when a millimetric drop is released on the surface of an oil of the same composition, contained in a tank and subjected to vertical oscillations of frequency and amplitude very close to the Faraday instability threshold. At appropriate values of the parameters of the system under study, the oil droplet jumps permanently on the surface of the vibrating liquid forming a localized wave-particle system, reminding the b…
Liquid-liquid phase separation occurs not only in bulk liquid, but also on surfaces. In physiology, the nature and function of condensates on cellular structures remain unexplored. Here, we study how the condensed protein TPX2 behaves on microtubules to initiate branching microtubule nucleation, which is critical for spindle assembly in eukaryotic cells. Using fluorescence, electron, and atomic force microscopies and hydrodynamic theory, we show that TPX2 on a microtubule reorganizes according to the Rayleigh-Plateau instability, like dew droplets patterning a spider web. After uniformly coati…
Hydrodynamics knots are not only promising elementary structures to study mass and momentum transfer in turbulent flows, but also potent analogs for other topological problems arising in particle physics. However, experimental studies of knots are highly challenging due to the limited control over knot generation and difficult observation of the resulting fast-paced multiscale flow evolution. In this paper, we propose using acoustic streaming to tie hydrodynamic knots in fluids. The method is contactless, almost instantaneous and is relatively insensitive to viscosity. Importantly, it allows s…
The present article experimentally and theoretically probes the evaporation kinetics of sessile saline droplets. Observations reveal that presence of solvated ions leads to modulated evaporation kinetics, which is further a function of surface wettability. On hydrophilic surfaces, increasing salt concentration leads to enhanced evaporation rates, whereas on superhydrophobic surfaces, it first enhances and reduces with concentration. Also, the nature and extents of the evaporation regimes constant contact angle or constant contact radius are dependent on the salt concentration. The reduced evap…
We present a lattice-gas (generalised Ising) model for liquid droplets on solid surfaces. The time evolution in the model involves two processes: (i) Single-particle moves which are determined by a kinetic Monte Carlo algorithm. These incorporate into the model particle diffusion over the surface and within the droplets and also evaporation and condensation, i.e. the exchange of particles between droplets and the surrounding vapour. (ii) Larger-scale collective moves, modelling advective hydrodynamic fluid motion, determined by considering the dynamics predicted by a thin-film equation. The mo…
Manipulating micro-scale object plays paramount roles in a wide range of fundamental researches and applications. At micro-scale, various methods have been developed in the past decades, including optical, electric, magnetic, aerodynamic and acoustic methods. However, these non-contact forces are susceptible to external disturbance, and so finding a way to make micro-scale object manipulation immune to external perturbations is challenging and remains elusive. Here we demonstrate a method based on new trapping mechanism to manipulate micro-scale object in a gas flow at ambient conditions. We f…
Acoustic mixing of droplets is a promising way to implement biosensors that combine high speed and minimal reagent consumption. To date, this type of droplet mixing is driven by a volume force resulting from the absorption of high-frequency acoustic waves in the bulk of the fluid. Here, we show that the speed of these sensors is limited by the slow advection of analyte to the sensor surface due to the formation of a hydrodynamic boundary layer. We eliminate this hydrodynamic boundary layer by using much lower ultrasonic frequencies to excite the droplet, which drives a Rayleigh streaming that …
Superradiance occurs when a collection of atoms exhibits cooperative, spontaneous emission of photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon in a hydrodynamic system consisting of a pair of vibrationally-excited cavities, coupled through their common wavefield, that spontaneously emit droplets via interfacial fracture. We show that the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated cavities. We further show that the amplified emission rate varies sinusoidally with distance between the cavities, th…
Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statistical distribution of the droplet position. We develop a discrete model for walkers on an elliptical corral with two dominant eigenmodes. These eigenmodes are excited periodically with each having random, but correlated, weights. At each iteration the model computes the horizontal propulsion of the droplet due to impacts with the fluid bath. The propulsion is calculated based on the interaction of the droplet with the…
Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physiochemical hydrodynamics. Recently, Li et al. (Phys. Rev. Lett., vol. 120, 2018, 224501) and Kim & Stone (J. Fluid Mech., vol. 850, 2018, pp. 769-783) reported a segregative behavior (i.e., demixing) in an evaporating binary droplet. In this work, by means of experiments and theoretical analysis, we investigate the flow dynamics after the occurrence of the phase segregation. As example, we take the 1,2-hexanediol-water binary droplet system. First, we experimentally reveal the over…
To understand the behavior of composite fluid particles such as nucleated cells and double-emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimenstion-two point. We adopt a dynamical system approach to model and characterize the coupled behavior of the t…
A millimetric bouncing droplet sustained on a vibrating bath becomes a moving wave source (particle) through periodically interacting with the local wave field it generates during the droplet-bath impact. By virtue of such particle-wave duality, the macroscopic hydrodynamic system imitates enigmatic behaviors of the quantum realm. Here we show that it is possible to create an integrated pilot-wave field to better prescribe the droplet trajectories, via amplified bath capillarity. This is demonstrated with a liquid metal droplet-bath system in which the local wave field generated by droplet bou…
On the hydrodynamic behaviour of the immersed boundary -- lattice Boltzmann method for wetting problems
The Cyprus Institute（塞浦路斯研究所）；Tor Vergata University of Rome（罗马托维塔大学）；Télécom Paris, IP Paris（巴黎电信学院，巴黎理工学院）；CNR - Istituto per le Applicazioni del Calcolo（意大利国家研究委员会计算应用研究所）；Inria and LIX (École Polytechnique), IP Paris（法国国家信息与自动化研究所与LIX实验室（巴黎综合理工学院），巴黎理工学院）；University of Cyprus（塞浦路斯大学）
