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 BC: Drops and Bubbles II |
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Chair: D. Legendre, Institut de Mecanique de Fluides de Toulouse Room: Salt Palace Convention Center 150 G |
Sunday, November 18, 2007 10:34AM - 10:47AM |
BC.00001: Buoyancy-Driven Motion of a Gas Bubble with Soluble Surfactants Metin Muradoglu Computations are performed to study the effects of soluble surfactants on the motion of a fully deformable gas bubble using a finite-difference/front-tracking method. The evolution equations of the interfacial and bulk surfactant concentrations are solved fully coupled with the incompressible Navier-Stokes equations using a non-linear equation of state that relates interfacial surface tension to surfactant concentration at the interface. The method is first validated for simple test cases and the computational results are found to be in a good agreement with the analytical solutions. It is then applied to study the effects of soluble surfactants on the motion of a buoyancy-driven bubble in a circular tube. It is shown that the terminal velocity of bubble reduces significantly as surfactant accumulates at the bubble interface and the terminal velocity of a contaminated bubble approaches to that of a solid sphere in the limit of creeping flow regime. In this regime, the results are found to be in a good agreement with available experimental data. The effects of governing nondimensional numbers such as Peclet numbers based on the interfacial and bulk surfactant diffusivities, elasticity, Damkohler, E$\ddot{o}$tv$\ddot{o}$s and Morton numbers are also investigated. [Preview Abstract] |
Sunday, November 18, 2007 10:47AM - 11:00AM |
BC.00002: Interaction between two spherical bubbles rising in a liquid Dominique Legendre, Yannick Hallez The main goal of the present study is to provide a complete description of the interaction between two bubbles for moderate bubble Reynolds number (20 $\le $ Re $\le $ 500, Re being based on the bubble diameter) and for positions described by the distance S (2.5 $\le $ S $\le $ 8, S being the ratio between the distance of centre and the bubble diameter) and (0\r{ } $\le \quad \theta \quad \le $ 90\r{ }) the angle formed between the line of centre and the horizontal. The value $\theta $=0\r{ } corresponds to the situation of two bubbles moving side by side (Legendre, Magnaudet and Mougin 2003 JFM, 497,133-166) and $\theta $=90\r{ } to the axis-symmetric situation of two bubbles moving in line (Yuan {\&} Prosperetti 1994 JFM, 278, 325-349). The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier-Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition and does not induce any rotation of the bubbles. The nature of the interaction is studied and the wake of the leading bubble is found to play a significant role in the attraction/repulsion mechanism. A general model for pair interaction is proposed. [Preview Abstract] |
Sunday, November 18, 2007 11:00AM - 11:13AM |
BC.00003: Path instablity of a rising bubble: Shape matters, Reynolds number doesn't! Roberto Zenit, Jacques Magnaudet The conditions for the transition to zigzagging trajectories for freely ascending bubbles were studied experimentally. To avoid surface contamination, we used silicon oils with shear viscosities ranging from 1.7 to 9.4 times that of water. Since these fluids are non-polar, as opposed to the case of water, the gas-liquid interfaces remain clean without the need of an ultra-pure environment. Using a 30 cm height cylindrical container, the shape and trajectory of millimetric-sized air bubbles were filmed with a high-speed camera. We found that the most important parameter for the transition from a rectilinear to a zigzagging trajectory is the bubble aspect ratio and not so much the Reynolds number. We found that the Reynolds number at incipient transition varied from 85 to 250, for decreasing liquid viscosity. Correspondingly, the bubble aspect ratio remained relatively constant ranging from 2.23 to 2.11 for the same set of conditions. Since vorticity at the bubble surface is almost independant of the Reynolds number and mostly depends on the bubble shape in the parameter range covered by our experiments, these results support the idea that surface vorticity, which in turn causes the wake to become unstable, is the principal cause for the transition to a oscillatory trajectory, as recently discussed by Magnaudet and Mougin (2007). [Preview Abstract] |
Sunday, November 18, 2007 11:13AM - 11:26AM |
