Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session AF: Drops and Bubbles I |
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Chair: John Hinch, Cambridge University Room: Tampa Marriott Waterside Hotel and Marina Florida Salon 4 |
Sunday, November 19, 2006 8:00AM - 8:13AM |
AF.00001: On the paradox of thermocapillary flow about a stationary bubble Ehud Yariv, Michael Shusser When a stationary bubble is exposed to an external temperature gradient, Marangoni stresses at the bubble surface result in fluid motion. A straight-forward attempt to calculate the influence of this thermocapillary flow upon the temperature distribution fails to provide well-behaved solution [Balasubramaniam \& Subramanian, {\it Phys. Fluids} {\bf 16}, 3131 (2004)]. This paradox is resolved here using regularization procedure which exploits the qualitative disparity in the long-range flow fields generated by stationary bubble and moving one. The regularization parameter is an (exponentially small) artificial bubble velocity $U$, which reflects the inability of any asymptotic expansion to satisfy the condition of exact bubble equilibrium. The solution is obtained using asymptotic matching of two separate Reynolds-number expansions: an inner expansion, valid at the bubble neighborhood, and remote outer expansion, valid far beyond the familiar Oseen region. This procedure provides well-behaved solution, which is subsequently used to evaluate the convection-induced correction to the hydrodynamic force exerted on the bubble. The independence of that correction upon $U$ confirms the adequacy of the regularization procdure to descibe the stationary-bubble case. The ratio of the calculated force to that pertaining to the classical pure-conduction limit [Young, Goldstein Block, {\it J. Fluid Mech.} {\bf 6}, 350 (1959)] is given by $1 - Ma/8+ o(Ma)$, where Ma is radius-based Marangoni number. [Preview Abstract] |
Sunday, November 19, 2006 8:13AM - 8:26AM |
AF.00002: A Criterion on Splitting a Micro Air Bubble Squeezed Between Two Solid Plates Sung Cho, Yuejun Zhao An air bubble sandwiched between two channel plates can be split into two daughter bubbles by switching the wettability in the middle of bubble base area in contact with the plates. Here the wettability switch can be easily achieved by applying an electrical potential to the electrode underneath the bubble contacting base surface, so called electrowetting-on-dielectric (EWOD) principle. However, it is found that there is a criterion that makes splitting possible only in certain conditions. For complete splitting, smaller channel gap, larger bubble size, wider splitting electrode and/or larger contact angle change by EWOD are preferred. This criterion is derived by a static analysis based on the static equilibrium condition and geometrical relations, and verified by a series of experiments using microfabricated testing devices. [Preview Abstract] |
Sunday, November 19, 2006 8:26AM - 8:39AM |
AF.00003: Behavior of a pair of bubbles rising side by side at high Reynolds number Toshiyuki Sanada, Ayaka Sato, Minori Shirota, Masao Watanabe We study experimentally the motion and the wake of a pair of non-spherical bubbles rising side by side at high Reynolds number. The motions of bubbles were recorded by a high-speed video camera. The wakes of bubbles were visualized by using photochromic dye that is colored with UV light irradiation. We observed vortex separation from bubbles' rear surface at their collision, resulting in a great decrease in rising velocity of bubbles. Applying an existing model for spherical bubble-wall interaction by taking into account non-spherical effects on translational velocities and characteristics at the collision, we found that the revised model accurately describes the trajectory of a pair of bouncing-approaching bubbles. On the contrary, in the case of bubbles bouncing repeatedly, the effect of wake instability of a pair of bubbles on the motion of bubbles rather than the effect of bubble-bubble interaction dominates. We clarify that the vortex separation is strongly related with vertical velocity fluctuation. [Preview Abstract] |
Sunday, November 19, 2006 8:39AM - 8:52AM |
