Approach and coalescence of liquid drops in air

Capillarity in Interfacial Liquids and Marbles: Mechanisms, Properties, and Applications

The mechanics of capillary force in biological systems have critical roles in the formation of the intra- and inter-cellular structures, which may mediate the organization, morphogenesis, and homeostasis of biomolecular condensates. Current techniques may not allow direct and precise measurements of the capillary forces at the intra- and inter-cellular scales. By preserving liquid droplets at the liquid-liquid interface, we have discovered and studied ideal models, i.e., interfacial liquids and marbles, for understanding general capillary mechanics that existed in liquid-in-liquid systems, e.g., biomolecular condensates. The unexpectedly long coalescence time of the interfacial liquids revealed that the Stokes equation does not hold as the radius of the liquid bridge approaches zero, evidencing the existence of a third inertially limited viscous regime. Moreover, liquid transport from a liquid droplet to a liquid reservoir can be prohibited by coating the droplet surface with hydrophobic or amphiphilic particles, forming interfacial liquid marbles. Unique characteristics, including high stability, transparency, gas permeability, and self-assembly, are observed for the interfacial liquid marbles. Phase transition and separation induced by the formation of nanostructured materials can be directly observed within the interfacial liquid marbles without the need for surfactants and agitation, making them useful tools to research the interfacial mechanics.

Measurement Methods for Droplet Adhesion Characteristics and Micrometer-Scale Quantification of Contact Angle on Superhydrophobic Surfaces: Challenges and Opportunities

Inspired by nature, superhydrophobic surfaces have been widely studied. Usually the wettability of a superhydrophobic surface is quantified by the macroscopic contact angle. However, this method has various limitations, especially for precision micro devices with superhydrophobic surfaces, such as biomimetic artificial compound eyes and biomimetic water strider robots. These precision micro devices with superhydrophobic surfaces proposed a higher demand for the quantification of contact angles, requiring contact angle quantification technology to have micrometer-scale measurement capabilities. In this review, it is proposed to achieve micrometer-scale quantification of superhydrophobic surface contact angles through droplet adhesion characteristics (adhesion force and contact radius). Existing contact angle quantification techniques and droplet characteristics' measurement methods were described in detail. The advancement of micrometer-scale quantification technology for the contact angle of superhydrophobic surfaces will enhance our understanding of superhydrophobic surfaces.

Coalescence of immiscible droplets in liquid environments

HYPOTHESIS

Droplet coalescence process is important in many applications and has been studied extensively when two droplets are surrounded by gas. However, the coalescence dynamics would be different when the two droplets are surrounded by an external viscous liquid. The coalescence of immiscible droplets in liquids has not been explored.

EXPERIMENTS

In the present research, the coalescence of two immiscible droplets in low- and high-viscosity liquids is investigated and compared with their miscible counterparts experimentally. The coalescence dynamics is investigated via high-speed imaging, and theoretical models are proposed to analyze the growth of the liquid bridge.

FINDINGS

We find that, the liquid bridge r evolves differently due to the constraint from the triple line in the bridge region, which follows r∝t2/3 for low-viscosity surroundings. While for high-viscosity surroundings, the liquid bridge grows at a constant velocity ur which varies with the surrounding viscosity μs as [Formula: see text] . In the later stage of the bridge growth, the bridge evolution again merges with the well-established power-law regime r∝t1/2, being either in low or high-viscosity liquids. Moreover, a new inertia-viscous-capillary timescale is proposed, which unifies the combined influence of inertia, viscous, and capillary forces on the evolution of the liquid bridge in liquid environments, highlighting the joint role of inertia and viscous resistance in the coalescence process.

Coalescence of biphasic droplets embedded in free standing smectic A films

We investigate micrometer-sized flat droplets consisting of an isotropic core surrounded by a nematic rim in freely suspended smectic A liquid-crystal films. In contrast to purely isotropic droplets which are characterized by a sharp edge and no long-range interactions, the nematic fringe introduces a continuous film thickness change resulting in long-range mutual attraction of droplets. The coalescence scenario is divided in two phases. The first one consists in the fusion of the nematic regions. The second phase involves the dissolution of a thin nematic film between the two isotropic cores. The latter has many similarities with the rupture of thin liquid films between droplets coalescing in an immiscible viscous liquid.

