Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session L13: Drops: Pinch-Off and Coalescence |
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Chair: Osman A. Basaran, Purdue University Room: 3020 |
Monday, November 24, 2014 3:35PM - 3:48PM |
L13.00001: Coalescence of surfactant covered drops Sumeet Thete, Krishnaraj Sambath, Osman Basaran Drop coalescence plays a central role in industry, e.g. emulsions, sintering, and inkjets, and in nature, e.g. raindrop growth. During coalescence, two drops touch and merge as a liquid neck connecting them grows from microscopic to macroscopic scales. In applications, the drops, while still Newtonian, may be covered with surfactant. Here, we use simulation to analyze the simplest of such problems: two identical drops covered with a monolayer of insoluble surfactant merging in air. The dynamics is analyzed by using as guide the recent work of Paulsen et. al. (2012) who revolutionized the understanding of the coalescence singularity for drops with clean interfaces by demonstrating that the asymptotic regime of coalescence must always involve a balance between inertial, viscous, and capillary forces. These authors summarized their findings by a phase diagram which showed that as coalescence proceeds, the dynamics transitions from this early inertially limited viscous regime to a late time inertial (Stokes) regime when drop viscosity is low (high). Among other things, the talk will highlight how the presence of surfactant modifies the phase diagram obtained by Paulsen et al. [Preview Abstract] |
Monday, November 24, 2014 3:48PM - 4:01PM |
L13.00002: Coalescence of Drops of a Power-law Fluid Pritish Kamat, Sumeet THete, Osman Basaran Drop coalescence is crucial in a host of industrial, household, and natural processes that involve dispersions. Coalescence is a rate-controlling process in breaking emulsions and strongly influences drop-size-distributions in sprays. In a continuum approach, coalescence begins by the formation of a microscopic, non-slender bridge connecting the two drops. Indefinitely large axial curvature at the neck results in local lowering of pressure that drives fluid from the bulk of the drops toward the neck, thereby causing the bridge radius $r(t)$ and height $z(t)$ to increase in time $t$. The coalescence of Newtonian drops in air has heretofore been thoroughly studied. Here, we extend these earlier studies by analyzing the coalescence of drops of power-law fluids because many fluids encountered in real applications, including cosmetic creams, shampoos, grease, and paint, exhibit power-law (deformation-rate thinning) rheology. On account of the non-slender geometry of the liquid bridge connecting the two drops $(z \ll r)$, we analyze the resulting free surface flow problem by numerical simulation. Among other results, we present and discuss the nature of flows and scaling behaviors for r and z as functions of the initial viscosity and power-law index $(0 < n\leq 1)$. [Preview Abstract] |
Monday, November 24, 2014 4:01PM - 4:14PM |
L13.00003: Damped coalescence cascade of a liquid drop Suin Shim, Heejae Jang, Howard Stone A drop of surfactant (sodium dodecyl sulfate) solution, falling on a bath of the same liquid, shows both normal and damped coalescence cascades while the effects of interfacial tension, viscosity, and gravity are strictly controlled. Unlike the normal coalescence cascade where stages of non-coalescence and partial coalescence alternate until the smallest drop totally coalesces, in the damped coalescence cascade regime, there is no apparent residence time between two successive partial coalescence events. We interpret the results by considering the natural vibration of the drop and the bath surface, and its effects on the drainage of the air film between the drop and the bath. [Preview Abstract] |
Monday, November 24, 2014 4:14PM - 4:27PM |
L13.00004: An experimental study of liquid drop - interface coalescence in the presence of surfactants Panagiota Angeli, Maxime Chinaud, Kai Li, Wei Wang Drop-interface coalescence has been the subject of many studies both theoretical and experimental. It is of particular interest for the oil industries particularly during the transportation of multiphase mixtures where coalescence rates can affect the stability and separation of dispersions. It is well-known that the presence of surfactants can significantly affect the coalescence rates. In this work a silicon oil -water system has been studied in a rectangular coalescence cell. Both rising oil drops and falling water drops coalescing with the water-oil interface have been investigated. A water soluble surfactant, SPAN 80, was used. High speed imaging has been performed to study the coalescence phenomenon and obtain the coalescence time of the drops with the interface with and without the presence of the surfactant. The velocity fields in the bulk fluid and in the liquid film forming between the drop and the interface were studied with shadowgraphy (bright field Particle Image Velocimetry). To increase the spatial resolution particularly in the liquid film microscope lenses were implemented. Results have been compared against existing literature. [Preview Abstract] |
