Session G16: Drops: Coalescence

Drop coalescence at any Reynolds number

When two drops touch, a fluid bridge forms between them and surface tension pulls this bridge wider, fighting against the viscosity of the fluid and the inertia of the drops. We present a new theoretical solution for the early-time behaviour of coalescence which includes both inertia and viscosity; earlier models neglect one or the other and so their predictions do not agree with experimental observations over the full range of fluid parameters. Our new solution is valid at early times for any Reynolds number and offers fresh insight into the physical processes governing this initial stage. Inertia plays a role on a scale proportional to $t^{1/2}$, but viscosity dominates on the smaller scales of the fluid bridge. The $t^{1/2}$ scale sets a boundary condition for the smaller scales, affecting the geometry of the curved surface and changing the prefactor in the rate of coalescence.   

Mist collection on parallel fiber arrays

Fog is an important source of fresh water in specific arid regions such as the Atacama Desert in Chile. The method used to collect water passively from fog, either for domestic consumption or research purposes, consists in erecting large porous fiber nets on which the mist droplets impact. The two main mechanisms involved with this process are the impact of the drops on the fibers and the drainage of the fluid from the net, while the main limiting factor is the clogging of the mesh by accumulated water. We consider a novel collection system, made of an array of parallel fibers, that we study experimentally with a wind mist tunnel. In addition, we develop theoretical models considering the coupling of wind flow, droplet trajectories and wetting of the fibers. We find that the collection efficiency strongly depends on the size and distribution of the drops formed on the fibers, and thus on the fibers diameter, inclination angle and wetting properties. In particular, we show that the collection efficiency is greater when large drops are formed on the fibers. By adjusting the fibers diameter and the inter-fiber spacing, we look for an optimal structure that maximizes the collection surface and the drainage, while avoiding flow deviations.   

Surface flows and bulk mixing by coalescence of dissimilar drops: experiments and numerical simulations

Merging of dissimilar drops, being of different size and/or composition is an essential part of multiple promising applications enabling release and mixing of various species in bespoken way. However, till now there is still a lack of understanding of the effect of the various factor involved on the kinetics of coalescence and the rate of mixing of the contents of the drops. This study is aimed at providing a thorough understanding of the merging process immediately after the rupture of the thin liquid film separating the drops initially. The effect of such parameters as the difference in size and surface tension of the merging drops, as well as the viscosity of the surrounding liquid phase, is investigated. Numerical simulations provide a deeper insight into the liquid redistribution during the merging. Their results are in good agreement with the experimental data and will be discussed during the talk.   

A multiphase ion-transport analysis of the electrostatic disjoining pressure: implications for binary droplet coalescence

Understanding the physics of emulsion coalescence is critical for the robust simulation of industrial solvent extraction processes, in which loaded organic and raffinate phases are separated via the coalescence of dispersed droplets. At the droplet scale, predictive collision-outcome models require an accurate description of the repulsive surface forces arising from electrical-double-layer interactions. The conventional disjoining-pressure treatment of double-layer forces, however, relies on assumptions which do not hold generally for deformable droplet collisions: namely, low interfacial curvature and negligible advection of ion species. This study investigates the validity bounds of the disjoining pressure approximation for low-inertia droplet interactions. A multiphase ion-transport model, based on a coupling of droplet-scale Nernst–-Planck and Navier–-Stokes equations, predicts ion-concentration fields that are consistent with the equilibrium Boltzmann distribution; indicating that the disjoining-pressure approach is valid for both static and dynamic interactions in low-Reynolds-number settings. The present findings support the development of coalescence kernels for application in macro-scale population balance modelling.   

Viscous Coalescence of Two Drops in a Saturated Vapor Phase

When two liquid drops come into contact, a microscopic liquid bridge forms between them and rapidly expands until the two drops merge into a single bigger drop. Numerous studies have been devoted to the investigation of the coalescence singularity in the case where the drops coalesce in a medium of negligible vapor pressure such as vacuum or air. However, coalescence of liquid drops may also take place in a medium of relatively high vapor pressure (condensable vapor phase), where the effect of the surrounding vapor phase should not be neglected, such as the merging of drops in clouds. In this study, we carry out Lattice Boltzmann numerical simulations to investigate the dynamics of viscous coalescence in a saturated vapor phase. Attention is paid to the effect of the vapor phase on the formation and growth dynamics of the liquid bridge in the viscous regime. We observe that the onset of the coalescence occurs earlier and the expansion of the bridge initially proceeds faster when the coalescence takes place in a saturated vapor compared to the coalescence in a non-condensable gas. The initially faster evolution of the coalescence process in the saturated vapor is caused by the vapor transport through condensation during the early stages of the coalescence.   