Dynamics of viscous droplet coalescence in the confined geometry of optical cells

The dynamics of quasi-two-dimensional coalescence of isotropic droplets in nematic liquid crystal environment was studied. Investigations were made in confined geometry of a Hele-Shaw optical cell with different transverse droplet sizes. The existence of three distinct dynamic regimes was found for coalescence, namely, short-, middle-, and long-time regimes. The fast dynamics of bridge transformation was visualized. At short time the dynamics of droplet transformation is similar to the transformation of free (three-dimensional) droplets. At later stages, two regimes of the coalescence at different timescales are determined by Poiseuille flow. Experimental data are discussed on the basis of existing theories.

Molecular dynamics simulation of the coalescence of surfactant-laden droplets

We investigate the coalescence of surfactant-laden water droplets by using several different surfactant types and a wide range of concentrations by means of a coarse-grained model obtained by the statistical associating fluid theory. Our results demonstrate in detail a universal mass transport mechanism of surfactant across many concentrations and several surfactant types during the process. Coalescence initiation is seen to occur via a single pinch due to aggregation of surface surfactant, and its remnants tend to become engulfed in part inside the forming bridge. Across the board we confirm the existence of an initial thermal regime with constant bridge width followed by a later inertial regime with bridge width scaling roughly as the square root of time, but see no evidence of an intermediate viscous regime. Coalescence becomes slower as surfactant concentration grows, and we see evidence of the appearance of a further slowdown of a different nature for several times the critical concentration. We anticipate that our results provide further insights in the mechanisms of coalescence of surfactant-laden droplets.

Measuring the Adhesion Force and the Spreading Radius between Droplets and a Solid Surface during Short-Time Spreading

When a droplet contacts a solid surface, the liquid spreads over the solid surface to minimize the total surface energy. This phenomenon is widespread in industrial production and nature, so research on droplet spreading is of great significance. Here, the adhesion force and the spreading radius during droplet spreading can be quantified using a highly sensitive photoelectric method. It is possible to study droplet spreading from two dimensions at the microscale. The adhesion force is measured by an optical lever, and the spreading radius is measured by an ultrafast electrical method. The measurement method allows the force resolution and the space-time resolution to reach the nanonewton lever and the nanosecond lever, respectively. We obtain the maximum spreading radius and the maximum adhesion force during short-time spreading through our technique. Moreover, we numerically simulate the droplet spreading process through the lattice Boltzmann solver and confirm the observed results. This study provides a new experimental technique for studying droplet spreading dynamics from multiple perspectives, which can deepen our understanding of droplet spreading and provide guidance for the development of new techniques.

Numerical Study of the Coalescence and Mixing of Drops of Different Polymeric Materials

In this study, we employ direct numerical simulation (DNS) to investigate the solutal hydrodynamics dictating the three-dimensional coalescence of microscopic, identical-sized sessile drops of different but miscible shear-thinning polymeric liquids (namely, PVAc or polyvinyl acetate and PMMA or polymethylmethacrylate), with the drops being in partially wetted configuration. Despite the ubiquitousness of the interaction of different dissimilar droplets in a variety of engineering problems ranging from additive manufacturing to understanding the behavior of photonic crystals, coalescence of drops composed of different polymeric and non-Newtonian materials has not been significantly explored. Interaction of such dissimilar droplets often involves simultaneous drop spreading, coalescence, and mixing. The mixing dynamics of the dissimilar drops are governed by interphase diffusion, the residual kinetic energy of the drops stemming from the fact that coalescence starts before the spreading of the drops have been completed, and the solutal Marangoni convection. We provide the three-dimensional velocity fields and velocity vectors inside the completely miscible, dissimilar coalescing droplets. Our simulations explicate the relative influence of these different effects in determining the flow field at different locations and at different time instances and the consequent mixing behavior inside the interacting drops. We also show the non-monotonic (in terms of the direction of migration) propagation of the mixing front of the miscible coalescing drops over time. We also establish that the overall mixing (on either side of the mixing front) speeds up as the Marangoni effects dictate the mixing. We anticipate that our study will provide an important foundation for studying miscible multi-material liquid systems, which will be crucial for applications such as inkjet or aerosol jet printing, lab-on-a-chip, polymer processing, etc.