BC.00004: A single bubble path transition from spiral to zigzag in dilute surfactant solution Yoshiyuki Tagawa, Wataru Kawaguchi, Ami Funakubo, Shu Takagi, Yoichiro Matsumoto The surfactant effect on a single bubble motion is so important that it changes whole bubbly flow structures. One of the surfactant key effects is to decrease bubble rise velocity. This phenomenon is described as Marangoni effect which is quantitatively investigated by many experiments and numerical calculations of straight rising bubbles. Some other previous researches studied a bubble trajectory transition from a zigzag trajectory to spiral in super purified water (Mougin et al. 2002). However, the surfactant effect on this 3D motion bubbles is not enough investigated. To investigate it in detail, we measured trajectories of single bubbles rising in a tank of 1300mm height filled with dilute surfactant solution. We observed a bubble motion transition from spiral to zigzag, which is just reverse transition of trajectories in super purified water. Considering our other measurement results of bubble trajectories in super purified water, those in different surfactant solution, and a profile of bubble rise velocity, we think this interesting result is explained by surfactant concentration on a bubble surface. We will discuss its mechanism in detail in our presentation. [Preview Abstract] |
Sunday, November 18, 2007 11:26AM - 11:39AM |
BC.00005: Zigzagging bubbles rising side by side Toshiyuki Sanada, Daiji Sone, Takayuki Saito The interaction between zigzagging bubbles (d=2.9mm) rising side by side and its surrounding liquid motion in quiescent water were experimentally investigated. Hypodermic needles and a bubble generator utilizing pressure oscillation were employed to exactly extract and highly reproduce the interaction between the liquid-phase motion and bubble motion at the collision. The recursive cross correlation PIV technique made it possible to obtain the accurate velocity field of the surrounding liquid motion of a pair of bubbles. The experiments were conducted by changing the initial bubble distance. As a result, the two types of velocity fluctuation of bubbles were mainly observed after the collisions. The first case, only the horizontal velocity of each bubbles obviously decreased. The second case, both the horizontal and the vertical velocity decreased. This difference is considered to be due to the different surrounding liquid motion, especially the formation of vorticity. [Preview Abstract] |
Sunday, November 18, 2007 11:39AM - 11:52AM |
BC.00006: Experimental study on wake structure of single rising clean bubble Ayaka Sato, Yuta Takedomi, Minori Shirota, Toshiyuki Sanada, Masao Watanabe Wake structure of clean bubble rising in quiescent silicone oil solution of photochromic dye is experimentally studied. A single bubble is generated, immediately after UV sheet light illuminates the part of the liquid just above the bubble generation nozzle in order to activate photochromic dye. Once the bubble passes across the colored part of the liquid, the bubble is accompanied by some portion of activated dye tracers; hence the flow structure in the rear of the single rising bubble is visualized. We capture stereo images of both wake structure and bubble motion. We study how wake structure changes with the increase in bubble size. We observe the stable axisymmetric wake structure, which is called `standing eddy' when bubble size is relatively small, and then wake structure becomes unstable and starts to oscillate with the increase in bubble size. With further increase in bubble size, a pair of streamwise vortices, which is called `double thread', is observed. We discuss in detail this transition from the steady wake to unsteady wake structure, especially double thread wake development and hairpin vortices shedding, in relation to the transition from rectilinear to spiral or zigzag bubble motions. [Preview Abstract] |
Sunday, November 18, 2007 11:52AM - 12:05PM |
