An experimental study on the coalescence process of binary droplets in oil under ultrasonic standing waves

The coalescence process of binary droplets in oil under ultrasonic standing waves was investigated with high-speed photography. Three motion models of binary droplets in coalescence process were illustrated: (1) slight translational oscillation; (2) sinusoidal translational oscillation; (3) migration along with acoustic streaming. To reveal the droplets coalescence mechanisms, the influence of main factors (such as acoustic intensity, droplet size, viscosity and interfacial tension, etc) on the motion and coalescence of binary droplets was studied under ultrasonic standing waves. Results indicate that the shortest coalescence time is achieved when binary droplets show sinusoidal translational oscillation. The corresponding acoustic intensity in this case is the optimum acoustic intensity. Under the optimum acoustic intensity, drop size decrease will bring about coalescence time decrease by enhancing the binary droplets oscillation. Moreover, there is an optimum interfacial tension to achieve the shortest coalescence time.     

Binary collision of a burning droplet and a non-burning droplet of xylene: Outcome regimes and flame dynamics

The binary collisions of a burning droplet and a non-burning droplet of xylene are experimentally investigated. The experimental parameters span an extensive range of Weber number and impact parameter, covering the collision outcome regimes of coalescence, reflexive separation, and stretching separation. A high-speed camera captures the temporal details of the collision process, involving flame spread, visible radiation, and flame distributions around droplets. For reflexive separation and stretching separation, the flame from the droplet spreads to the ligament, surrounding it during the interaction process, and then spreads around separated droplets and satellite droplets. Highly-interactive flames are formed in-between the droplets, with very sooty flames generated for most collisions. For the coalescence case, a swirling flame forms around the rotating coalesced droplet. For similar Weber numbers, visible flame radiation is compared for different collision regimes. The visible flame radiation changes more significantly for the reflexive and stretching separation cases than it does for the coalescence case. The change of the averaged visible flame radiation for reflexive separation and stretching separation is more than two times higher than that for coalescence. The map of three different collision regimes is plotted in the Weber number versus impact parameter domain and compared with available theoretical model predictions. Although the different outcomes of collision with the presence of flame can be well predicted by the model, using fluid properties determined by the averaged properties of the two droplets, the dynamics of the detailed processes involved in the collisions are very interesting and have strong implications on overall combustion behavior that go well beyond the mapped regimes.     

Microdroplet targeting induced by substrate curvature

Fundamental understanding of the wettability of curved substrates is crucial for the applications of microdroplets in colloidal science, microfluidics, and heat exchanger technologies. Here we report via lattice Boltzmann simulations and energetic analysis that microdroplets show an ability of transporting selectively to appropriate substrates solely according to substrate shape(curvature), which is called the substrate-curvature-dependent droplet targeting because of its similarity to protein targeting by which proteins are transported to the appropriate destinations in the cell. Two dynamic pathways of droplet targeting are identified: one is the Ostwald ripening-like liquid transport between separated droplets via evaporating droplets on more curved convex(or less curved concave) surfaces and growing droplets on less curved convex(or more curved concave) surfaces, and the other is the directional motion of a droplet through contacting simultaneously substrates of different curvatures. Then we demonstrate analytically that droplet targeting is a thermodynamically driven process. The driving force for directional motion of droplets is the surface-curvature-induced modulation of the work of adhesion, while the Ostwald ripening-like transport is ascribed to the substrate-curvature-induced change of droplet curvature radius. Our findings of droplet targeting are potentially useful for a tremendous range of applications, such as microfluidics, thermal control, and microfabrication.     

Decompressing emulsion droplets favors coalescence

The destabilization process of an emulsion under flow is investigated in a microfluidic device. The experimental approach enables us to generate a periodic train of droplet pairs, and thus to isolate and analyze the basic step of the destabilization, namely, the coalescence of two droplets which collide. We demonstrate a counterintuitive phenomenon: coalescence occurs during the separation phase and not during the impact. Separation induces the formation of two facing nipples in the contact area that hastens the connection of the interfaces prior to fusion. Moreover, droplet pairs initially stabilized by surfactants can be destabilized by forcing the separation. Finally, we note that the fusion mechanism is responsible for a cascade of coalescence events in a compact system of droplets where the separation is driven by surface tension.     