Viscous coalescence of unequally sized spherical and cylindrical doublets

A coalescence model is developed for pairs of unequally sized particles, assuming surface tension driven flow opposed by viscosity. The flow field is extensional, biaxial for spheres and planar for cylinders. The balance of surface energy and viscous dissipation results in a system of two ordinary differential equations for each of the two doublet shapes studied. The solution of the differential equations provides growth of neck radius (or width) as well as surface and cross-sectional area evolution. For an infinitely large size ratio, the model describes the coalescence of a sphere or a cylinder with a semi-infinite wall of the same material. The model is compared to some numerical simulations and experimental measurements available in the literature. The comparison to experiments includes PDMS spheres, macromolecule-rich droplets, spherical bitumen particles, and a smectic circular island with a meniscus.

Toward Unveiling the Anomalies Associated with the Spontaneous Spreading of Droplets

The liquid droplet spreads over a solid surface to minimize the surface energy when brought in direct contact with the surface. The spreading process is rapid in the early stages, tends to slow down during its progress, and has resulted in peculiarity due to the experimental difficulties in the accurate determination of the contact line radius. In the present numerical study, we found that drop spreading begins with a viscosity-dominated Stokes regime, where contact radius scales as r ∼ t for a wide range of drop liquid viscosities. Subsequent to the Stokes regime, the inertial regime is observed where contact radius scales as r ∼ t^0.5 for low- to medium-viscous droplets, whereas for very high viscous drops, the spreading dynamics is completely dominated by the viscous regime. It is also found that the equilibrium wetting condition does not affect the power-law scaling for the contact radius of the drop. The amplitude of capillary waves induced across the interface of the drop is observed to be sufficiently high to cause necking and ejection of satellite drops from the main drop during its spreading for low-viscous liquids from complete wetting to partial wetting conditions. A regime plot between the Ohnesorge number and advancing contact angle of the substrate is presented to demarcate the regions of damped waves without pinch-off and drop spreading with satellite drops.

Quasi-two-dimensional coalescence of nematic and isotropic droplets and Rayleigh-Plateau instability in flat optical cells

We investigated the coalescence of nematic droplets in an isotropic environment and that of isotropic droplets in a nematic environment in quasi-two-dimensional geometry of a flat optical cell. Two different regimes of coalescence were found. In the circular meniscus between the nematic and isotropic regions both nematic and isotropic phases exist. As a result, two bridges form at coalescence: a nematic and an isotropic bridge. In this work, we focus on the situation when nematic wets the cell surface. The coalescence of nematic droplets starts near the cell surfaces where the droplet bridge from the nematic phase is formed. An outer bridge connecting the isotropic environment is localized in the middle of the cell. When the outer bridge gets thinner it becomes unstable and breaks up. A series of pinch-offs leads to the formation of satellite droplets. On the contrary, when isotropic droplets coalesce, the coalescence starts in the middle of the cell and breaking of the bridges occurs without instability and without the formation of satellite droplets. Breakup of the outer bridge is a new example of Rayleigh-Plateau instability in addition to actively studied transformation and breaking of filaments and stretched droplets.

Coalescence of Microscopic Polymeric Drops: Effect of Drop Impact Velocities

In this paper, we employ the direct numerical simulation (DNS) method for probing three-dimensional, axisymmetric coalescence of microscale, power-law-obeying, and shear-thinning polymeric liquid drops of identical sizes impacting a solid, solvophilic substrate with a finite velocity. Unlike the cases of drop coalescence of Newtonian liquid drops, coalescence of non-Newtonian polymeric drops has received very little attention. Our study bridges this gap by providing (1) the time-dependent, three-dimensional (3D) velocity field and 3D velocity vectors inside two coalescing polymeric drops in the presence of a solid substrate and (2) the effect of the drop impact velocity (on the solid substrate), quantified by the Weber number (We), on the coalescence dynamics. Our simulations reveal that the drop coalescence is qualitatively similar for different We values, although the velocity magnitudes involved, the time required to attain different stages of coalescence, and the time needed to attain equilibrium vary drastically for finitely large We values. Finally, we provide detailed simulation-based, as well as physics-based, scaling laws describing the growth of the height and the width of the bridge (formed due to coalescence) dictating the 3D coalescence event. Our analyses reveal distinct scaling laws for the growth of bridge height and width for early and late stages of coalescence as a function of We. We also provide simulation-based coalescence results for the case of two unequal sized drops impacting on a substrate (nonaxisymmetric coalescence) as well as results for axisymmetric coalescence for drops of different rheology. We anticipate that our findings will be critical in better understanding events such as inkjet or aerosol jet polymer printing, dynamics of polymer blends, and many more.

