A single light-driven Janus particle confined in a very thin oil droplet at an air--water interface displays intriguing dynamics. While laser activation induces rapid horizontal motion (1mm/s--1cm/s) by thermal Marangoni flow, the particle exhibits unexpected periodic circular motions or intermittent irregular motions. We show that the periodic trajectories are the result of a coupling between the self-propulsion of the particle and the spatiotemporal droplet thickness changes. We propose a simple model where the properties of the active particle trajectories are governed by capillary forces and torques due to the confinement of the particle in the thin droplet.
The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear Poisson-Boltzmann theory and compared with numerical results from non-linear Poisson-Boltzmann theory. The excess liquid-liquid interfacial tension with respect to the pure, salt-free liquid-liquid interfacial tension is found to decompose into a curvature-independent part due to short-ranged interfacial effects and a curvature-dependent electrostatic contribu…
The sensitive and reliable in-droplet chemical analysis benefits from the enhanced partition of an analyte into the droplets. This work, we will show that chemical reactions in surface nanodroplets can shift the partition of analytes from a highly diluted solution to the droplets. Seven types of organic acids with partition coefficients (LgP) ranging from -0.7 to 1.87 are used as model analytes dissolved in an oil solution that are extracted from the flow into aqueous nanodroplets immobilized on a substrate. The timescale of integrated extraction and reaction in droplets was represented by the…
Spontaneous rotation of a droplet induced by the Marangoni flow is analyzed in a two-dimensional system. The droplet with the small particle which supplies a surfactant at the interface is considered. We calculated flow field around the droplet using Stokes equation and found that advective nonlinearity breaks symmetry for rotation. Theoretical calculation indicates that the droplet spontaneously rotates when the radius of the droplet is an appropriate size. The theoretical results were validated through comparison with the experiments.
Dynamic Permeability in Metastable Droplet Interfacial Bilayers
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；The Molecular Foundry（分子发现所）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
Bacterial turbulence drives interfacial waves and shape dynamics in phase-separated droplets
School of Physics and Astronomy, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University（上海交通大学物理与天文学院、自然科学研究院和MOE-LSC）；Fujian Provincial Key Laboratory for Soft Functional Materials Research, Research Institute for Biomimetics and Soft Matter, Department of Physics, Xiamen University（厦门大学物理系仿生与软物质研究院福建省软功能材料研究重点实验室）；Universal Biology Institute, Graduate School of Science, The University of Tokyo（东京大学理学研究科全球生物学研究所）
We demonstrate that emulsion droplets stabilized by interfacial particles become unstable beyond a size threshold set by gravity. This holds not only for colloids but supra-colloidal glass beads, using which we directly observe the ejection of particles near the droplet base. The number of particles acting together in these ejection events decreases with time until a stable acorn-like configuration is reached. Stability occurs when the weight of all remaining particles is less than the interfacial binding force of one particle. We also show the importance of the curvature of the droplet surfac…
Living microorganisms in confined systems typically experience an affinity to populate boundaries. The reason for such affinity to interfaces can be a combination of their directed motion and hydrodynamic interactions at distances larger than their own size. Here we will show that self-propelled Janus particles (polystyrene particles partially coated with platinum) immersed in droplets of water and hydrogen peroxide tend to accumulate in the vicinity of the liquid/gas interface. Interestingly, the interfacial accumulation occurs despite the presence of an evaporation-driven flow caused by a so…
For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by accounting for the competition between bulk energy and interfacial tension. The nucleation process in liquid crystals is less understood. We numerically investigate nucleation in monolayered nematogenic films using a mesoscopic framework, in particular, we study the mor- phology and kinetic pathway in spontaneous formation and growth of droplets of the stable phase in the metastable background. The parameter $κ$ that quantifies the anisotropic elastic energy plays a centr…
Nature is remarkably adept at using interfaces to build structures, encapsulate reagents, and regulate biological processes. Inspired by Nature, we describe flexible polymer-based ribbons, termed "mesoscale polymers" (MSPs), to modulate interfacial interactions with liquid droplets. This produces unprecedented hybrid assemblies in the forms of flagellum-like structures and MSP-wrapped droplets. Successful preparation of these hybrid structures hinges on interfacial interactions and tailored MSP compositions, such as MSPs with domains possessing distinctly different affinity for fluid-fluid int…
Statistics and morphologies of stable droplets in scalar active fluids
Institute for Theoretical Physics IV, University of Stuttgart（斯图加特大学理论物理第四研究所）；STFC Hartree Centre（英国科学与技术设施委员会哈特里中心）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托尔大学H.H.威尔斯物理实验室）
本研究针对标量活性流体中稳定液滴的特性，通过数值模拟Active Model B+模型，验证了噪声对相转变的偏移作用，发现单一参数可调控液滴的数量、密度与分形维数，还观测到液滴相深处的六方晶格转变，完善了活性流体相分离的理论认知。
We propose a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and assuming isotropic surface energy at the oil-water interface, we numerically solve the resulting shape equations to elucidate the three-dimensional droplet geometry. We obtain a plethora of shapes as a function…
Droplet-based microfluidics has emerged as a powerful technology for the miniaturization and automation of biochemical assays. The replacement of surfactants by nanoparticles as interfacial stabilizers has gained increasing interest. However, the stabilization mechanism of droplets by nanoparticles in microchannels is poorly understood, drastically hindering the development of practical applications. Current methods for droplet stabilization involve a trade-off between low droplet production throughput and waste of large number of nanoparticles. Here, we introduce a modification to the droplet…
We simulate the response of a particle-stabilized emulsion droplet in an external force field, such as gravity, acting equally on all $N$ particles. We show that the field strength required for breakup (at fixed initial area fraction) decreases markedly with droplet size, because the forces act cumulatively, not individually, to detach the interfacial particles. The breakup mode involves the collective destabilization of a solidified particle raft occupying the lower part of the droplet, leading to a critical force per particle that scales approximately as $N^{-1/2}$.
