Moving contact lines of more than two phases dictate a large number of interfacial phenomena. Despite its significance to fundamental and applied processes, the contact lines at a junction of four-phases (two immiscible liquids, solid and gas) have been addressed only in a few investigations. Here, we report an intriguing phenomenon that follows after the four phases of oil, water, solid and gas make contact through the coalescence of two different three-phase contact lines. We combine experimental study and theoretical analysis to reveal and rationalize the dynamics exhibited upon the coalescence between the contact line of a micron-sized oil droplet and the receding contact line of a millimetre-sized water drop that covers the oil droplet on the substrate. We find that after the coalescence a four-phase contact line is formed for a brief period. However, this quadruple contact line is not stable, leading to a `droplet splitting' effect and eventual expulsion of the oil droplet from the water drop. We then show that the interfacial tension between the different phases and the viscosity of oil droplet dictate the splitting dynamics. More viscous oils display higher resistance to the extreme deformations of the droplet induced by the instability of the quadruple contact line and no droplet expulsion is observed for such cases.
The coalescence of two resting liquid droplets in a saturated vapor phase is investigated by Lattice Boltzmann simulations in two and three dimensions. We find that, in the viscous regime, the bridge radius obeys a t^{1/2}-scaling law in time with the characteristic time scale given by the viscous time. Our results differ significantly from the predictions of existing analytical theories of viscous coalescence as well as from experimental observations. While the underlying reason for these deviations is presently unknown, a simple scaling argument is given that describes our results well.
The coalescence of droplets plays a crucial role in nature and modern technology. Various experimental and theoretical studies explored droplet dynamics in 3D and on 2D solid or liquid substrates. In this paper, we demonstrate the coalescence of isotropic droplets confined in thin quasi-2D liquids -- overheated smectic films. We observe the merging of micrometer-sized flat droplets using high-speed-imaging and analyse the shape transformations of the droplets on the timescale of milliseconds. Our studies reveal the scaling laws of the coalescence time, which exhibits a different dependence on …
This fluid dynamics video shows the different interaction mechanisms of coalescence-induced droplet jumping during condensation on a nanostructured superhydrophobic surface. High speed imaging was used to show jumping behavior on superhydrophobic copper oxide and carbon nanotube surfaces. Videos demonstrating multi-jumping droplets, jumping droplet return to the surface, and droplet-droplet electrostatic repulsions were analyzed. Experiments using external electric fields in conjunction with high speed imaging in a custom built experimental chamber were used to show that all coalescence-induce…
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 …
For the first time we observed formation of small satellite droplets from the bridge at droplet coalescence. Investigations were made using a Hele-Shaw cell in the two-phase region at nematic-isotropic phase transition. In previous works on coalescence it was considered that before start of coalescence there exists a bridge between the outer fluid connecting regions on the two sides of the droplets (outer bridge). After start of coalescence a bridge connecting the two droplets appears (droplet bridge) and the outer bridge is broken. For the first time we have shown that there are coalescence p…
The dynamics of droplets on substrates has a strong impact on microfluidic systems ranging from commercially available lab-on-chip systems to state of the art developments in open microfluidics. Coalescence of micro and nano droplets on a substrate has been studied extensively, but in previous studies the focus has been on the interface movement. Here, we use computer simulations to investigate coalescence of droplets immersed in another liquid, in an inertia-dominated regime and also investigate the droplet's internal flow field. It is found that qualitatively the dynamics is similar to coale…
Recent investigations on the coalescence of polymeric droplets on a solid substrate have reported strong disagreements; the heart of the issue is whether coalescence of polymeric drops is similar to that of Newtonian fluid and is independent of molecular relaxation, or whether the role of entanglement of polymeric chains leads to a transition kinetics different from that of Newtonian fluid. Via this report, we resolve the disagreements through a discussion on the effects of merging method on the dominant forces governing the coalescence process, i.e., inertia, dissipation, and relaxation. Our …
Coalescence-induced alignment of anisotropic particles in drying sessile droplets
Forschungszentrum Jülich（于利希研究中心）；Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2)（亥姆霍兹埃尔朗根-纽伦堡可再生能源研究所（IET-2））；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