Digital droplet infusion

Infusion pumps have been widely used in clinical settings for the administration of medications and fluids. We present the digital droplet infusion (DDI) device, a low-cost, high-precision digital infusion system, utilizing a microfluidic discretization unit to convert continuous flow into precisely delivered droplet aliquots and a valving unit to control the duration and frequency of flow discretization. The DDI device relies on a distinct capillarity-dominated process of coalescence and pinch-off of droplets for flow digitization, which is monitored by a pair of conductive electrodes located before and after the junction. The digital feedback-controlled flow rate can be employed to adjust a solenoid valve for refined infusion management. With this unique digital microfluidic approach, the DDI technology enables a simple yet powerful infusion system with an ultrahigh resolution of digital droplet transfer volume, as small as 57 nL, which is three orders of magnitude lower than that of clinical standard infusion pumps, as well as a wide range of digitally adjustable infusion rates ranging from 0.1 mL h^-1 to 10 mL h^-1, in addition to an array of programmable infusion profiles and safety features. Its modular design enables fast assembly using only off-the-shelf and 3D-printed components. Overall, benefiting from its simple device architecture and excellent infusion performance, the DDI technology has great potential to become the next-generation clinical standard for drug delivery with its high precision and ultimate portability at a low cost.

Universality in coalescence of polymeric fluids

A pendant drop merging with a sessile drop and subsequently forming a single daughter drop is known to exhibit complex topologies. But their dynamics are yet to be probed for fluids exhibiting characteristic relaxation time scales while undergoing the deformation process. Here, we unveil a universal temporal evolution of the neck radius of the daughter drop during the coalescence of two polymeric drops. Such a generalization does not rely on the existence of previously explored viscous and inertial dominated regimes for simpler fluids but is fundamentally premised on a unique topographical evolution with essential features of interest exclusively smaller than the dominant scales of the flow. Our findings are substantiated by a theoretical model that considers the drops under coalescence to be partially viscous and partially elastic in nature. These results are substantiated with high-speed imaging experiments on drops of polyacrylamide (PAM), polyvinyl alcohol (PVA), polyethylene oxide (PEO), and polyethylene glycol (PEG). The observations herein are expected to hold importance for a plethora of diverse processes ranging from biophysics and microfluidics to the processing of materials in a wide variety of industrial applications.

Dynamics of island-meniscus coalescence in free-standing smectic films

In free-standing smectic films islands (regions of larger thickness than the film) can be considered as two-dimensional analogues of liquid droplets in a three-dimensional medium. The dynamics of droplet coalescence is an important but up to now incompletely solved problem in non-equilibrium mechanics. Here, we report on our investigations of island coalescence with the film meniscus. This phenomenon is analogous to the coalescence of a 3D droplet with a flat liquid surface. We found that the time evolution of island dimension is described by universal power-law dependencies for different stages of coalescence. Limited agreement with existing theory was found. In particular, in the final stage of coalescence the domain dynamics differs from theoretical predictions.

Self similarity of liquid droplet coalescence in a quasi-2D free-standing liquid-crystal film

Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biological systems. The process of merging of liquid objects has been studied during the past years experimentally and theoretically in different geometries. We introduce a unique system that allows a quasi two-dimensional description of the coalescence process: Micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We find that the bridge connecting the droplets grows linearly in time during the initial stage of coalescence, both with respect to its height and lateral width. We also verify self-similar dynamics of the bridge during the first stage of coalescence. We compare our results with a model based on the thin sheet equations. Our experiments confirm that the most important geometrical parameter influencing the coalescence rate is the contact angle of the droplets.