AF.00004: Visualization of wake structure and non-axisymmetric motion of a single rising bubble Tomoki Ono, Toshiyuki Sanada, Minori Shirota, Masao Watanabe Wake structure of zigzagging or spiraling motion of a single rising bubble was experimentally investigated. A single bubble was produced in a silicone oil pool. Bubbles wake was visualized by using Photochromic dye which turns optically opaque by UV light irradiation. Images both bubble motion and wake structure were captured by using stereo high-speed video camera. As results, a pair of vortex filaments, which is referred to as a double-threaded wake, was observed in the wake of bubble rising in non-axisymmetry. When a rising bubble turned the heading direction, both bubble wake rotation and mutual exchange between a pair of vortex filaments were observed. In the case of a bubble rising in zigzagging motion with shape oscillation, periodical generation of horse-shoe type vortices was observed. It is confirmed that the non-axisymmetric bubble motion, either zigzagging or spiraling, is strongly associated with shedding of wake vortices behind bubbles. [Preview Abstract] |
Sunday, November 19, 2006 8:52AM - 9:05AM |
AF.00005: Effect of Shear on Electrohydrodynamic-Driven Suspension of Bubbles Marrivada Reddy, Asghar Esmaeeli When a bubble with a certain dielectric properties, is suspended in a fluid with different dielectric properties, and is immersed in a uniform electric field, it will experience surface deformation and flow circulation. The direction of the circulation and the sense of the surface deformation depend on the relative importance of the electric conductivity ratio and the permittivity ratios of the bubble and suspending fluid. These effects play a major role in the microstructure formation of suspension of bubbles. In the case of bubbles moving near the wall, the velocity gradient will also influence the motion. To explore the effect of velocity gradient on the pattern formation, we impose a shear force on the electrohydrodynamic-driven suspension of bubbles. We use a front tracking/finite difference method to solve the momentum and ``leaky-dielectric'' electrohydrodynamic equations. Dynamics of binary- and multi-bubble interactions will be studied as a function of different shear rates. [Preview Abstract] |
Sunday, November 19, 2006 9:05AM - 9:18AM |
AF.00006: On the collision between small solid particules and spherical bubbles Dominique Legendre, Vincent Sarrot, Pascal Guiraud The capture of solid particles by bubbles is present in many processes in mining industries, water purification. An overall efficiency is usually defined as the ratio between the number of particles captured by a bubble and the number of particles located in the volume swept by the bubble. The aim of this work is to consider the collision event and more precisely the effect of the bubble contamination on the collision efficiency. For this purpose, this study focuses on the collision mechanism between a spherical bubble and small particles when particles are small enough to follow the streamlines of the flow generated by the bubble motion. This situation corresponds to the one classically encountered in a lot of flotation processes. This study is based on Direct Numerical Simulation (DNS) and analytical justifications. Numerical results are obtained for a wide range of bubble Reynolds numbers (based on bubble diameter db) and for different angles of contamination. The collision efficiency is found to be significantly dependent on both the Reynolds number and the level of contamination. [Preview Abstract] |
Sunday, November 19, 2006 9:18AM - 9:31AM |
AF.00007: Lagrangian Statistics of Slightly Buoyant Droplets in Isotropic Turbulence Balaji Gopalan, Edwin Malkiel, Joseph Katz This project examines the dynamics of slightly buoyant diesel droplets in isotropic turbulence using high speed in-line digital Holographic PIV. A cloud of droplets with specific gravity of 0.85 is injected into the central portion of an isotropic turbulence facility. The droplet trajectories are measured in a 50x50x50 mm\^{}3 sample volume using high speed in-line digital holography. An automated program has been developed to obtain accurate time history of droplet velocities. Data analysis determines the PDF of velocity and acceleration in three dimensions. The time histories enable us to calculate the three dimensional Lagrangian velocity autocorrelation function, and from them the diffusion coefficients. Due to buoyancy the vertical diffusion time scale exceeds the horizontal one by about 65{\%} .The diffusion coefficients vary between 2.8 cm\^{}2/sec in the horizontal direction to 5.5 cm\^{}2/sec in the vertical direction. For droplets with size varying from 2 to 11 Kolmogorov scales there are no clear trends with size. The variations of diffusion rates for different turbulent intensities and the effect of finite window size are presently examined. For shorter time scales, when the diffusion need not be Fickian the three dimensional trajectories can be used to calculate the generalized dispersion tensor and measure the time elapsed for diffusion to become Fickian. [Preview Abstract] |
Sunday, November 19, 2006 9:31AM - 9:44AM |