The coalescence between growing droplets is important for the surface coverage and spatial arrangements of droplets on surfaces. In this work, total internal reflection fluorescence (TIRF) microscopy is utilized to in-situ investigate the formation of nanodroplets around the rim of a polymer microcap, with sub-micron spatial and millisecond temporal resolution. We observe that the coalescence among droplets occurs frequently during their growth by solvent exchange. Our experimental results show that the position of the droplet from two merged droplets is related to the size of the parent dropl…
This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of fascinating phenomena can be observed. In particular, the interaction may result in the actuation of the droplet system, i.e. its displacement over a finite length. In order to control this displacement, we consider droplets confined on a hydrophilic stripe created by plasma-treating a PDMS substrate. This controlled actuation opens up unexplored opportunities…
Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biolog-ical systems. The process of merging of liquid objects has been studied during the pastyears experimentally and theoretically in different geometries. We introduce a uniquesystem that allows a quasi two-dimensional description of the coalescence process,micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We findthat the bridge connecting the droplets grows linearly in time during the initial stage ofcoalescence, both with respect to its height and lateral width. We also verify self…
Combining high-speed photography with electric current measurement, we investigate the electrocoalescence of Pickering emulsion droplets. Under high enough electric field, the originally-stable droplets coalesce via two distinct approaches: normal coalescence and abnormal coalescence. In the normal coalescence, a liquid bridge grows continuously and merges two droplets together, similar to the classical picture. In the abnormal coalescence, however, the bridge fails to grow indefinitely; instead it breaks up spontaneously due to the geometric constraint from particle shells. Such connecting-th…
An important strategy to stabilize emulsions is to arrest coalescence of the constituent droplets with an opposing rheological force. Colloidal particles adsorbed on the surface of emulsion droplets in a Pickering emulsion become increasingly crowded during successive coalescence events because the combined surface area of coalescing droplets is less than that of the constituent droplets. Beyond a critical density, the particles form a rigid shell around the droplet and inhibit both relaxation of the droplet shape and further coalescence. The resulting droplets have a nonuniform distribution o…
Using molecular dynamics simulations and scaling arguments, we investigate the coalescence preference dynamics of liquid droplets in a phase-segregating off-critical, single-component fluid. It is observed that the preferential distance of the product drop from its larger parent, during a coalescence event, gets smaller for large parent size inequality. The relative coalescence position exhibits a power-law dependence on the parent size ratio with an exponent $q \simeq 3.1$. This value of $q$ is in strong contrast with earlier reports $2.02$ and $5.01$ in the literature. The dissimilarity is e…
The stability of shapes formed by three viscoelastic droplets during their arrested coalescence has been investigated using micromanipulation experiments. Addition of a third droplet to arrested droplet doublets is shown to be controlled by the balance between interfacial pressures driving coalescence and internal elasticity that resists total consolidation. The free fluid available within the droplets controls the transmission of stress during droplet combination and allows connections to occur via formation of a neck between the droplets. The anisotropy of three-droplet systems adds complexi…
The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution.
Dynamics of the pendant drop coalescing with a sessile drop to form a single daughter droplet is known to form a bridge. The bridge evolution begins with a point contact between the two drops leading to a liquid neck of size comparable to the diameter of the drops. To probe this phenomenon in polymeric fluids, we quantify the neck radius growth during coalescence using high speed imaging. In the current study, we unveil the existence of three regimes on basis of concentration ratio $c/c^*$ namely, inertio-elastic $c/c^*<c_e/c^*$, viscoelastic $c_e/c^*<c/c^*<20$ and elasticity dominated regimes…
The stable configurations formed by two viscoelastic, ellipsoid-shaped droplets during their arrested coalescence has been investigated using micromanipulation experiments. Ellipsoidal droplets are produced by millifluidic emulsification of petrolatum into a yield stress fluid that preserves their elongated shape. The liquid meniscus between droplets can transmit stress and instigate movement of the droplets, from their initial relative position, in order to minimize doublet surface energy. The action of the liquid meniscus causes the ellipsoidal droplets to undergo rolling and restructuring e…
The expected universal dynamics associated with the initial stage of droplet coalescence are difficult to study visually due to the rapid motion of the liquid and the awkward viewing geometry. Here we employ an electrical method to study the coalescence of two inviscid droplets at early times. We measure the growth dynamics of the bridge connecting the two droplets and observe a new asymptotic regime inconsistent with previous theoretical predictions. The measurements are consistent with a model in which the two liquids coalesce with a slightly deformed interface.
