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

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.

Atomic-Scale Tracking of Dynamic Nucleation and Growth of an Interfacial Lead Nanodroplet

Revealing the evolutional pathway of the nucleation and crystallization of nanostructures at the atomic scale is crucial for understanding the complex growth mechanisms at the early stage of new substances and spices. Real-time discrimination of the atomic mechanism of a nanodroplet transition is still a formidable challenge. Here, taking advantage of the high temporal and spatial resolution of transmission electron microscopy, the detailed growth pathway of Pb nanodroplets at the early stage of nucleation was directly observed by employing electron beams to induce the nucleation, growth, and fusion process of Pb nanodroplets based on PbTiO3 nanowires. Before the nucleation of Pb nanoparticles, the atoms began to precipitate when they were irradiated by electrons, forming a local crystal structure, and then rapidly and completely crystallized. Small nanodroplets maintain high activity and high density and gradually grow and merge into stable crystals. The whole process was recorded and imaged by HRTEM in real time. The growth of Pb nanodroplets advanced through the classical path and instantaneous droplet coalescence. These results provide an atomic-scale insight on the dynamic process of solid/solid interface, which has implications in thin-film growth and advanced nanomanufacturing.

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.

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.

Dynamics of capillary coalescence and breakup: Quasi-two-dimensional nematic and isotropic droplets

We observed the 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 the nematic-isotropic phase transition. In previous works on coalescence it was considered that before the start of coalescence there exists a bridge between the outer fluid connecting regions on the two sides of the droplets (outer bridge). After the start of coalescence, a bridge connecting the two droplets appears (droplet bridge) and the outer bridge is broken. We have shown that there are coalescence processes where after the start of coalescence both the droplet bridge and the outer bridge can exist. This cardinally changes the coalescence process. During the first coalescence stage the size of the outer bridge decreases and the size of the droplet bridge increases. During the second stage the outer bridge becomes unstable which leads to pinch-off, formation of pointed end domains, secondary instability, splitting of pointed end domains, and formation of satellite droplets. We found the linear dependence of the minimum bridge radius on time near bridge breakup. This behavior confirms the capillary viscous regime of bridge breakup. Our work connects two areas of fluid dynamics: coalescence and breakup with formation of satellite droplets.

Benard-Marangoni convection within isotropic droplets in overheated free standing smectic films

We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions.

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.

On Droplet Coalescence in Quasi-Two-Dimensional Fluids

Coalescence of droplets plays a crucial role in nature and modern technology. Various experimental and theoretical studies explored droplet dynamics in three-dimensional (3D) and on 2D solid or liquid substrates. In this paper, we demonstrate the complete coalescence of isotropic droplets in thin quasi-2D liquids-overheated smectic films. We observe the merging of micrometer-sized flat droplets using high-speed imaging and analyze 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 the droplet geometry from that in the case of droplets on a solid substrate. A theoretical model is proposed to explain the difference in behavior.