Monday, November 24, 2014 4:27PM - 4:40PM |
L13.00005: Simulations of the pinch-off and coalescence of conical droplets Casey Bartlett, Guillaume Genero, James Bird In the presence of electric fields, pairs of liquid drops can be rapidly drawn together such that, at contact, the deformed interface resembles a double-cone. Following contact, these drop pairs are observed to either coalesce or recoil. Here we use high-resolution numerical simulations to highlight the impact of the initial double-cone angle on drop coalescence. The results demonstrate a self-similar behavior at intermediate scales for both coalescence and recoil that is independent of the other length-scales in the problem and is consistent with previous experiments. [Preview Abstract] |
Monday, November 24, 2014 4:40PM - 4:53PM |
L13.00006: Coalescence of liquid drops is governed by surface tension driven capillary pressure in the inertial regime Md Mahmudur Rahman Droplet coalescence is a complex hydrodynamic phenomenon where it has been thought that, at the moment of contact, a singularity occurs due to the inversion of one of its two radii of curvature. However, the effect of this singularity cannot be observed experimentally through coalescence of liquid drops in three dimensions. A recent study examined coalescence mathematically in the inertial regime where no such singularity is assumed. After coalescence happens in the ``viscous'' regime, hydrodynamic scaling starts working with a certain bridge radius other than a singular point. In our experimental analysis, we studied coalescence in a confined geometry where drops were sandwiched in the Hele-Shaw cell. We observed very well defined mixing interface which signifies that early coalescence (`viscous' regime) is not a hydrodynamic phenomenon, rather its characteristics may be evaluated from molecular dynamics analysis. Our experiment will be helpful in studying coalescence of liquid drops in any given shape through mathematical modeling where initial bridge radius can be assumed or determined through other means. [Preview Abstract] |
Monday, November 24, 2014 4:53PM - 5:06PM |
L13.00007: Coalescence of drops in the Hele-Shaw geometry John Davidson, Donghee Lee, Md. Mahmudur Rahman, Sangjin Ryu Coalescence of drops is an interfacial fluid dynamics phenomenon commonly occurring in engineering devices as well as in nature. The physics of such coalescence has been studied mainly for three-dimensional (spherical drops) and semi-infinite two-dimensional (hemispherical drops) geometries. In contrast, the coalescence of drops in the pseudo two-dimensional geometries has been less documented. To investigate the coalescence of two drops of the same liquid in the Hele-Shaw geometry, we observed with the high-speed videography the neck growth of the two coalescing drops squeezed between two parallel hydrophobic surfaces. We also studied the effects of differences in liquid properties on the scaling behavior of coalescence. [Preview Abstract] |
Monday, November 24, 2014 5:06PM - 5:19PM |
L13.00008: Coalescence of Drops Due to a Constant Force Interaction in a Viscous Quiescent Fluid John Frostad, Alexandra Paul, Gary Leal A Cantilevered-Capillary Force Apparatus is used to study the time scale for the coalescence of two droplets compressed together with a constant force. Power-law trends for the coalescence time as a function of droplet radius and compression force are measured. The measurements are compared against several different scaling theories from the literature. One of the existing theories is found to correctly predict the dependence on the droplet radius, but all of the theories over-predict the dependence on the force. A transition is also measured in the coalescence process from a predominately deterministic to a predominately stochastic process. A qualitative explanation for this transition is provided via scaling arguments. [Preview Abstract] |
Monday, November 24, 2014 5:19PM - 5:32PM |