Coalescence of holes in two-dimensional free-standing smectic films

We investigate in free-standing smectic films coalescence of holes (circular regions with thickness smaller than the surrounding film). This process can be considered as a two-dimensional analog of coalescence of bubbles in a three-dimensional fluid. A high speed video camera was used to study the evolution of domains at different stages of coalescence. Special attention was given to investigations of the dependence of the size of the bridge between two holes at the initial stage of coalescence, which was considered in numerous theoretical works and bears information on the coalescence mechanism. It is established that the scaling law is applicable for the description of the transformation of bridges for holes of different radius R. We found that in the regime corresponding to the experimental situation the length of the bridge H increases with the scaling law H/R=(t/τ_{R})^{1/2}. The characteristic time τ_{R} determined from the scaling law is larger than the theoretical time, which can be connected with dissipation of energy both in the film and inside the holes.

Digital microfluidic meter-on-chip

The accurate monitoring and control of liquid flow at low flow rates have become increasingly important in contemporary biomedical research and industrial monitoring. Inspired by the drop-counting principle implemented in a clinical gravity drip, we propose a novel microfluidic flowmetry technology for polydimethylsiloxane (PDMS)-based conventional microfluidic devices, known as a microfluidic digital meter-on-chip (DMC), to achieve on-chip and localized microflow measurements with ultrahigh precision and a wide tunable range. The DMC technology primarily relies on capillarity, unlike a gravity drip, to induce a characteristic interfacial droplet pinch-off process, from which digital microflowmetry devices can discretize continuous flow into countable transferred liquid units with consistent quantifiable volumes. Enabled by the passive discretization principle and optical transparency, the DMC device requires no external energy input or bulky control equipment, and a non-contact wireless optical detection scheme using a smartphone can be conveniently used as a readout module. Moreover, the DMC technology achieves an ultrahigh flow-to-frequency sensitivity (6.59 Hz (μL min^-1)^-1) and resolution (droplet transfer volume down to 2.5 nL, nearly two orders of magnitude smaller than in previously reported work, resulting in ultralow flow rates of 1 μL min^-1). In addition, the flow rate measurement range covers up to 80 μL min^-1 and down to at least 150 nL min^-1 (over 100 times lower than reported similar digital flowmetry on the same time scale) using the current device configuration. Benefiting from its simple device architecture and adaptability, the versatile DMC technology can be seamlessly integrated with various microfluidic and nanofluidic devices for drug delivery and biochemical analysis, serving as a promising technology platform for next-generation highly demanding microflow measurements.

Universality in the viscous-to-inertial coalescence of liquid droplets

We present a theory on the coalescence of 2 spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved to yield an exact solution without free parameters, with its 2 asymptotic approximations reproducing the well-known scaling relations in the inertially limited viscous and inertial regimes. The viscous-to-inertial crossover observed in previous research is also recovered by the theory, rendering the collapse of data of different viscosities onto a single curve.

Self-Sustained Coalescence-Breakup Cycles of Ferrodrops under a Magnetic Field

The self-sustained coalescence-breakup cycles of ferrodrops were investigated for the first time by a high-speed camera under various magnetic fields. Under an axial magnetic field, the upper ferrodrop would deform into a conic shape before coalescing with the bottom ferropeak. Within 0.2 ms after coalescence, the minimum width of the expanding neck obeys a power-law relationship with time, while the exponents increase with the magnetic field and deviate with a decreasing trend in the later coalescence. The cone angle of the upper ferrodrop before coalescence gradually decreases while it increases before breakup with the magnetic field. A critical magnetic field around 35 mT was reported, above which the ferrofluid column undergoes the periodic phenomenon of coalescence and breakup. The frequency for the whole coalescence-breakup cycle increases exponentially with the applied magnetic field. A simplified force balance allows capturing the periodic mechanism involved in this driven harmonic oscillator.