BC.00007: Dynamics of swarms of buoyancy-driven bidispersed bubbles at O(100) Reynolds number Asghar Esmaeeli Direct numerical simulations of buoyancy-driven bubbly flows, where the flow around each bubble is fully resolved and viscosity, inertia, and surface tension are accounted for, have already been used to study bubbly flows up to O(100) Reynolds number. While these simulations have yielded considerable new insight into the dynamics of homogeneous bubbly flows in terms of the correlations of the average behavior of the flow with the microstructure, so far the majority of them have been concerned with the flows comprising of equal sized (monodispersed) bubbles. In real applications, however, the bubbles will have a spectrum of sizes and since the buoyant forces scale up with the bubble size, it is expected that the dynamics of bubbly flows will be drastically influenced by the size distribution of the bubbles. Studies on bidispersed bubbly systems constitute a good starting point for elucidating the role of size distribution effect. However, so far only a handful of such studies have been performed. The goal of the current investigations is to extend the parameter range of the earlier studies by performing large scale simulations of three-dimensional bi-dispersed bubbles. Here, the main controlling parameters are the ratio of the void fractions of species and the volume ratio of the bubbles. The investigations will be, therefore, focused on characterizing the global behavior of the bubbly systems as a function of these parameters. [Preview Abstract] |
Sunday, November 18, 2007 12:05PM - 12:18PM |
BC.00008: Buoyancy-driven drop squeezing through a constriction Thomas Ratcliffe, Alexander Zinchenko, Robert Davis Emulsion flow through a granular material is of fundamental importance to many applications (e.g., oil filtration through underground reservoirs). To understand these complex flow systems, the effect of drop squeezing on the emulsion flow rate and the critical conditions when the drops become trapped must be determined. As a related model problem, the buoyancy-driven axisymmetric motion of an emulsion drop through a torus is considered by experiments and by theory using a boundary-integral method. For the latter, the problem is reduced to a system of well-behaved second-kind integral equations for the fluid velocity on the drop and the Hebeker density on the solid surfaces (Zinchenko {\&} Davis, 2006, J. Fluid Mech. vol. 564, pp. 227-266). During squeezing through the constriction, the trends for the drop-solid spacing (as small as 0.1-1{\%} of the drop size) and the drop's velocity deceleration (up to 10$^{4}$ times) are explored in detail. A critical Bond number for trapping to occur is found for different squeezing conditions (drop-to-torus size ratio, drop-to-opening size ratio, and drop-to-surrounding fluid viscosity ratio). In experiments, our focus is to verify the predictions and to determine when surface roughness neglected in the theory has an effect on the squeezing process. [Preview Abstract] |
Sunday, November 18, 2007 12:18PM - 12:31PM |
BC.00009: Falling to Floating Transitions of Solid Spheres in a Bubbly Fluid Michael Higley, Andrew Belmonte We present experimental observations of the trajectories and average velocities of solid spheres falling through a curtain of rising bubbles in water. For the quiescent case (no bubbles), the Reynolds numbers are on the order of 1,000, and the average terminal velocity is determined by the form (inertial) drag. The main effect of the bubbles is to slow down the spheres. In some regimes (larger or heavier spheres), the paths followed by the spheres in the bubble stream are nearly indistinguishable from their paths without bubbles. In other regimes (smaller or lighter spheres), an apparently random lateral motion is the dominant feature. [Preview Abstract] |
Sunday, November 18, 2007 12:31PM - 12:44PM |
BC.00010: Vertical Migration of a Gas Bubble and Non-Aqueous Phase Liquid Drop In A Noncircular Capillary Filled With Water During Phase Change Kent Udell, Hae-Won Choi The upward migration of a denser non-aqueous phase (oil) liquid drop attached to a gas bubble inside a square capillary tube originally filled with water was studied for unheated and heated conditions. Under heated conditions where vaporization occurred, the bubble-liquid combinatory body vertical migration velocities increased with time and were greater than those of unheated bodies of similar geometry. An approximate model based on Stoke's flow is presented that suggests a relationship between the gas bubble length, the oil drop length and the upward migration velocity such that the migration velocity vary linearly with the body force. The model is in excellent agreement with the experimental data. Based on the data and theoretical considerations, it is concluded that the Gravity number, defined as the ratio of gravity forces to viscous forces, is constant at a value near 60,000 for all conditions examined. It is also speculated that a constant Gravity number would be observed for bubble-liquid drop flow in porous media as well. [Preview Abstract] |
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