Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session BF: Drops and Bubbles III |
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Chair: Sarah Case, University of Chicago Room: Salt Palace Convention Center 151 G |
Sunday, November 18, 2007 10:34AM - 10:47AM |
BF.00001: Non-Coalescence of Oppositely Charged Droplets Andrew Belmonte, W.D. Ristenpart, F. Dollar, D.A. Weitz, H.A. Stone We demonstrate the existence of a critical electric force above which oppositely charged droplets do not coalesce. The application of an external electric field causes appropriately positioned and oppositely charged droplets to migrate toward one another in a viscous oil. Upon contact, surface tension acts to pull the droplets together. For low droplet charge or applied field strengths, the droplets coalesce, but at higher charges or field strengths the droplets are repelled from one another after contact - they appear to bounce off one another. We derive the critical conditions for bouncing based on a competition between charge transfer, viscosity, and surface tension. These results have broad implications for applications where charged drops are manipulated by electric fields, including microfluidics, atmospheric science, and electrospray ionization. [Preview Abstract] |
Sunday, November 18, 2007 10:47AM - 11:00AM |
BF.00002: Explicit numerical simulation of binary drop collision in a linear shear field at finite Reynolds numbers Mark Biggs In this presentation, we will report an immiscible lattice-gas automata based study of the collision of two initially spherical drops suspended in a second liquid subject to a one-dimensional linear shear field. Capillary numbers ranging from Ca = 0.06 to Ca = 0.8 were investigated for the Reynolds numbers Re = 5/2$^{n}$ for $n$ = 0, {\ldots}, 4. A range of collision scenarios were observed ranging from coalescence in the compressional and extensional quadrants both with and without secondary drop formation, to collisions we term `kiss-and-break' in which the drops coalesce before separating again to form two or more drops, and non-coalescence. Limited results suggest that the regions of the parameter space associated with the various collision scenarios are not separated by distinct boundaries but, rather, transition zones in which the probabilities of the two outcomes vary in a complementary fashion from one to the other. The critical Capillary number is a strong function of the Reynolds number up to Re = 1.25 where it becomes largely independent of the Reynolds number. The nature of the variation of the `film thickness' during collisions is a function of both Capillary and Reynolds numbers. The dimensionless `film drainage time' increases with Capillary number and decreases as the Reynolds number increases to Re = 2.5 where it ceases to change with Re. [Preview Abstract] |
Sunday, November 18, 2007 11:00AM - 11:13AM |
BF.00003: Effect of Tracer Particles on Binary Droplet Coalescence in Liquids Jungyong Kim, Ellen Longmire Pairs of water/glycerin drops were injected into silicone oil and traveled on downward trajectories before colliding. Simultaneous dual-field PIV measurements were obtained to characterize coalescence and rebounding behavior for Weber numbers [\textit{We}] of 1-50 for a range of collision angles \textit{$\theta $} below the horizontal. First, both fluids were seeded with TiO$_{2}$ for PIV measurement. Then, additional experiments were performed with no tracer particles in the silicone oil to determine whether particles affect the coalescence. When both fluids were seeded, the drops rebounded for \textit{We} $<$ 10 and coalesced for \textit{We} $>$ 10. Based on the current data, this boundary applies for 22\r{ } $<$ \textit{$\theta $ } $<$ 35\r{ }, but shifts to higher \textit{We} with increasing collision angle. For the experiments with unseeded ambient fluid, the drops rebounded for \textit{We} $<$ 10. However, both coalescence and rebounding occurred for 10 $<$ \textit{We} $<$ 17. For cases with seeded ambient fluid, the rupture location was always in the lower portion of the thin film between the drops. However, for cases with unseeded ambient fluid, the rupture location was more variable. Details of these behaviors will be discussed in the presentation. Supported by Petroleum Research Fund (42939-AC9) and NSF (CTS-0320327). [Preview Abstract] |
Sunday, November 18, 2007 11:13AM - 11:26AM |
BF.00004: Experiments on the Dynamics of Droplets in Turbulent Flows Gregory Bewley, Kelken Chang, Holger Nobach, Haitao Xu, Eberhard Bodenschatz We report experiments on the settling and coalescence of micron size water droplets in a turbulent airflow. The turbulence is generated in an 80 x 80 x 100 cm$^3$ tank using two opposing arrays of 32 randomly triggered loudspeaker driven jets. Using a combination of PDPA, LDV and 3-d particle tracking we report data on the evolution of the droplet size distribution, the radial distribution function, and the droplet settling velocity. By varying the Reynolds number of the flow, we observe droplets with Stokes and Froude numbers in the range of 0.05 to 5, where the Stokes and Froude numbers gauge the importance of droplet inertia and setting velocity relative to the fluid time and velocity scales. We then compare our results with models and numerical simulations of inertial particle sedimentation. [Preview Abstract] |
Sunday, November 18, 2007 11:26AM - 11:39AM |
