Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session EH: Drops III: Collisions and Coalescence |
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Chair: Paul Steen, Cornell University Room: 101H |
Sunday, November 22, 2009 4:15PM - 4:28PM |
EH.00001: Coalescence of Low-Viscosity Liquids J.D. Paulsen, S.R. Nagel When two fluid drops come into contact, a dramatic topological transformation occurs as the drops coalesce. The speed and geometry of this finite-time singularity make it difficult to study optically, so we use an electrical method to probe coalescence at early times.\footnote{J. C. Burton, J. E. Rutledge, and P. Taborek, Phys. Rev. Lett. $\bf{92}$, 244505 (2004).}$^,$\footnote{S. C. Case and S. R. Nagel, Phys. Rev. Lett. $\bf{100}$, 084503 (2008).} For low-viscosity liquids, we measure a resistance that varies as $t^{-1}$ at early times and as $t^{-1/2}$ at late times. In the inviscid case, these power laws have been interpreted with a model in which the drops coalesce at a slightly deformed interface.$^2$ In order to test further predictions of this model, we study coalescence at faster rates than previously attainable. We have previously shown that the crossover time between these power laws increases with viscosity, depends weakly on the surrounding gas pressure, but does not depend on the weight of the gas.\footnote{J. D. Paulsen, J. C. Burton, and S. R. Nagel, DCMP 2009.} We further explore outer-fluid effects by replacing the ambient gas with a liquid, showing that the crossover time is delayed with increasing outer-fluid viscosity. [Preview Abstract] |
Sunday, November 22, 2009 4:28PM - 4:41PM |
EH.00002: The effect of interfacial slip on the drainage time to coalescence between two droplets L. Gary Leal, Kostas Tsiglifis, Arun Ramachandran, Anshuman Roy A fundamental question that arises in the coalescence of two drops in a flow is the dependence of the drainage time $t_{d}$ prior to film rupture on the capillary number \textit{Ca } and the dimensionless Hamaker constant, which is inversely proportional to the square of the drop radius, $R^{-2}$. Prior investigations from our group have shown that predictions of this relationship based on both scaling theory and numerical simulations deviate qualitatively from experimental data. We believe that a possible explanation for these discrepancies is a breakdown of the continuum flow model for the extremely thin films that are realized prior to film rupture. Such a breakdown would most likely first manifest itself as a violation of the no-slip condition at fluid interfaces. In this work, we examine the effect of interfacial slip on the dependence of the drainage time with capillary number for different \textit{$\lambda $} via boundary integral simulations. Interfacial slip is modeled via the Navier-slip condition, and the slip parameter employed in the simulations is predicted using the work of Goveas and Frederickson [\textit{Eur. Phys. J. B} \textbf{2}, 79--92 (1998) ]. The agreement with the scaling exponents of $t_{d}$ versus \textit{Ca }and$ R$ is improved, but the absolute values of the drainage times are lower than the experimental values. Possible reasons for these deviations are explored. [Preview Abstract] |
Sunday, November 22, 2009 4:41PM - 4:54PM |
EH.00003: A critical angle for electrocoalescence of conical droplets James Bird, William Ristenpart, Andrew Belmonte, Howard Stone Oppositely charged droplets suspended in air attract one another and, when the droplets are sufficiently close, electrical stresses deform the leading edges into cones. Here we investigate whether or not the liquid cones coalesce immediately following contact. Using high-speed imaging, we find that the coalescence behavior depends on the cone angle, which we control by varying the drop size and the applied voltage across the drops. The two drops coalesce when the slopes of the cones are small, but recoil when the slopes exceed a critical value. We propose a surface energy model (volume-constrained area minimization) to describe the transition between these two responses. The model predicts a critical cone intercept angle of $30.8^\circ$, which is in good agreement with our measurements. [Preview Abstract] |
Sunday, November 22, 2009 4:54PM - 5:07PM |