Thermocapillary delay of drop coalescence

We present the results of a combined experimental and theoretical investigation of drop coalescence. Particular attention is given to elucidating how the time to coalescence, or residence time, is affected by a temperature difference between drop and bath. Experiments show that the residence time increases as the temperature difference to the 2/3 power. This simple scaling is rationalized through consideration of the thermal Marangoni flows induced.   

Coalescence of a Drop inside another Drop

Coalescence dynamics of a pendent drop sitting inside another drop, has been studied experimentally and in numerical simulations. Using an in-house fabricated composite micro-nozzle, a smaller salt-water drop is introduced inside a larger oil drop which is pendent in a tank containing the same liquid as the inner drop. On touching the surface of outer drop, the inner drop coalesces with the surrounding liquid forming a vortex ring, which grows in time to form a mushroom-like structure. The initial dynamics at the first bridge opening up is quantified using Particle Image Velocimetry (PIV), while matching the refractive index of the two liquids. The phenomenon is also numerically simulated using the open-source code Gerris. The problem is fully governed by two non-dimensional parameters: the Ohnesorge number and the diameter ratios of the two drops. The validated numerical model is used to better understand the dynamics of the phenomenon. In some cases a coalescence cascade is observed with liquid draining intermittently and the inner drop reducing in size.   

Adaptive-mesh-refinement simulation of partial coalescence cascade of a droplet at a liquid-liquid interface

A three-dimensional (3D) adaptive mesh refinement (AMR) algorithm on structured Cartesian grids is developed, and supplemented by a mesoscopic multiphase-flow solver based on state-of-the-art lattice Boltzmann methods (LBM). Using this in-house AMR-LBM routine, we present fully 3D simulations of partial coalescence of a liquid drop with an initially flat interface at small Ohnesorge and Bond numbers. Qualitatively, our numerical simulations are in excellent agreement with experimental observations. Partial coalescence cascades are successfully observed at very small Ohnesorge numbers (Oh ≈ 10-4). The fact that the partial coalescence is absent in similar 2D simulations suggests that the Rayleigh-Plateau instability may be the principle driving mechanism responsible for this phenomenon.   

Effect of Surfactants on Drop Coalescence at Liquid/liquid Interfaces

In this paper the coalescence of a drop with a liquid-liquid interface was investigated experimentally using Particle Image Velocimetry (PIV). Initially the drop rest on the interface was studied. It was found that during drop rest the interface deformed before rupture, and the deformation increased with increasing surfactant concentration. The results from PIV showed that two counter-rotating vortices formed inside the droplet during the rupture process which moved from the bottom to the top of the drop. The evolutions of vortices for three surfactant concentrations will be presented. The vortices moved faster in lower surfactant concentrations compared to the higher ones. The intensities of the vortices in different concentrations were also calculated. After the rupture, for low surfactant concentrations, the intensities increased with time and reached a maximum while at later times they decreased. At high surfactant concentrations, the increase and subsequent decrease in intensity was not as pronounced.   

The Effect of a Yield Stress on the Drainage of the Thin Film Between Two Colliding Newtonian Drops

Coalescence of drops immersed in fluids possessing a yield stress has been of interest to many industries such as the oil extraction, cosmetics and food industries. Unfortunately, a theoretical understanding of the drainage of the thin film of Bingham fluid (a model yield stress fluid) that develops between two drops undergoing a collision is still lacking, with the exception of two prior studies (Can. J. Chem. Eng., vol. 65, pp. 384-390, 1987, and J. Phys. Chem., vol. 90, pp. 6054-6059, 1986.) that make ad-hoc assumptions about the film shape. In this work, we examine this problem via a combination of scaling analysis and numerical simulations based on the lubrication analysis. There are four key features of the film drainage process of Bingham fluids. First, the introduction of a yield stress in the suspending fluid retards the drainage process relative to Newtonian fluid of the same viscosity. Second, the drainage time shows a minimum with respect to the capillary number. Third, the effect of yield stress on the drainage process becomes more pronounced at higher capillary numbers and lower Hamaker constant. Lastly, below a critical height, drainage can be arrested completely due to the yield stress. This critical height scales as ${\tau _{0}^{2} R^{3}} \mathord{\left/ {\vphantom {{\tau_{0}^{2} R^{3}} {\gamma ^{2}}}} \right. \kern-\nulldelimiterspace} {\gamma^{2}}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.51in,height=0.17in]{310720161.eps}} \label{fig1} \end{figure} , where $\tau_{0} $ is the yield stress, $R$ is the drop radius and $\gamma $ is the interfacial tension, and is, surprisingly, independent of the force colliding the drops. This and other distinguishing characteristics of the drainage process will be elucidated in the presentation.