Droplets coalescing on flat surfaces tend to end up with the smaller droplet migrating into the larger one. We report a counter-intuitive droplet coalescence pattern on a superhydrophilic cylindrical wire, where the larger droplet is pulled toward the smaller one. Consequently, the center of the combined mass significantly moves toward, often beyond, the original location of the smaller droplet. This phenomenon occurs primarily because the viscous friction that a droplet experiences on a cylindrical wire is not positively correlated with the size of the droplet, unlike the droplets coalescing …
The mechanisms for phase separation in highly concentrated emulsions when subjected to a thermal phase transition remain to be elucidated. Here, we create a hexagonally close-packed monodisperse emulsion in 2D and show that during a cool-heat cycle, the emulsion fully destabilizes akin to phase separation. The mechanism for this catastrophic destabilization is found to be spontaneous coalescence initiation that synchronously occurs between every solidified droplet and its neighbors. This synchronous coalescence initiation establishes system-wide network connectivity in the emulsion causing lar…
We numerically study the coalescence dynamics of two sessile droplets with radii $R_0$. The droplets are placed on top of a rigid substrate with a contact angle of $θ_{eq.} = π/9$. Having a highly wettable substrate ($θ_{eq} \ll π/2$) theory predicts that the bridge height ($h_0$) scales according to $h_0(t) \sim t^{2/3}.$ This behavior can be altered with e.g. surface tension gradients ($\partial_xγ\neq 0$). These gradients appear for example with heat transfer, surfactants or having different but miscible liquids. Instead of coalescence, these gradients can lead to a stable two droplet state…
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…
Solvent exchange is a simple method to produce surface nanodroplets on a substrate for a wide range of applications by displacing a solution of good solvent, poor solvent and oil (Solution A) by a poor solvent (Solution B). In this work, we show that the growth and coalescence of nanodroplets on a homogeneous surface is mediated by the viscosity of the solvent. We show that at high flow rates of viscous Solution B, the final droplet volume deviates from the scaling law that correlates final droplet volume to the flow rate of non-viscous Solution B, reported in previous work. We attribute this …
We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fraction and viscosity ratio under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for about 20 % concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To sing…
In this work has been proposed a numerical scheme with the aim of simulate the coalescence process between water drops immersed in a continuous phase (n-heptane). This numerical scheme is based in the Finite Volume method and two different values for the initial velocity of the drops were chosen. Depending of the initial velocity of collision some scenarios emerge, such as: permanent coalescence, formation of satellite drops etc. For some snap shots the streamlines are calculated for the different process of permanent coalescence. These streamlines allow the understanding of the dynamics of th…
The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains itself, throughout the viscous hydrodynamic regime, by a `coalescence-induced coalescence' mechanism. Scaling is recovered (with length scale $l \sim t$, as in $d=3$). The crossover to the inertial hydrodynamic regime is delayed even longer than in $d=3$; on entering it, full symmetry is finally restored and we find $l\sim t^{2/3}$, regardless of the initial s…
Coalescence is an important hydrodynamic event that frequently takes place in nature as well as in industry. Here we provide an experimental study on short time dynamics of water coalescence, particularly when a water droplet comes in contact with a flat water surface, by utilizing high-resolution high-penetration ultrafast X-ray microscopy. Our results demonstrate a possibility that an extreme curvature difference between a drop and a flat surface can significantly modify the hydrodynamics of water coalescence, which is unexpected in the existing theory. We suggest a plausible explanation for…
It is demonstrated that non-coalescent droplets of acetone can be formed on liquid substrates. The fluid flows around and in an acetone droplet hovering on water are recorded to shed light on the mechanisms which might lead to non-coalescence. For sufficiently low impact velocities, droplets undergo a damped oscillation on the surface of the liquid substrate but at higher velocities clean bounce-off occurs. Comparisons of experimentally observed static configurations of floating droplets to predictions from a theoretical model for a small non-wetting rigid sphere resting on a liquid substrate …
We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a single droplet and a pair of droplets are calculated and a universal droplet-droplet pair potential is obtained. The interaction of dispersed droplets via the ordered phase is attractive at large distances and repulsive at short distances, which results in a well defined preferred separation for two droplets and topological stabilization of the emulsion. This int…
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…
In this paper is described a numerical scheme that is used to simulate the coalescence process between clusters of water drops immersed in a continuous hydrocarbon phase (n-heptane). Two different values for the initial velocity of the drops were chosen. Depending of the initial velocity of collision some scenarios emerge, such as: permanent coalescence, formation of satellite drops etc. For some snap shots the streamlines are calculated for the different process of permanent coalescence. These streamlines allow the understanding of the dynamics of the droplets immersed on the n-heptane phase.
We have discovered the existence of polydisperse High Internal-Phase-Ratio Emulsions (HIPE) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organize themselves in the available space according to Apollonian packing rules. These polydisperse HIPE are formed during emulsification of surfactant-poor compositions of oil-surfactant-water two-phase systems. Their droplet size-distributions evolve spontaneously towards power laws with the Apollonian exponent. Small-Angle X-Ray Scattering performed on aged HIPEs demonstrated that the droplet packing structure…
Results from the state-of-the-art molecular dynamics simulations are presented for both equilibrium and nonequilibrium dynamics following vapor-liquid transition in a single component Lennard-Jones system. We have fixed the overall density close to the vapor-branch of the coexistence curve so that the liquid phase forms droplet structure in the background of vapor phase. In the equilibrium case, the motion of a single droplet is studied in both microcanonical and canonical ensembles, in the latter case a hydrodynamics preserving Nosé-Hoover thermostat was used to control the temperature. The d…
Emulsions are a central component of many modern formulations in food, pharmaceuticals, agrichemicals and personal care products. The droplets in these formulations are limited to being spherical as a consequence of the interfacial tension between the dispersed phase and continuous phase. The ability to control emulsion droplet morphology and stabilise non-spherical droplets would enable the modification of emulsion properties such as stability, substrate binding, delivery rate and rheology. One way of controlling droplet microstructure is to apply an elastic film around the droplet to prevent…
We present a phase field model (PFM) for simulating complex crack patterns including crack propagation, branching and coalescence in rock. The phase field model is implemented in COMSOL and is based on the strain decomposition for the elastic energy, which drives the evolution of the phase field. Then, numerical simulations of notched semi-circular bend (NSCB) tests and Brazil splitting tests are performed. Subsequently, crack propagation and coalescence in rock plates with multiple echelon flaws and twenty parallel flaws are studied. Finally, complex crack patterns are presented for a plate s…