Hydrodynamics of passing-over motion during binary droplet collision in shear flow

A combined experimental and numerical study is undertaken to investigate the hydrodynamic characteristics of single-phase droplet collision in a shear flow. The passing-over motion of interactive droplets is observed, and the underlying hydrodynamic mechanisms are elucidated by the analysis of the motion trajectory, transient droplet deformation and detailed hydrodynamic information (e.g., pressure and flow fields). The results indicate that the hydrodynamic interaction process under shear could be divided into three stages: approaching, colliding, and separating. With the increasing confinement, the interaction time for the passing-over process is shorter and the droplet processes one higher curvature tip and more stretched profile. Furthermore, the lateral separation Δy/R₁ exhibits larger decrease in the approaching stage and the thickness of the lubrication film is decreased during the interaction. As the initial lateral separation increases, the maximum trajectory shift by the collision interaction is getting smaller. During the collision between two droplets with different sizes, the amplitude of the deformation oscillation of the larger droplet is decreased by reducing the size ratio of the smaller droplet to the bigger one.     

Dynamical model for chemically driven running droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets--reaction-limited and saturated regime--are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.     

微尺度下锥形微操作探针表面液滴形成的研究（英）

基于液滴的转移方法可实现微操作任务中微对象的拾取,锥形操作探针则常作为一种毛细力微操作执行工具。主要研究在空气冷凝模式下锥形探针端面的液滴形成。建立了微液滴形成的数学模型,主要包括初始液滴的形成、液滴的合并和液滴的移动,研究了影响操作液滴的关键参数,分析表明:过冷度决定最小液滴半径。对单液滴的生长机制进行理论分析,并通过数值求解的方法模拟了锥形操作探针端面的液滴形成。搭建实验测试平台,实验研究了微尺度下锥形微操作探针端面的液滴形成。实验结果表明:在空气冷凝模式下,操作探针端面能够形成微液滴。经过初始液滴的形成,液滴的合并和移动等过程最终可形成稳定的微液滴,且不同锥顶角下液滴的形成呈现多样化。     

Field-induced motion of ferrofluids through immiscible viscous media: Testbed for restorative treatment of retinal detachment

Biocompatible, hydrophobic ferrofluids comprised of magnetite nanoparticles dispersed in polydimethylsiloxane show promise as materials for the treatment of retinal detachment. This paper focuses on the motion of hydrophobic ferrofluid droplets traveling through viscous aqueous media, whereby the movement is induced by gradients in external fields generated by small permanent magnets. A numerical method was utilized to predict the force on a spherical droplet, and then the calculated force was used to estimate the time required for the droplet to reach the permanent magnet. The calculated forces and travel times were verified experimentally.     

电场对协流式微流控装置中乳液液滴生成行为的调控机理

建立了直流电场作用下协流式微流控装置中单乳液液滴乳化生成过程的非稳态理论模型,并开展了数值模拟研究,揭示了电场对液滴乳化生成动力学行为的调控机理,阐明了流场/电场参数对液滴乳化生成特性的影响规律.研究结果表明:沿流体流动方向施加静电场可在电物性参数不同的两相流体界面法线方向上产生指向内相流体的电场力,进而强化了内相流体界面的颈缩和断裂,提升了液滴生成速率和形变程度,减小了液滴生成尺寸;在同一毛细数下,随着电毛细数的增大,乳液乳化流型由每周期仅有单一液滴生成的滴式流型转变为每周期有一个主液滴并伴随有卫星液滴生成的滴式流型;随着毛细数和电毛细数的增大,黏性拖曳力以及电场力作用增强,使内相流体颈缩过程后期更容易形成细长型液线,从而有助于诱发液线上产生Rayleigh-Plateau不稳定现象,继而促进卫星液滴的形成.     

Collisions of Two-Phase Liquid Droplets in a Heated Gas Medium

The paper presents the experimental research findings for the integral characteristics of processes developing when two-phase liquid droplets collide in a heated gas medium. The experiments were conducted in a closed heat exchange chamber space filled with air. The gas medium was heated to 400–500 °C by an induction system. In the experiments, the size of initial droplets, their velocities and impact angles were varied in the ranges typical of industrial applications. The main varied parameter was the percentage of vapor (volume of bubbles) in the droplet (up to 90% of the liquid volume). The droplet collision regimes (coalescence, bounce, breakup, disruption), size and number of secondary fragments, as well as the relative volume fraction of vapor bubbles in them were recorded. Differences in the collision regimes and in the distribution of secondary fragments by size were identified. The areas of liquid surface before and after the initial droplet breakup were determined. Conditions were outlined in which vapor bubbles had a significant and, on the contrary, fairly weak effect on the interaction regimes of two-phase droplets.     