Coalescence of viscous two-dimensional smectic islands

Freestanding smectic films give a unique possibility to study two-dimensional coalescence. We report experimental investigations in freestanding films and detailed analysis of coalescence of islands, circular regions of larger thickness than the surrounding film. The driving force of island coalescence is the dislocation tension on the boundary between the island and the film. The obtained experimental results enable one to perform complex analysis of two-dimensional coalescence in Stokes regime and compare it to theoretical predictions. The applicability of scaling arguments for the description of the peculiarities of domain dynamics is demonstrated. The whole process of coalescence is well described by the analytical solution adapted to our case of islands in freestanding smectic films.

Controllable internal mixing in coalescing droplets induced by the solutal Marangoni convection of surfactants with distinct headgroup architectures

Through several complementary experiments, an investigation of the bulk and interfacial flows that emerged during the coalescence of two water-in-oil droplets with asymmetric compositional properties was performed. By adding surfactant to one of the coalescing droplets and leaving the other surfactant-free, a strong interfacial tension gradient (i.e., solutal Marangoni) driving energy between the merging droplets generated pronounced internal mixing. The contributions of two distinct types of surfactant, anionic ammonium lauryl sulfate (ALS) and cationic cetyltrimethylammonium bromide (CTAB) on the rate of coalescence bridge expansion and on the generation of opposing flows during coalescence were investigated. All coalescence experiments supported the power law relation between the radius of the expanding connective liquid bridge and time, r_b ∝ t^1/2. However, the presence of surfactant decreased the magnitude of the prefactor in this relationship due to induced interfacial solutal Marangoni convection. Experiments showed that packing efficiency, diffusivity, and bulk concentration of the selected surfactant are vital in solutal Marangoni convection and thus the degree and timescale of internal mixing between merging droplets, which has yet to be adequately discussed within the literature. Denser interfacial packing efficiency and lower diffusivity of CTAB produced stronger opposing bulk and interfacial flow as well as greater bulk mixing. A discussion of how optimized surfactant selection and solutal Marangoni convection can be used for passively inducing convective mixing between coalescing drops in microfluidic channels when viscosity modulation is not feasible is provided.

Contact Interaction of Two Oil Lenses Floating on Surface of Deionized Water

Droplets on the surface of liquid play an important role in a variety of areas, including the petroleum industry, pollution control, and environmental processes. In this work, we study the contact interaction between two floating oil lenses on the surface of immiscible water. The contact interaction between the two floating oil lenses can be divided into three different regimes: (a) the collision involving deformation for low-viscous oils, (b) the direct coalescence for high-viscous oils, and (c) the coexistence (noncoalescence) of oil lenses at relatively high temperatures. The temperature dependence of the coalescence time for the coalescence of two silicone-oil lenses of large viscosities follows the Arrhenius equation.

Coalescence of sessile microdroplets subject to a wettability gradient on a solid surface

While there are intensive studies on the coalescence of sessile macroscale droplets, there is little study on the coalescence of sessile microdroplets. In this paper, the coalescence process of two sessile microdroplets is studied by using a many-body dissipative particle dynamics numerical method. A comprehensive parametric study is conducted to investigate the effects on the coalescence process from the wettability gradient, hydrophilicity of the solid surface, and symmetric or asymmetric configurations. A water bridge is formed after two microdroplets contact. The temporal evolution of the coalescence process is characterized by the water bridge's radii parallel to the solid surface (W_{m}) and perpendicular to the solid surface (H_{m}). It is found that the changes of both H_{m} and W_{m} with time follow a power law; i.e., H_{m}=β_{1}τ^{β} and W_{m}=α_{1}τ^{α}. The growth of H_{m} and W_{m} depends on the hydrophilicity of the substrate. W_{m} grows faster than H_{m} on a hydrophilic surface, and H_{m} grows faster than W_{m} on a hydrophobic surface. This is due to the strong competition between capillary forces induced by the water-bridge curvature and the solid substrate hydrophobicity. Also, flow structure analysis shows that regardless of the coalescence type once the liquid bridge is formed the liquid flow direction inside the capillary bridge is to expand the bridge radius. Finally, we do not observe oscillation of the merged droplet during the coalescence process, possibly due to the significant effects of the viscous forces.