We calculate ion distributions near a planar oil-water interface within non-linear Poisson-Boltzmann theory, taking into account the Born self-energy of the ions in the two media. For unequal self-energies of cations and anions, a spontaneous charge separation is found such that the water and oil phase become oppositely charged, in slabs with a typical thickness of the Debye screening length in the two media. From the analytical solutions, the corresponding interfacial charge density and the contribution to the interfacial tension is derived, together with an estimate for the Yukawa-potential …
The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. T…
Interfacially arrested melting in thin films: capillarity-driven suspension of phase transitions
Zhejiang Key Laboratory of Extreme Environment Functional Materials, Yiwu Research Institute of Fudan University（复旦大学义乌研究院极端环境功能材料浙江省重点实验室）；Shanghai Frontiers Science Research Base of Intelligent Optoelectronics and Perception, Institute of Optoelectronics, Fudan University（复旦大学光电研究院上海智能光电子与感知前沿科学基地）；Max Planck Institute of Colloids and Interfaces（马克斯·普朗克胶体与界面研究所）
The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free-energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free-energy is anisotropic, and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed …
A thin polymeric film in contact with a fluid body may leach low-molecular-weight compounds into the fluid. If this fluid is a small droplet, the compound concentration within the liquid increases due to ongoing leaching in combination with the evaporation of the droplet. This may eventually lead to an inversion of the transport process and a redistribution of the compounds within the thin film. In order to gain an understanding of the compound redistribution, we apply a macroscopic model for the evaporation of a droplet and combine that with a diffusion model for the compound transport. In th…
We study water-in-oil emulsion droplets, running the Belousov-Zhabotinsky reaction, that form a new type of active matter unit. These droplets, stabilised by surfactants dispersed in the oil medium, are capable of internal chemical oscillations and also self-propulsion due to dynamic interfacial instabilities that result from the chemical reactions. The chemical oscillations can couple via the exchange of activator and inhibitor type of reaction intermediates across the droplets under precise conditions of surfactant bilayer formation between the droplets. Here we present the synchronization b…
Surface tension plays a ubiquitous role in phase transitions including condensation or evaporation of atmospheric liquid droplets. Especially, understanding of interfacial thermodynamics of the critical nucleus of 1 nm scale is important for molecular characterization of the activation energy barrier of nucleation. Here, we investigate surface tension of spherical nanodroplets with both molecular dynamics and density functional theory, and find that surface tension decreases appreciably below 1 nm radius, whose analytic expression is consistently derived from the classic Tolman's equation. In …
We compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For PS films on O…
Theoretical calculations, computer simulations and experiments indicate the possible existence of a ferromagnetic liquid state, although definitive experimental evidence is lacking. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture. Since liquid droplets are deformable, the droplet shape is coupled with the magnetization texture. In a thin-film geometry in zero applied field, the droplet has a circular shape and a rotating magnetization texture with a point vortex at the center. We calculate the elongation and magnetization texture of such ferrom…
When a surfactant-stabilised oil droplet with an ultralow interfacial tension is trapped in the focus of two laser beams and pulled apart (by moving the laser beams) a configuration of two droplets connected by a thin tether of oil results. The tether radius depends on the ratio of the bending modulus to the renormalized interfacial tension, which takes into account the spontaneous curvature of the interface. The force exerted by the tether on the droplets is shown to be asymmetric with respect to the phase inversion temperature of the emulsion, in agreement with experiment. Fluid can be pumpe…
A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how t…
The wetting of solid surfaces can be manoeuvred by altering the energy balance at the interfacial region. While electric field acts favourably to spread a droplet on a rigid surface, this tendency may be significantly suppressed over soft surfaces, considering a part of the interfacial energy being utilized to deform the solid elastically by capillary forces. Here, we bring out a unique mechanism by virtue of which addition of nano-particles to the droplet brings in a favourable recovery of the electro-spreading characteristics of a soft surface, by realizing an alteration in the effective die…
We study self-propelled dynamics of a droplet due to a Marangoni effect and chemical reactions in a binary fluid with a dilute third component of chemical product which affects the interfacial energy of a droplet. The equation for the migration velocity of the center of mass of a droplet is derived in the limit of an infinitesimally thin inter- face. We found that there is a bifurcation from a motionless state to a propagating state of droplet by changing the strength of the Marangoni effect.