Sliding behavior of water droplets on line-patterned hydrophobic surfaces

We prepared line-patterned hydrophobic surfaces using fluoroalkylsilane (FAS) and octadecyltrimethoxysilane (ODS) then investigated the effect of line direction on sliding behavior of water droplets by direct observation of the actual droplet motion during sliding. Water droplets slide down with a periodic large deformation of the contact line and sliding velocity fluctuation that occurred when they crossed over the 500-μm ODS line regions in FAS regions on a Si surface tilted at 35°. These behaviors are less marked for motion on a 100-μm line surface, or on lines oriented parallel to the slope direction. Smaller droplets slide down with greater displacement in the line direction on 500-μm line patterning when the lines were rotated at 13° in-plane for the slope direction. This sliding behavior depended on the droplet size and rotation angle, and is accountable by the balance between gravitational and retentive forces.     

On the coalescence of sessile drops with miscible liquids

Sessile drops sitting on highly wettable solid substrates fuse in qualitatively different ways after contact, depending on the surface tension gradients between the mixing droplets. In early time evolution the drop coalescence can be fast or delayed (intermittent). In long time evolution a secondary drop formation can occur. We study numerically droplet dynamics during coalescence in two and three spatial dimensions, within a phase field approach. We discuss criteria to distinguish different coalescence regimes. A comparison with recent experiments will be done.     

Hindered and enhanced coalescence of drops in stokes flows

We analyze axisymmetric near-contact motion of two drops under the action of an external force or imposed flow. It is shown that hydrodynamic stresses in the near-contact region that are associated with the outer (drop-scale) flow can qualitatively affect the drainage of the thin fluid film separating the drops. If this far-field stress acts radially inward, film drainage is arrested at long times; exponential film drainage occurs if this stress acts outward. An asymptotic analysis of the stationary long-time film profile is presented for small-deformation conditions, and the critical strength of van der Waals attraction for film rupture is calculated. The effect of an insoluble surfactant is also considered. Hindered and enhanced drop coalescence are not predicted by the current theories, because the influence of the outer flow on film drainage is ignored.     

The droplet size distribution in the late stage of phase separation

We consider a collection of droplets during the late stage of phase separation in a closed system. Its coarsening is driven by surface energy and leads asymptotically to a linear growth of the mean droplet volume with time (Ostwald ripening). The droplets grow either from the supersaturated uncondensed phase (coalescence) or by collisions with subsequent fusion (coagulation). The combination of both mechanisms leads asymptotically to a self-similar evolution of the size distribution of the droplets when the coagulation kernel is homogeneous with degree zero. We calculate the scaled droplet size distribution for Brownian and constant kernel and compare the effects of coagulation with the effects of correlation and screening discussed in the literature. We compare our results for the asymptotic scaled distribution with computer simulations for the combined coalescence and coagulation processes.     

The physics of 2D microfluidic droplet ensembles

We review non-equilibrium many-body phenomena in ensembles of 2D microfluidic droplets. The system comprises of continuous two-phase flow with disc-shaped droplets driven in a channel, at low Reynolds number of 10⁻⁴–10⁻³$10^{-4}–10^{-3}$. The basic physics is that of an effective potential flow, governed by the 2D Laplace equation, with multiple, static and dynamic, boundaries of the droplets and the walls. The motion of the droplets induces dipolar flow fields, which mediate 1/r²$1/r^2$ hydrodynamic interaction between the droplets. Summation of these long-range 2D forces over droplet ensembles converges, in contrast to the divergence of the hydrodynamic forces in 3D. In analogy to electrostatics, the strong effect of boundaries on the equations of motion is calculated by means of image dipoles. We first consider the dynamics of droplets flowing in a 1D crystal, which exhibits unique phonon-like excitations, and a variety of nonlinear instabilities—all stemming from the hydrodynamic interactions. Narrowing the channel results in hydrodynamic screening of the dipolar interactions, which changes salient features of the phonon spectra. Shifting from a 1D ordered crystal to 2D disordered ensemble, the hydrodynamic interactions induce collective density waves and shocks, which are superposed on single-droplet randomized motion and dynamic clustering. These collective modes originate from density–velocity coupling, whose outcome is a 1D Burgers equation. The rich observational phenomenology and the tractable theory render 2D droplet ensembles a suitable table-top system for studying non-equilibrium many-body physics with long-range interactions.     