BF.00005: Theory of Head-on Collision of Binary Droplets: Bouncing, Coalescence and Interface Evolution Peng Zhang, Chung K. Law Droplet collision, coalescence, and bouncing are frequent events in dense sprays. A comprehensive theory was formulated to describe the dynamics of these processes for the head-on collision of two identical droplets. Specific interest was placed on predicting the coalescence and bouncing responses, including descriptions of the droplet deformation, the viscous loss through droplet internal motion, the dynamics and rarefied nature of the gas film between the colliding droplets, and the destruction and thereby merging of the colliding interfaces due to the van der Waals attractive force. The theoretical results agree well with previous experimental observations. Specifically, it is theoretically confirmed that as the impact inertial increases, collision of alkane droplets at one atmospheric pressure results in merging, bouncing and merging again, with the predicted merging Weber numbers agree well with the experimental data. Furthermore, the effects of ambient pressure and the rheological properties of the liquid were investigated. It is shown that while bouncing is absent for water droplets at atmospheric pressure, it occurs at higher pressures. Similarly, while bouncing is observed for alkane droplets at atmospheric pressure, it is absent at lower pressures. [Preview Abstract] |
Sunday, November 18, 2007 11:39AM - 11:52AM |
BF.00006: Electro-coalescence: Effects of a D.C. electric field on droplet coalescence at a planar interface Hamarz Aryafar, Pirouz Kavehpour In these series of experiments, we investigate the effects of an electric field on a water droplet suspended in a silicone oil medium coalescing into a pool of water. A neutrally-charged water droplet is deposited inside a layer of silicone oil slightly above a planar silicone oil-water interface. By introducing a DC electric field, we apply additional forces to the interface and droplet. In most cases, the presence of the electric field causes the droplet to initiate coalescence. The effect of this additional field in the conjunction with the effect of other physical properties of liquids such as viscosity and interfacial tension are studied by utilizing a digital high-speed camera. The characteristics of this phenomenon are compared with those of equivalent systems in absence of the electric field. Along with the presences of a lower electric field threshold must be surpassed in ordered to create instantaneous coalescence, a relationship between partial coalescence and electric field strength is observed. [Preview Abstract] |
Sunday, November 18, 2007 11:52AM - 12:05PM |
BF.00007: Rupture process during drop coalescence at a planar interface: time scales and instabilities Pirouz Kavehpour, Hamarz Aryafar As a drop approaches the surface of an undisturbed pool of its own liquid, it can develop a protective layer of the ambient fluid underneath it, such that it will not immediately coalesce across the interface. The current work analyzes the time dependent behavior of the ambient fluid film as it ruptures during coalescence. Identifying Ohnesorge number as the dimensionless parameter for coalescence processes, relevant power laws have been found to describe the time dependent radial retraction of the fluid film in viscous and inertial dominated regimes. For a range of Ohnesorge number, the rim of the ruptured film becomes unstable and forms tendril-like structures. The conditions for this phenomenon to occur will be presented. [Preview Abstract] |
Sunday, November 18, 2007 12:05PM - 12:18PM |
BF.00008: Coalescence in low-viscosity fluids Sarah Case The coalescence of two liquid drops occurs very rapidly. To study the very early stages of coalescence, we measured the resistance and capacitance of the coalescing region using an electrical method [1] modified for high-frequency alternating-current response. A drop of aqueous NaCl solution is suspended in air above a second drop of the same solution. A constant voltage is maintained across the system. The lower drop is grown until it touches the upper drop, at which point a rapidly widening bridge forms between them. Our measurements allow us to obtain information regarding the characteristic bridge radius $r$ and the characteristic length $d$. We observe a new asymptotic regime at early times inconsistent with previous theoretical predictions. We interpret this in terms of a slight flattening of the drop tips before coalescence. Our data taken at various drop radii as well as at various approach velocities of the two drops is consistent with this interpretation. \newline [1] J. C. Burton, J. E. Rutledge, and P. Taborek, Phys. Rev. Lett., 92, 244505 (2004) [Preview Abstract] |
Sunday, November 18, 2007 12:18PM - 12:31PM |
BF.00009: ABSTRACT WITHDRAWN |
Sunday, November 18, 2007 12:31PM - 12:44PM |
BF.00010: Pearling of drops sliding down a plane in partial wetting conditions. Laurent Limat, Jacco Snoeijer, Nolwenn Le Grand-Piteira, Howard Stone, Jens Eggers A drop sliding down a plane exhibits surprising shape changes when its velocity is increased. Oval at low velocity, it develops a ``corner'' when the drop velocity exceeds a critical value. The rear front adopts a conical shape, i.e develops a point singularity at the receding contact line. At even higher velocities, the corner evolves towards a cusp and later a tail that breaks into smaller droplets. We propose a simple model of this ``pearling'' transition in the limit of slender drops, for which the lateral scale is much smaller than the longitudinal one. We show that for a given capillary number, there are two different possible cone angle values, one stable, the other unstable. Above a critical capillary number, this model predicts the disappearance of these two solutions, the critical value of the half opening angle of the corner being of order 24 degrees. In this new regime, solutions involving a long rivulet left behind the drop appear, that can ultimately breaks into droplets. These calculations are in good agreement with experiments performed on silicon oil drops sliding down a plane coated with fluoropolymers. [Preview Abstract] |
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