EH.00004: Deformation and merging of droplets at different electric potentials Dong Wook Lee, In Seok Kang In the present work, two droplets which are attached to different electrodes are faced each other and then, approaching each other very slowly, deformation and merging of the two droplet were closely watched using high-speed camera. It was found from the observation that this phenomenon can be separated into three phases; deformation, liquid bridge formation, merging. First, in the deformation phase surface tension and electric force achieve the equilibrium and the deformed shape is stable. Second, in the liquid bridge formation phase electric force is much bigger than surface tension and the liquid bridge is made very quickly between the tips of droplets. Lastly, in the merging phase the two droplets are merging because of surface tension. We focused the minimum distance to make liquid bridge and to merge the two droplets under constant potential difference. Finally, we performed numerical simulation using level set method and compared the experimental result with the numerical result. [Preview Abstract] |
Sunday, November 22, 2009 5:07PM - 5:20PM |
EH.00005: Non-coalescence of oppositely charged drops W.D. Ristenpart, J.C. Bird, A. Belmonte, F. Dollar, H.A. Stone Electrically induced droplet motion manifests itself in processes as diverse as storm cloud formation, commercial ink-jet printing, petroleum and vegetable oil dehydration, electrospray ionization in mass spectrometry, electrowetting and lab-on-a-chip manipulations. An important issue in practical applications is the tendency for adjacent drops to coalesce, and oppositely charged drops have long been assumed to experience an attractive force that favors their coalescence. Here we report the existence of a critical field strength above which oppositely charged drops do not coalesce. We observe that appropriately positioned and oppositely charged drops migrate towards one another in an applied electric field; but whereas the drops coalesce as expected at low field strengths, they are repelled from one another after contact at higher field strengths. Qualitatively, the drops appear to ``bounce'' off one another. We directly image the transient formation of a meniscus bridge between the bouncing drops, and propose that this temporary bridge is unstable with respect to capillary pressure when it forms in an electric field exceeding a critical strength. The observation of oppositely charged drops bouncing in strong electric fields should affect our understanding of any process involving charged liquid drops, including de-emulsification, electrospray ionization and atmospheric conduction. [Preview Abstract] |
Sunday, November 22, 2009 5:20PM - 5:33PM |
EH.00006: Partial Coalescence of Oppositely Charged Drops J.C. Creasey, B.S. Hamlin, W.D. Ristenpart Oppositely charged drops fail to coalesce above a critical field strength, despite the attractive force between the opposite charges [1]. Here we investigate the coalescence behavior at intermediate field strengths for charged water drops in oil, and we report that under many conditions the droplets undergo partial coalescence, i.e., a smaller daughter droplet is expelled. This partial coalescence is highly sensitive to the ionic strength of the droplets. For a given field strength, there exists a critical ionic strength above which the drops completely fail to coalesce and below which they partially coalesce. We explore the roles of charge density, drop size, inertia and viscous drag on the partial coalescence behavior and we interpret the results in terms of a competition between the respective time scales for hydrodynamic motion and ionic conduction. [1] Ristenpart, Bird, Belmonte, Dollar \& Stone, \emph{Nature}, in press (2009). [Preview Abstract] |
Sunday, November 22, 2009 5:33PM - 5:46PM |
EH.00007: A New Approach to Modeling Drop-Pair Collisions: Predicting the Outcome through a Fluidic-Mechanical System Analogy Paul Van Noordt, Carlos Hidrovo The study of microfluidics has proven to be of great value in many engineering and scientific applications. Because of the small scales involved, microfluidics requires only small sample sizes, which can result in shorter reaction and analysis times, relatively cheap costs, and little waste. In this study, we investigate the process of two drops colliding head-on in order to gain a better understanding of the mechanisms that govern the outcome of the collision. The relationship between kinetic and surface energy of the colliding drops is considered, as is the viscosity of the intervening gaseous medium, as factors that govern the outcome. The collision process is modeled by a squeeze-flow problem involving both planar and non-planar geometry, with attention given to the deformation of the interacting surfaces. Based on the nature of the collision process, an analogy is made between the fluidic systems of colliding liquid bodies and a mechanical mass-spring-damper system. Examination of the analogous mechanical system yields the derivation of an effective damping ratio, $\zeta ^{\ast}$, which is used to predict the outcome of the drop-drop collision. Predictions made by utilizing the effective damping ratio are then compared to numerical results and experimental data found in the literature. [Preview Abstract] |