Tip-streaming generates micron- and submicron- sized droplets when a thin thread pulled from the pointy end of a drop disintegrates. Here, we report streaming from the equator of a drop placed in a uniform electric field. The instability generates concentric fluid rings encircling the drop, which break up to form an array of microdroplets in the equatorial plane. We show that the streaming results from an interfacial instability at the stagnation line of the electrohydrodynamic flow, which creates a sharp rim. The flow draws from the rim a thin sheet which destabilizes and sheds fluid cylinder…
In-situ characterization of minute amounts of complex fluids is a challenge. Magnetic Rotational Spectroscopy (MRS) with submicron probes offers flexibility and accuracy providing desired spatial and temporal resolution in characterization of nanoliter droplets and thin films when other methods fall short. MRS analyzes distinct features of the in-plane rotation of a magnetic probe, when its magnetic moment makes full revolution following an external rotating magnetic field. The probe demonstrates a distinguishable movement which changes from rotation to tumbling to trembling as the frequency o…
We study the adsorption of a fluid in the grand canonical ensemble occurring at a planar heterogeneous wall which is decorated with a chemical stripe of width $L$. We suppose that the material of the stripe strongly preferentially adsorbs the liquid in contrast to the outer material which is only partially wet. This competition leads to the nucleation of a droplet of liquid on the stripe, the height $h_m$ and shape of which (at bulk two-phase coexistence) has been predicted previously using mesoscopic interfacial Hamiltonian theory. We test these predictions using a microscopic Fundamental Mea…
Suspensions of spherical active particles often show microphase separation. At a continuum level, coupling their scalar density to fluid flow, there are two distinct explanations. Each involves an effective interfacial tension: the first mechanical (causing flow) and the second diffusive (causing Ostwald ripening). Here we show how the negative mechanical tension of contractile swimmers creates, via a self-shearing instability, a steady-state life cycle of droplet growth interrupted by division whose scaling behavior we predict. When the diffusive tension is also negative, this is replaced by …
We study the effect of surface fields on the interfacial properties of a binary polymer melt confined between two parallel walls. Each wall attracts a different component of the blend by a non-retarded van der Waals potential. An interface which runs parallel to the surfaces is stabilized in the center of the film. Using extensive Monte Carlo simulations we study the interfacial properties as a function of the film thickness, the strength of the surface forces and the lateral size over which the profiles across the film are averaged. We find evidence for capillary wave broadening of the appare…
From biological tissues to layers of paint, macroscopic non-porous materials with the capacity to swell when brought in contact with an appropriate solvent are ubiquitous. Here, we study experimentally and theoretically one of the conceptually simplest of such systems, the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental setup, we observe fast absorption leading to a radially spreading axisymmetric blister. Employing a linear poroelastic framework and thin-layer scalings, we develop a non-linear one-dimensional diffusion equation for the evolution of the b…
When a droplet is generated, the ligament connecting the drop to the nozzle thins down and eventually pinches off. Adding solid particles to the liquid phase leads to a more complex dynamic, notably by increasing the shear viscosity. Moreover, it introduces an additional length scale to the system, the diameter of the particles, which eventually becomes comparable to the diameter of the ligament. In this paper, we experimentally investigate the thinning and pinch-off of drops of suspensions with two different sizes of particles. We characterize the thinning for different particle size ratios a…
In our daily lives, after shaking a salad dressing, we see the coarsening of oil droplets suspended in vinegar. Such a demixing process is observed everywhere in nature and also of technological importance. For a case of high droplet density, domain coarsening proceeds with interdroplet collisions and the resulting coalescence. This phenomenon has been explained primarily by the so-called Brownian coagulation mechanism: stochastic thermal forces exerted by molecules induce random motion of individual droplets, causing accidental collisions and subsequent interface-tension driven coalescence. C…