L13.00009: Coalescence of Liquid Drops: Modelling, Computation and Scaling James Sprittles, Yulii Shikhmurzaev The coalescence of two liquid drops surrounded by a viscous gas is simulated by a computational approach which resolves the unprecedentedly small spatio-temporal scales which have recently been accessed experimentally. A systematic study of the parameter space of practical interest allows the influence of the governing parameters in the system to be identified and the role of viscous gas to be determined. In particular, it is shown that the viscosity of the gas suppresses the formation of toroidal bubble predicted in some cases when the gas' dynamics are neglected. Considering the entire parameter space allows us to examine the accuracy of various ``scaling laws'' proposed for different ``regimes'' and, in doing so, to (a) reveal certain inconsistencies in recent works and (b) develop a new scaling law for the inertial regime which captures experimental data from the literature remarkably well. Notably, the conventional model is shown to reproduce many qualitative features of the initial stages of coalescence observed experimentally, such as a collapse of calculations onto a ``master curve'' but, quantitatively, overpredicts the speed of coalescence. Finally, a phase diagram of parameter space, differing from previously published ones, is used to illustrate the key findings. [Preview Abstract] |
Monday, November 24, 2014 5:32PM - 5:45PM |
L13.00010: Inverted Break-up Behaviour in Continuous Inkjet (CIJ) Printing Claire McIlroy, Oliver Harlen, Neil Morrison Although droplet creation during continuous jetting of Newtonian fluids has been widely studied, unsolved problems surrounding the break-up dynamics remain. Jetting through a nozzle creates a stream of liquid that is rendered unstable by surface tension. This instability creates a succession of main drops connected by thin filaments, with drop separation determined by the fastest growing wavelength. In order to control break-up and increase printing speeds, continuous inkjet (CIJ) printing exploits the effects of finite amplitude modulations in the jet velocity profile giving conditions where jet stability deviates from the usual Rayleigh behaviour. To explore these non-linear effects, we have developed a one-dimensional jetting model. In particular, we identify a modulation range for which pinching occurs upstream of the connecting filament, rather than downstream -- a phenomenon we call ``inverted'' break-up. Furthermore, this behaviour can be controlled by the addition of harmonics to the initial driving signal. Our results are compared to full axisymmetric simulations in order to incorporate the effects of nozzle geometry. [Preview Abstract] |
Monday, November 24, 2014 5:45PM - 5:58PM |
L13.00011: Dynamic behaviors of oppositely charged emulsion droplets Zhou Liu, Hans M. Wyss, Alberto Fernandez-Nieves, Ho Cheung Shum In this work, we investigate the dynamic behaviors of two oppositely charged emulsion droplets. Using an electrocapillary number and separation distance between droplets, we have characterized three types of droplet behaviors in electric field. Besides the common seen coalescence, two qualitatively different dynamic behaviors are identified: fuse-and-split and periodic non-coalescence. In fuse-and-split regime, the droplets fuse into a jet, which subsequently breaks up into two droplets. In periodic non-coalescence regime, the droplets contact and bounce away periodically without coalescence. Further analysis indicates that the applied voltage always decreases dramatically upon droplets' contact due to spikes of discharging current. Thus, the electric field strength drops and surface tension quickly dominates over electric stress upon droplet's contact. By analyzing capillary instability, all the observed dynamic states can be attributed to the different initial shapes of dumbbell-like jet formed upon droplets' contact. By controlling the initial separation distance between droplets, the shapes of the jet and thus the resultant dynamics can be precisely manipulated. [Preview Abstract] |
Monday, November 24, 2014 5:58PM - 6:11PM |
L13.00012: Multiscale computations of thin films between colliding drops Bahman Aboulhasanzadeh, Sadegh Dabiri, Gretar Tryggvason In multiphase flows thin films frequently appear between fluid blobs colliding with each other. These films can become very thin and be difficult to resolve accurately in numerical simulations, particularly in DNS of many co-flowing drops, requiring very fine resolution and resulting in excessive computational cost due to very fine uniform grids or time consuming adaptive mesh refinement. Here, we describe an algorithm for detecting thin films using a front tracking method. We propose a subscale model to describe the physics and the evolution of a thin film between two drops. We also demonstrate the importance of correctly reconstructing the viscosity field on getting a grid independent solution. Comparison between results for a fully resolved film on a fine grid and simulations using a much coarser grid plus the model for the description of the film, show good agreement. This study was funded by NSF Grant CBET-1132410. [Preview Abstract] |
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