Sunday, November 22, 2009 5:46PM - 5:59PM |
EH.00008: Characteristics of Unequal Size Drop Collisions Jungyong Kim, Ellen Longmire, Man Sik Kim Pairs of water/glycerin drops were injected into silicone oil and traveled on downward trajectories before colliding. Unequal size drop collisions with drop size ratios ($D_{s}/D_{L})$ of 0.7 and 0.5 were investigated. Simultaneous dual-field PIV measurements were obtained to characterize coalescence and rebounding behavior. The initial injection angle and tube height were adjusted to access appropriate impact parameters. In the current study, the collision angle of the large drop was, in general, shallower than that of the small drop, and a range of velocity ratios and impact parameters was examined. Coalescence occurs above \textit{We*} = 11 similar to collision outcomes for equal size drops. As drop size ratio decreases, the intervening film deforms more. If the velocity ratio $u_{L}/u_{s} \quad <$ 1, the interface remains deformed at coalescence, but if $u_{L}/u_{s} \quad >$ 1, the interface flattens before coalescence. The rupture location varies due to the asymmetry of the drops. As collision offset increases (B $>$ 0), the film rupture time is shortened and mixing of the fluid within the drops is enhanced after coalescence. These results will be compared with the behavior observed previously for equal size drop collisions. [Preview Abstract] |
Sunday, November 22, 2009 5:59PM - 6:12PM |
EH.00009: Bifurcation and Stability of a System of $n$ Coupled Droplet Oscillators with $S_n$ symmetry David Slater, Paul Steen The dynamics of a large array of interacting droplets is of interest in a variety of applications and, on its own, as a nonlinear dynamical system. A network of $n$ spherical-cap droplet oscillators are coupled via a central reservoir such that the system has $S_n$ symmetry. Under a constant-volume constraint, the inviscid case is modeled as a system of $n-1$ second order differential equations. Surface tension resists the inertia of deformations from the spherical shape. The symmetry of the system is important. In particular, independent of the equations, equilibrium solutions can be categorized by symmetry group into families, each with some $p$ large and some $q = n-p$ small droplets. Within each family stability is invariant, which greatly reduces the number of cases to consider. Equilibrium curves and their stability are calculated analytically for an arbitrary number of droplets in the preferred coordinate space. For small volumes, the only equilibrium state is stable and corresponds to all identical droplets. For larger volumes, a multitude of equilibrium states exist, each having the property that all droplets have equal radius of curvature. Nearly all these equilibrium are unstable, the only stable configuration being one droplet large and the rest small. The nonlinear dynamics of the three droplet case is examined numerically and exhibits quasiperiodic, periodic and chaotic dynamics. [Preview Abstract] |
Sunday, November 22, 2009 6:12PM - 6:25PM |
EH.00010: Dynamics of bubbles and drops in a Hele-Shaw cell Ko Okumura, Ayako Eri, Maria Yokota Bubbles created in liquid and drops moving in another immiscible liquid are easy to be observed from the side when enclosed in thin space made by two parallel plates, i.e. in a Hele-Shaw cell, and the results thus obtained should be interesting to be compared with three dimensional counterparts to find dimensional crossover. We show two such experimental examples: (1) thinning dynamics of liquid film encapsulating an air bubble and (2) coalescence dynamics of a liquid drop to the bath phase of the same liquid. Our experimental results are well explained by simple theories, providing the physical understanding of the phenomena. [Preview Abstract] |
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