Coalescence of viscous liquid drops

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.

A Review on the Coalescence of Confined Drops with a Focus on Scaling Laws for the Growth of the Liquid Bridge

The surface-tension-driven coalescence of drops has been extensively studied because of the omnipresence of the phenomenon and its significance in various natural and engineering systems. When two drops come into contact, a liquid bridge is formed between them and then grows in its lateral dimensions. As a result, the two drops merge to become a bigger drop. The growth dynamics of the bridge are governed by a balance between the driving force and the viscous and inertial resistances of involved liquids, and it is usually represented by power-law scaling relations on the temporal evolution of the bridge dimension. Such scaling laws have been well-characterized for the coalescence of unconfined or freely suspended drops. However, drops are often confined by solid or liquid surfaces and thus are a different shape from spheres, which affects their coalescence dynamics. As such, the coalescence of confined drops poses more complicated interfacial fluid dynamics challenges compared to that of unconfined drops. Although there have been several studies on the coalescence of confined drops, they have not been systematically reviewed in terms of the properties and geometry of the confining surface. Thus, we aim to review the current literature on the coalescence of confined drops in three categories: drop coalescence on a solid surface, drop coalescence on a deformable surface, and drop coalescence between two parallel surfaces with a small gap (i.e., Hele-Shaw cell), with a focus on power-law scaling relations, and to suggest challenges and outlooks for future research on the phenomena.

Dynamics of Droplet Coalescence on Hydrophobic Fibers in Oil: Morphology and Liquid Bridge Evolution

Although droplet self-jumping on hydrophobic fibers is a well-known phenomenon, the influence of viscous bulk fluids on this process is still not fully understood. In this work, two water droplets' coalescence on a single stainless-steel fiber in oil was investigated experimentally. Results showed that lowering the bulk fluid viscosity and increasing the oil-water interfacial tension promoted droplet deformation, reducing the coalescence time of each stage. While the total coalescence time was more influenced by the viscosity and under-oil contact angle than the bulk fluid density. For water droplets coalescing on hydrophobic fibers in oils, the expansion of the liquid bridge can be affected by the bulk fluid, but the expansion dynamics exhibited similar behavior. The drops begin their coalescence in an inertially limited viscous regime and transition to an inertia regime. Larger droplets did accelerate the expansion of the liquid bridge but had no obvious influence on the number of coalescence stages and coalescence time. This study can provide a more profound understanding of the mechanisms underlying the behavior of water droplet coalescence on hydrophobic surfaces in oil.

Spreading, pinching, and coalescence: the Ohnesorge units

Understanding the kinematics and dynamics of spreading, pinching, and coalescence of drops is critically important for a diverse range of applications involving spraying, printing, coating, dispensing, emulsification, and atomization. Hence experimental studies visualize and characterize the increase in size over time for drops spreading over substrates, or liquid bridges between coalescing drops, or the decrease in the radius of pinching necks during drop formation. Even for Newtonian fluids, the interplay of inertial, viscous, and capillary stresses can lead to a number of scaling laws, with three limiting self-similar cases: visco-inertial (VI), visco-capillary (VC) and inertio-capillary (IC). Though experiments are presented as examples of the methods of dimensional analysis, the lack of precise values or estimates for pre-factors, transitions, and scaling exponents presents difficulties for quantitative analysis and material characterization. In this tutorial review, we reanalyze and summarize an elaborate set of landmark published experimental studies on a wide range of Newtonian fluids. We show that moving beyond VI, VC, and IC units in favor of intrinsic timescale and lengthscale determined by all three material properties (viscosity, surface tension and density), creates a complementary system that we call the Ohnesorge units. We find that in spite of large differences in topological features, timescales, and material properties, the analysis of spreading, pinching and coalescing drops in the Ohnesorge units results in a remarkable collapse of the experimental datasets, highlighting the shared and universal features displayed in such flows.

Viscoelastic necking dynamics between attractive microgels

HYPOTHESIS

Microgels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer-solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. We hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales.

EXPERIMENTS

We simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics.

FINDINGS

We evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.

When Elasticity Affects Drop Coalescence

The breakup and coalescence of drops are elementary topological transitions in interfacial flows. The breakup of a drop changes dramatically when polymers are added to the fluid. With the strong elongation of the polymers during the process, long threads connecting the two droplets appear prior to their eventual pinch-off. Here, we demonstrate how elasticity affects drop coalescence, the complement of the much studied drop pinch-off. We reveal the emergence of an elastic singularity, characterized by a diverging interface curvature at the point of coalescence. Intriguingly, while the polymers dictate the spatial features of coalescence, they hardly affect the temporal evolution of the bridge. These results are explained using a novel viscoelastic similarity analysis and are relevant for drops created in biofluids, coating sprays, and inkjet printing.