Self-propelled droplets

Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own ‘exhausts’ allows to additionally study collective phenomena.     

Numerical assessment of ultrasound supported coalescence of water droplets in crude oil

In this study, a numerical assessment of the coalescence of binary water droplets in water-in-oil emulsion was conducted. The investigation addressed the effect of various parameters on the acoustic pressure and coalescence time of water droplets in oil phase. These include transducer material, initial droplet diameter (0.05–0.2 in), interfacial tension (0.012–0.082 N/m), dynamic viscosity (10.6–530 mPas), temperature (20–100 °C), US (ultra sound) frequency (26.04–43.53 kHz) and transducer power (2.5–40 W). The materials assessed are lead zirconate titanate (PZT), lithium niobate (LiNbO₃), zinc oxide (ZnO), aluminum nitride (AlN), polyvinylidene fluoride (PVDF), and barium titanate (BaTiO₃). The numerical simulation of the binary droplet coalescence showed good agreement with experimental data in the literature. The US implementation at a fixed frequency produced enhanced coalescence (t = 5.9–8.5 ms) as compared to gravitational settling (t = 9.8 ms). At different ultrasound (US) frequencies and transducer materials, variation in the acoustic pressure distribution was observed. Possible attenuation of the US waves, and the subsequent inhibitive coalescence effect under various US frequencies and viscosities, were discussed. Moreover, the results showed that the coalescence time reduced across the range of interfacial tensions which was considered. This reduction can be attributed to the fact that lower interfacial tension produces emulsions which are relatively more stable. Hence, at lower interface tension between the water and crude oil, there was more resistance to the coalescence of the water droplets due to their improved emulsion stability. The increment of the Weber number at higher droplet sizes leads to a delay in the recovery of the droplet to spherical forms after their starting deformation. These findings provide significant insights that could aid further developments in demulsification of crude oil emulsions under varying US and emulsion properties.     

Coalescence of spreading droplets on a wettable substrate

We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as t1/2. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as ho3/2/Ro. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.     

Self-propelled running droplets on solid substrates driven by chemical reactions

We study chemically driven running droplets on a partially wetting solid substrate by means of coupled evolution equations for the thickness profile of the droplets and the density profile of an adsorbate layer. Two models are introduced corresponding to two qualitatively different types of experiments described in the literature. In both cases an adsorption or desorption reaction underneath the droplets induces a wettability gradient on the substrate and provides the driving force for droplet motion. The difference lies in the behavior of the substrate behind the droplet. In case I the substrate is irreversibly changed whereas in case II it recovers allowing for a periodic droplet movement (as long as the overall system stays far away from equilibrium). Both models allow for a non-saturated and a saturated regime of droplet movement depending on the ratio of the viscous and reactive time scales. In contrast to model I, model II allows for sitting drops at high reaction rate and zero diffusion along the substrate. The transition from running to sitting drops in model II occurs via a super- or subcritical drift-pitchfork bifurcation and may be strongly hysteretic implying a coexistence region of running and sitting drops.     

Droplets sliding on fibres

We present the results of a combined experimental and theoretical investigation of oil droplets sliding on fibres. First, both the axisymmetric shape and the motion of a droplet on a vertical fibre are described. The motion is shown to result from a balance between the droplet weight and the viscous stresses. On a long-term range, the droplet loses some mass through coating the fibre, which decreases its velocity. In a second time, we rationalize the behaviour of a droplet that encounters a junction between vertical and horizontal fibres. Depending on its size, the droplet may cross the junction or remain blocked. The transition is well described by an ordinary differential equation equivalent to a damped harmonic oscillator truncated to the neighbourhood of the horizontal fibre. This simple system is the basic element for more complex fiber networks that would be useful in microfluidic applications involving droplets.