Note: A top-view optical approach for observing the coalescence of liquid drops

We developed a new device that is capable of top-view optical examination of the coalescence of liquid drops. The device exhibits great potential for visualization, particularly for the early stage of liquid bridge expansion, owing to the use of a high-speed shadowgraph technique. The fluid densities of the two approaching drops and that of the ambient fluid are carefully selected to be negligibly different, which allows the size of the generated drops to be unlimitedly large in principle. The unique system design allows the point of coalescence between two drops to serve as an undisturbed optical pathway through which to image the coalescence process. The proposed technique extended the dimensionless initial finite radius of the liquid bridge to 0.001, in contrast to 0.01 obtained for conventional optical measurements. An examination of the growth of the bridge radius for a water and oil-tetrachloroethylene system provided results similar to Paulsen's power laws of the inertially limited viscous and inertial regimes. Furthermore, a miniscule shift in the center of the liquid bridge was detected at the point of crossover between the two regimes, which can be scarcely distinguished with conventional side-view techniques.

Droplet impact on deep liquid pools: Rayleigh jet to formation of secondary droplets

The impact of droplets on a deep pool has applications in cleaning up oil spills, spray cooling, painting, inkjet printing, and forensic analysis, relying on the changes in properties such as viscosity, interfacial tension, and density. Despite the exhaustive research on different aspects of droplet impact, it is not clear how liquid properties can affect the instabilities leading to Rayleigh jet breakup and number of daughter drops formed after its pinch-off. In this article, through systematic experiments we investigate the droplet impact phenomena by varying viscosity and surface tension of liquids as well as impact speeds. Further, using numerical simulations, we show that Rayleigh-Plateau instability is influenced by these parameters, and capillary time scale is the appropriate scale to normalize the breakup time. Based on Ohnesorge number (Oh) and impact Weber number (We), a regime map for no breakup, Rayleigh jet breakup, and crown splash is suggested. Interestingly, crown splash is observed to occur at all Ohnesorge numbers; however, at high Oh, a large portion of kinetic energy is dissipated, and thus the Rayleigh jet is suppressed regardless of high impact velocity. The normalized required time for the Rayleigh jet to reach its peak varies linearly with the critical height of the jet.

Liquid marble and water droplet interactions and stability

The interactions between two individual water droplets were investigated in air using a combination of coalescence rig and high speed video camera. This combination allows the visualization of droplet coalescence dynamics with millisecond resolution which provides information on droplet stability. Bare water droplets coalesced rapidly upon contact, while droplet stability was achieved by coating the droplets with polystyrene particles carrying pH-responsive poly[2-(diethylamino)ethyl methacrylate] hairs (PDEA-PS particles) to form liquid marbles. The asymmetric interaction of a water droplet (pH 3 or 10) armoured with the PDEA-PS particles (liquid marble) with a bare droplet at pH 3 exhibited intermediate stability with coalescence observed following an induction time. The induction time was longer for the pH 10 liquid marble, where the PDEA-PS particles have a hydrophobic surface, than in the case of a pH 3 liquid marble, where the PDEA-PS particles have a hydrophilic surface. Furthermore, film formation of PDEA-PS particles on the liquid marble surface with toluene vapour confirmed capsule formation which prevented coalescence with the neighbouring water droplet instead wetting the capsule upon contact within 3 milliseconds. This study illuminates the stability of individual particle-stabilized droplets and has potential impact on processes and formulations which involve their interaction.

Coalescence of bubbles and drops in an outer fluid

When two liquid drops touch, a microscopic connecting liquid bridge forms and rapidly grows as the two drops merge into one. Whereas coalescence has been thoroughly studied when drops coalesce in vacuum or air, many important situations involve coalescence in a dense surrounding fluid, such as oil coalescence in brine. Here we study the merging of gas bubbles and liquid drops in an external fluid. Our data indicate that the flows occur over much larger length scales in the outer fluid than inside the drops themselves. Thus, we find that the asymptotic early regime is always dominated by the viscosity of the drops, independent of the external fluid. A phase diagram showing the crossovers into the different possible late-time dynamics identifies a dimensionless number that signifies when the external viscosity can be important.

Demonstrating microdroplet coalescence for tailored and biodegradable microgel fabrication

Coalescence of microdroplets, mimicking Nature, has been exploited to form gelatin microparticles. The microgels are biodegradable and biocompatible.