AF.00008: Mixing within a drop immersed in a fluid and subjected to translation and unsteady rotation. Rodolphe Chabreyrie, Pushpendra Singh, Nadine Aubry, Tounsia Benzekri, Cristel Chandre, Xavier Leoncini The flow within a spherical drop induced by an external flow consisting of unsteady translation and rotation is studied using dynamical systems theory and direct numerical simulation tools. The goal being to optimize mixing within the drop, particle trajectories are traced and Liouville sections plotted from the corresponding Stokes flow. Both regular dynamics and chaotic advection are shown to occur. In the case of the latter, the chaotic sea may be rather localized within the drop. Parameter values are then varied in order to optimize the volume of the chaotic region. These results are then compared to those obtained by using direct numerical simulations based on the Level Set Method (LSM). [Preview Abstract] |
Sunday, November 19, 2006 9:44AM - 9:57AM |
AF.00009: Cavity rippling during the entry of solid objects into water Torben Grumstrup, Andrew Belmonte The post-impact pinch-off of the cavity formed behind a projectile (solid object or fluid drop) often leads to the volumetric oscillation of the entrained air bubble, accompanied by acoustic emissions. Here we present experimental observations of a well-defined rippling of the air cavity behind different types of solid projectiles. The ripples begin just after the pinch-off (deep seal) of the cavity, simultaneous with the acoustic emission, and are typically fixed in the lab frame. The ripple wavelength scales linearly with both the diameter of the projectile and its velocity, consistent with a scaling based on the Minnaert frequency of an axisymmetric cavity. [Preview Abstract] |
Sunday, November 19, 2006 9:57AM - 10:10AM |
AF.00010: Non-continuous Froude number scaling for the closure depth of a cylinder cavity Stephan Gekle, Raymond Bergmann, Arjan van der Bos, Devaraj van der Meer, Detlef Lohse A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and symmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude$^{1/3}$ power-law. Instead, it displays three distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior by incorporating the influence of the capillary waves which are created as the cylinder passes the water surface into the analysis of the collapse. Our work thus gives further evidence for the non-universality of the void collapse. [Preview Abstract] |
Sunday, November 19, 2006 10:10AM - 10:23AM |
AF.00011: Growth and dissolution of an encapsulated microbubble used for diagnostic ultrasound Kausik Sarkar, Pankaj Jain Steady dissolution of a bubble with two gases and a permeable shell has been modeled. At first the shell is modeled without elasticity. Factors such as permeability of the shell, surface tension, mole fraction of the osmotic agent, gas concentration in the bulk have been varied to study the growth and the time scale for dissolution of the bubble. It has been found that the inclusion of shell elasticity also plays a vital role in the growth and dissolution of the bubble. [Preview Abstract] |
Sunday, November 19, 2006 10:23AM - 10:36AM |
AF.00012: An Experimental Investigation of the Implosion of Cylindrical Shell Structures C. Ikeda, D. Wiegert, A. Wetzel, X. Liu, J.H. Duncan The implosion of gas-filled cylindrical shell structures in a high-pressure water environment is studied experimentally in a 6-foot diameter implosion tank. The models tested were made of aluminum (outer diameter $D = 1.25$~inches, wall thickness $t = 0.029$~ inches) and brass ($D = 1.0 $~inches, $t = 0.016$~inches). Cylinder length to diameter ($L/D$) ratios between 5 and 10 were examined. Internally fitted end caps (3/8 inch thick) were used to seal the cylinder. The water-filled implosion tank was slowly pressurized by adding high-pressure nitrogen gas to a small gas ullage space above the water until the model imploded. The resulting pressure waves were recorded at nine positions inside the tank. The motion of the cylinder was recorded by a high-speed digital movie camera at 24,000 frames per second. Preliminary results show that, as predicted by shell stability theory, the ambient collapse pressure increases as $L/D$ decreases. With an $L/D$ ratio of 10, the cylinder flattens out forming two lobes while at $L/D = 5$ a three lobe shape is formed. The ratio of the maximum shock pressure to ambient collapse pressure at a distance of 5 inches away from the cylinder is 0.2857 for the aluminum cylinder (collapse pressure = 280~psi) and 0.1429 for the brass cylinder (collapse pressure = 105~ psi). Collapse modes and shock pressures at shorter $L/D$ will be discussed. [Preview Abstract] |
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