Coalescence of low-viscosity fluids in air

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.

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.

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.

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.

Initial coalescence of a drop at a planar liquid surface

The initial coalescence of a pendant drop at bulk liquid was jointly investigated by an ultrahigh-speed DC electrical device, a high-speed camera, and a fast micro-Particle Image Velocimetry (micro-PIV). Extended to highly viscous non-Newtonian liquids, the variation of the coalescing width vs time confirms the distinct regimes reported for drop-drop configuration: linear in the inertially limited viscous regime; square root in the inertial regime; possibly a transient viscous regime in between with a logarithmic correction. The measured flow fields during coalescence reveal the transformation of surface energy to kinetic energy, so that the highly located inertia could play a dominant role in relation to the viscous force.

Droplet Coalescence is Initiated by Thermal Motion

The classical notion of the coalescence of two droplets of the same radius R is that surface tension drives an initially singular flow. In this Letter we show, using molecular dynamics simulations of coalescing water nanodroplets, that after single or multiple bridges form due to the presence of thermal capillary waves, the bridge growth commences in a thermal regime. Here, the bridges expand linearly in time much faster than the viscous-capillary speed due to collective molecular jumps near the bridge fronts. Transition to the classical hydrodynamic regime only occurs once the bridge radius exceeds a thermal length scale l_{T}∼sqrt[R].

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.

Dynamic measurements and simulations of airborne picolitre-droplet coalescence in holographic optical tweezers

We report studies of the coalescence of pairs of picolitre aerosol droplets manipulated with holographic optical tweezers, probing the shape relaxation dynamics following coalescence by simultaneously monitoring the intensity of elastic backscattered light (EBL) from the trapping laser beam (time resolution on the order of 100 ns) while recording high frame rate camera images (time resolution <10 μs). The goals of this work are to: resolve the dynamics of droplet coalescence in holographic optical traps; assign the origin of key features in the time-dependent EBL intensity; and validate the use of the EBL alone to precisely determine droplet surface tension and viscosity. For low viscosity droplets, two sequential processes are evident: binary coalescence first results from the overlap of the optical traps on the time scale of microseconds followed by the recapture of the composite droplet in an optical trap on the time scale of milliseconds. As droplet viscosity increases, the relaxation in droplet shape eventually occurs on the same time scale as recapture, resulting in a convoluted evolution of the EBL intensity that inhibits quantitative determination of the relaxation time scale. Droplet coalescence was simulated using a computational framework to validate both experimental approaches. The results indicate that time-dependent monitoring of droplet shape from the EBL intensity allows for robust determination of properties such as surface tension and viscosity. Finally, the potential of high frame rate imaging to examine the coalescence of dissimilar viscosity droplets is discussed.

Drop coalescence in technical liquid/liquid applications: a review on experimental techniques and modeling approaches

The coalescence phenomenon of drops in liquid/liquid systems is reviewed with particular focus on its technical relevance and application. Due to the complexity of coalescence, a comprehensive survey of the coalescence process and the numerous influencing factors is given. Subsequently, available experimental techniques with different levels of detail are summarized and compared. These techniques can be divided in simple settling tests for qualitative coalescence behavior investigations and gravity settler design, single-drop coalescence studies at flat interfaces as well as between droplets, and detailed film drainage analysis. To model the coalescence rate in liquid/liquid systems on a technical scale, the generic population balance framework is introduced. Additionally, different coalescence modeling approaches are reviewed with ascending level of detail from empirical correlations to comprehensive film drainage models and detailed computational fluid and particle dynamics.

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.

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.

Coalescence of Pickering emulsion droplets induced by an electric field

Combining high-speed photography with electric current measurement, we investigate the electrocoalescence of Pickering emulsion droplets. Under a 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-then-breaking cycles repeat multiple times, until a stable connection is established. In depth analysis indicates that the defect size in particle shells determines the exact merging behaviors: when the defect size is larger than a critical size around the particle diameter, normal coalescence will show up, while abnormal coalescence will appear for coatings with smaller defects.

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.

Perturbed breakup of gas bubbles in water: memory, gas flow, and coalescence

The pinch-off of an air bubble from an underwater nozzle ends in a singularity with a remarkable sensitivity to a variety of perturbations. I report on experiments that break both the axial (i.e., vertical) and azimuthal symmetry of the singularity formation. The density of the inner gas influences the axial asymmetry of the neck near pinch-off. For denser gases, flow through the neck late in collapse changes the pinch-off dynamics. Gas density is also implicated in the formation of satellite bubbles. The azimuthal shape oscillations described by Schmidt et al. can be initiated by anisotropic boundary conditions in the liquid as well as with an asymmetric nozzle shape. I measure the n=3 oscillatory mode and observe the nonlinear, highly three-dimensional outcomes of pinch-off with large azimuthal perturbations. These are consistent with prior theory.

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.