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.

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.

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.

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.

Wetting dynamics in two-liquid systems: Effect of the surrounding phase viscosity

This paper reports the experimental results of a water droplet spreading on a glass substrate submerged in an oil phase. The radius of the wetted area grows exponentially over time forming two distinct regimes. The early time dynamics of wetting is characterized with the time exponent of 1, referred to as the viscous regime, which is ultimately transitioned to the Tanner's regime with the time exponent of 0.1. It is revealed that an increase in the ambient phase viscosity over three decades considerably slows down the rate of three-phase contact line movement. A scaling law is developed where the three-phase contact line velocity is a function of both spreading radius and mean viscosity, close to the geometric mean of the droplet and ambient fluids' viscosities. Using the proposed scaling and mean viscosity, all plots of spreading radius for different viscosity ratios collapse to a master curve. Furthermore, several cases with multiple rupture and spreading points, i.e., wetting in a nonideal system, are considered. The growth of an equivalent wetting radius in a multiple point spreading system is predicted by the developed scaling law.

Coalescence-Induced Jumping of Nanodroplets on Textured Surfaces

Conducting experimental studies on nanoscale droplet coalescence using traditional microscopes is a challenging research topic, and views differ as to whether the spontaneous removal can occur in the coalescing nanodroplets. Here, a molecular dynamics simulation is carried out to investigate the coalescence process of two equally sized nanodroplets. On the basis of atomic coordinates, we compute the liquid bridge radii for various cases, which is described by a power law of spreading time, and these nanodroplets undergo coalescence in the inertially limited-viscous regime. Moreover, coalescence-induced jumping is also possible for the nanodroplets, and the attraction force between surface and water molecules plays a crucial role in this process, where the merged nanodroplets prefer to jump away from those surfaces with lower attraction force. When the solid-liquid interaction intensity and surface structure parameters are varied, the attraction force is shown to decrease with decreasing surface wettability intensity and solid fraction.

Coalescence Processes of Droplets and Liquid Marbles

The coalescence process of droplets and, more recently, of liquid marbles, has become one of the most essential manipulation schemes in digital microfluidics. This process is indispensable for realising microfluidic functions such as mixing and reactions at microscale. This paper reviews previous studies on droplet coalescence, paying particular attention to the coalescence of liquid marbles. Four coalescence systems have been reviewed, namely, the coalescence of two droplets freely suspended in a fluid; the coalescence of two sessile droplets on a solid substrate; the coalescence of a falling droplet and a sessile droplet on a solid substrate; and liquid marble coalescence. The review is presented according to the dynamic behaviors, physical mechanisms and experimental parameters of the coalescence process. It also provides a systematic overview of how the coalescence process of droplets and liquid marbles could be induced and manipulated using external energy. In addition, the practical applications of liquid marble coalescence as a novel microreactor are highlighted. Finally, future perspectives on the investigation of the coalescence process of liquid marbles are proposed. This review aims to facilitate better understanding of the coalescence of droplets and of liquid marbles as well as to shed new insight on future studies.

Sintering of polydisperse viscous droplets

Sintering-or coalescence-of compacts of viscous droplets is driven by the interfacial tension between the droplets and the interstitial gas phase. The process, which occurs in a range of industrial and natural settings, such as the manufacture of ceramics and the welding of volcanic ash, causes the compact to densify, to become stronger, and to become less permeable. We investigate the role of droplet polydispersivity in sintering dynamics by conducting experiments in which populations of glass spheres with different size distributions are heated to temperatures above the glass transition interval. We quantify the progress of sintering by tracking changes in porosity with time. The sintering dynamics is modeled by treating the system as a random distribution of interstitial gas bubbles shrinking under the action of interfacial tension only. We identify the scaling between the polydispersivity of the initial droplets and the dynamics of bulk densification. The framework that we develop allows the sintering dynamics of arbitrary polydisperse populations of droplets to be predicted if the initial droplet (or particle) size distribution is known.

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.

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.