Biological microswimmers are known to navigate upstream of an external flow (positive rheotaxis) in trajectories ranging from linear, spiral to oscillatory. Such rheotaxis stems from the interplay between the motion and complex shapes of the microswimmers, e.g. the chirality of the rotating flagella, the shear flow characteristics, and the hydrodynamic interaction with a confining surface. Here, we show that an isotropic, active droplet microswimmer exhibits a unique oscillatory rheotaxis in a microchannel despite its simple spherical geometry. The swimming velocity, orientation, and the chemi…
To explore and react to their environment, living micro-swimmers have developed sophisticated strategies for locomotion - in particular, motility with multiple gaits. To understand the physical principles associated with such a behavioural variability,synthetic model systems capable of mimicking it are needed. Here, we demonstrate bimodal gait switching in autophoretic droplet swimmers. This minimal experimental system is isotropic at rest, a symmetry that can be spontaneously broken due to the nonlinear coupling between hydrodynamic and chemical fields, inducing a variety of flow patterns tha…
Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling.By modelling the droplet lattice as a memory-endowed system with spatially nonlocal coupling, we herein rationalise the form and onset of instability in this new class of dynamical oscillator. We i…
The article experimentally reveals and theoretically establishes the influence of electric fields on the evaporation kinetics of pendant droplets. It is shown that the evaporation kinetics of saline pendant droplets can be augmented by the application of an external alternating electric field. The evaporation behaviour is modulated by an increase in the field strength and frequency. The classical diffusion driven evaporation model is found insufficient in predicting the improved evaporation rates. The change in surface tension due to field constraint is insufficient for explaining the observed…
Active colloidal rafts perform swimming strokes that propel their host droplets
Université de Bordeaux（波尔多大学）；Collège de France（法兰西公学院）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Meiji University（明治大学）
We report an experimental observation of an instability in gas of constant density (air) with an initial non-uniform seeding of small droplets that develops as a planar shock wave passes through the gas-droplet mix. The seeding non-uniformity is produced by vertical injection of a slow-moving jet of air pre-mixed with glycol droplets into the test section of a shock tube, with the plane of the shock parallel to the axis of the jet. After the shock passage, we observe development of two counter-rotating vortices in the plane normal to that axis. The physical mechanism of the instability we obse…
Diffraction of walking drops by a standing Faraday wave
Department of Mathematics, MIT（麻省理工学院数学系）；Department of Mechanical Engineering, Boston University（波士顿大学机械工程系）；Department of Mathematics, UNC, Chapel Hill（北卡罗来纳大学教堂山分校数学系）
We study the detention statistics of self-propelling droplet microswimmers attaching to microfluidic pillars. These droplets show negative autochemotaxis: they shed a persistent repulsive trail of spent fuel that biases them to detach from pillars of a certain size after orbiting them just once. We have designed a microfluidic assay recording swimmers in pillar arrays of varying diameter, derived detention statistics via digital image analysis and interpreted these statistics via the Langevin dynamics of an active Brownian particle (ABP) model. By comparing data from orbits with and without re…
We observe electro-hydrodynamically driven turbulent flows at low Reynolds numbers in a two-fluid emulsion consisting of micron-scale droplets. In the presence of electric fields, the droplets produce interacting hydrodynamic flows which result in a dynamical organization at a spatial scale much larger than the size of the individual droplets. We characterize the dynamics associated with these structures by both video imaging and a simultaneous, in situ, measurement of the time variation of the bulk Reynolds stress with a rheometer. The results display scale invariance in the energy spectra in…
In this paper, we present TLBfind, a GPU code for simulating the hydrodynamics of droplets along with a dynamic temperature field. TLBfind hinges on a two-dimensional multi-component lattice Boltzmann (LB) model simulating a concentrated emulsion with finite-size droplets evolving in a thermal convective state, just above the transition from conduction to convection. The droplet concentration of the emulsion system is tenable, and at the core of the code lies the possibility to measure a large number of physical observables characterising the flow and droplets. Furthermore, TLBfind includes a …
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as the ones used for macro-droplets? To the greatest degree, this question should be addressed to the moving contact-line problem. The problem is naturally multiscale, where even using a slip boundary condition results in spurious numerical solutions and transcendental stagnation regions in modelling in the vicinity of the contact line. In this publication, it ha…
An isolated charge-neutral droplet in a uniform electric field experiences no net force. However, a droplet pair can move in response to field-induced dipolar and hydrodynamic interactions. If the droplets are identical, the center of mass of the pair remains fixed. Here, we show that if the droplets have different properties, the pair experiences a net motion due to nonreciprocal interactions. We analyze the three-dimensional droplet trajectories using asymptotic theory, assuming spherical droplets and large separations, and numerical simulations based on a boundary integral method. The dynam…
We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application of dynamical systems theory tools. As an illustration of the utility of the symmetry reduction, we apply it to a model of the pilot-wave system with a central harmonic force. We begin our analysis by identifying local bifurcations and the onset of chaos. We then describe the emergence of chaotic regions and their merging bifurcations, which lead to the form…
This article explores the governing role of the internal hydrodynamics and advective transport within sessile colloidal droplets on the self assembly of nanostructures to form floral patterns. Water acetone binary fluid and Bi2O3 nanoflakes based complex fluids are experimented with. Microliter sessile droplets are allowed to vaporize and the dry out patterns are examined using scanning electron microscopy. The presence of distributed self assembled rose like structures is observed. The population density, structure and shape of the floral structures are noted to be dependent on the binary flu…