Probing the micro-rheological properties of aerosol particles using optical tweezers

The use of optical trapping techniques to manipulate probe particles for performing micro-rheological measurements on a surrounding fluid is well-established. Here, we review recent advances made in the use of optical trapping to probe the rheological properties of trapped particles themselves. In particular, we review observations of the continuous transition from liquid to solid-like viscosity of sub-picolitre supersaturated solution aerosol droplets using optical trapping techniques. Direct measurements of the viscosity of the particle bulk are derived from the damped oscillations in shape following coalescence of two particles, a consequence of the interplay between viscous and surface forces and the capillary driven relaxation of the approximately spheroidal composite particle. Holographic optical tweezers provide a facile method for the manipulation of arrays of particles allowing coalescence to be controllably induced between two micron-sized aerosol particles. The optical forces, while sufficiently strong to confine the composite particle, are several orders of magnitude weaker than the capillary forces driving relaxation. Light, elastically back-scattered by the particle, is recorded with sub-100 ns resolution allowing measurements of fast relaxation (low viscosity) dynamics, while the brightfield image can be used to monitor the shape relaxation extending to times in excess of 1000 s. For the slowest relaxation dynamics studied (particles with the highest viscosity) the presence and line shape of whispering gallery modes in the cavity enhanced Raman spectrum can be used to infer the relaxation time while serving the dual purpose of allowing the droplet size and refractive index to be measured with accuracies of ±0.025% and ±0.1%, respectively. The time constant for the damped relaxation can be used to infer the bulk viscosity, spanning from the dilute solution limit to a value approaching that of a glass, typically considered to be >10(12) Pa s, whilst the frequencies of the normal modes of the oscillations of the particle can be used to infer surface properties. We will review the use of optical tweezers for studying the viscosity of aerosol particles and discuss the potential use of this micro-rheological tool for probing the fundamental concepts of phase, thermodynamic equilibrium and metastability.

Approach and coalescence of liquid drops in air

The coalescence of liquid drops has conventionally been thought to have just two regimes when the drops are brought together slowly in vacuum or air: a viscous regime corresponding to the Stokes-flow limit and a later inertially dominated regime. Recent work [Proc. Natl. Acad. Sci. 109, 6857 (2012)] found that the Stokes-flow limit cannot be reached in the early moments of coalescence, because the inertia of the drops cannot be neglected then. Instead, the drops are described by an "inertially limited viscous" regime, where surface tension, inertia, and viscous forces all balance. The dynamics continue in this regime until either viscosity or inertia dominate on their own. I use an ultrafast electrical method and high-speed imaging to provide a detailed description of coalescence near the moment of contact for drops that approach at low speed and coalesce as undeformed spheres. These measurements support a description of coalescence having three regimes. Signatures both before and after contact identify a threshold approach speed for deformation of the drops by the ambient gas.

Simulations of droplet coalescence in simple shear flow

Simulating droplet coalescence is challenging because small-scale (tens of nanometers) phenomena determine the behavior of much larger (micrometer- to millimeter-scale) droplets. In general, liquid droplets colliding in a liquid medium coalesce when the capillary number is less than a critical value. We present simulations of droplet collisions and coalescence in simple shear flow using the free-energy binary-liquid lattice Boltzmann method. In previous simulations of low-speed collisions, droplets coalesced at unrealistically high capillary numbers. Simulations of noncoalescing droplets have not been reported, and therefore, the critical capillary number for simulated collisions was unknown. By simulating droplets with radii up to 100 lattice nodes, we determine the critical capillary number for coalescence and quantify the effects of several numerical and geometric parameters. The simulations were performed with a well-resolved interface, a Reynolds number of one, and capillary numbers from 0.01 to 0.2. The ratio of the droplet radius and interface thickness has the greatest effect on the critical capillary number. As in experiments, the critical capillary number decreases with increasing droplet size. A second numerical parameter, the interface diffusivity (Péclet number) also influences the conditions for coalescence: coalescence occurs at higher capillary numbers with lower Péclet numbers (higher diffusivity). The effects of the vertical offset between the droplets and the confinement of the droplets were also studied. Physically reasonable results were obtained and provide insight into the conditions for coalescence. Simulations that match the conditions of experiments reported in the literature remain computationally impractical. However, the scale of the simulations is now sufficiently large that a comparison with experiments involving smaller droplets (≈10 μm) and lower viscosities (≈10(-6) m(2)/s, the viscosity of water) may be possible. Experiments at these conditions are therefore needed to determine the interface thickness and Péclet number that should be used for predictive simulations of coalescence phenomena.

The inexorable resistance of inertia determines the initial regime of drop coalescence

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering, and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a cross-over region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram.

Viscous to inertial crossover in liquid drop coalescence

Using an electrical method and high-speed imaging, we probe drop coalescence down to 10 ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that, at a sufficiently low approach velocity where deformation is not present, the drops coalesce with an unexpectedly late crossover time between a regime dominated by viscous and one dominated by inertial effects. We argue that the late crossover, not accounted for in the theory, can be explained by an appropriate choice of length scales present in the flow geometry.

Coalescence driven by line tension in thin nematic films

Thin nematic films deposited on liquid substrates provide a unique situation to investigate coalescence: the whole process can be followed under microscope over a wide range of times, and temperature allows us to monitor the surface viscosity of the surrounding fluid. For the first time, the complete scenario of 2D coalescence has been recorded for a given system in both inviscid limit and viscous environment, enabling us to identify the successive routes of dissipation. In particular, 2D "viscous bubbles" of the surrounding viscous fluid with a bulbous shape formed in the gap between coalescing films are observed. Available models are adapted to our specific case and account satisfactorily for the whole process.

Some specificities of wetting by cyanobiphenyl liquid crystals

The present paper provides an up to date restatement of the wetting behaviour of the series of cyanobiphenyl liquid crystals (LCs) on usual substrates, i.e. oxidized silicon wafers, water and glycerol, at both the macroscopic and microscopic scale, in the nematic range of temperature. We show that on water the systems are close to a wetting transition, especially 5CB and 7CB. In that case, the wetting behaviour is controlled by the presence of impurities. On a mesoscopic scale, we observe for all our (thin LC film-substrate) systems an identical, complex, but well defined general scenario, not accounted for by the available models. In the last part, we present a study on line tension which results from the specific organization of LCs at the edge of the nematic film. We report preliminary results on two-dimensional film coalescence where this line tension plays a major role.

Coalescence of low-viscosity fluids in air

An electrical method is used to study the early stages of coalescence of two low-viscosity drops. A drop of aqueous NaCl solution is suspended in air above a second drop of the same solution, which is grown until the drops touch. At that point a rapidly widening bridge forms between them. By measuring the resistance and capacitance of the system during this coalescence event, one can obtain information about the time dependence of the characteristic bridge radius and its characteristic height. At early times, a new asymptotic regime is observed that is inconsistent with previous theoretical predictions. The measurements at several drop radii and approach velocities are consistent with a model in which the two liquids coalesce with a slightly deformed interface.

Hydrodynamic instabilities of viscous coalescing droplets

Droplets coalescing at a planar fluid-fluid interface are studied in detail in the Stokes regime with high speed photography. Attention is paid to the expansion of the interfacial bridge, formed between the droplet and interface, as it expands during the process. We report a hydrodynamic instability at the rim of the interfacial bridge. As the rim becomes unstable, it forms a series of tendrils which themselves become unstable and produce micron sized droplets. We show that rim stability depends on drop and medium viscosities as well as the rim geometry.

Tissue engineering by self-assembly of cells printed into topologically defined structures

Understanding the principles of biological self-assembly is indispensable for developing efficient strategies to build living tissues and organs. We exploit the self-organizing capacity of cells and tissues to construct functional living structures of prescribed shape. In our technology, multicellular spheroids (bio-ink particles) are placed into biocompatible environment (bio-paper) by the use of a three-dimensional delivery device (bio-printer). Our approach mimics early morphogenesis and is based on the realization that the genetic control of developmental patterning through self-assembly involves physical mechanisms. Three-dimensional tissue structures are formed through the postprinting fusion of the bio-ink particles, in analogy with early structure-forming processes in the embryo that utilize the apparent liquid-like behavior of tissues composed of motile and adhesive cells. We modeled the process of self-assembly by fusion of bio-ink particles, and employed this novel technology to print extended cellular structures of various shapes. Functionality was tested on cardiac constructs built from embryonic cardiac and endothelial cells. The postprinting self-assembly of bio-ink particles resulted in synchronously beating solid tissue blocks, showing signs of early vascularization, with the endothelial cells organized into vessel-like conduits.

Hydrodynamics of droplet coalescence

We study droplet coalescence in a molecular system with a variable viscosity and a colloid-polymer mixture with an ultralow surface tension. When either the viscosity is large or the surface tension is small enough, we observe that the opening of the liquid bridge initially proceeds at a constant speed set by the capillary velocity. In the first system we show that inertial effects become dominant at a Reynolds number of about 1.5+/- 0.5 and the neck then grows as the square root of time. In the second system we show that decreasing the surface tension by a factor of 10(5) opens the way to a more complete understanding of the hydrodynamics involved.