Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session LR: Bubbles III |
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Chair: Alberto Aliseda, University of Washington Room: Long Beach Convention Center 203C |
Monday, November 22, 2010 3:35PM - 3:48PM |
LR.00001: Strain-softening elasticity model of the encapsulation of an ultrasound contrast microbubble Shirshendu Paul, Kausik Sarkar, Flemming Forsberg Micron size bubbles have been clinically approved as contrast agents in diagnostic ultrasound imaging. These bubbles are stabilized with an encapsulation made of surface-active materials such as surfactants, lipids or proteins. We have developed interfacial viscoelastic models for the encapsulation and determined the material properties of commercial contrast agents. Now, we modify this model to account for strain softening in large nonlinear bubble oscillation. Two non-linear models--interfacial elasticity varying linearly and exponentially with area fraction--are developed. The model parameters are determined using experimentally measured attenuation of ultrasound through a solution of contrast agent Sonazoid. Models are then investigated for their ability to compare with experimentally observed scattered non-linear response. They also display recently observed ``compression-only'' behavior and skewed-resonance. The model response is discussed in detail along with a comparison with the model due to Marmottant et al. [Preview Abstract] |
Monday, November 22, 2010 3:48PM - 4:01PM |
LR.00002: Bubble dynamics in a Hele-Shaw cell Saul Piedra, Eduardo Ramos We study theoretically the dynamics of air bubbles ascending in a water filled Hele-Shaw cell. The bubble position and shape, and the flow inside and outside the bubble are calculated by solving a two-dimensional model that comprises the mass and momentum conservation equations coupled with a front tracking technique. The shape of the bubble is determined by the motion of the water surrounding the bubble, and the surface tension. The effect of the walls of the Hele-Shaw cell is accounted for in the model by including a brake term proportional to the corresponding component of the bubble centroid velocity in the momentum conservation equation. The proportionality constant is a free parameter. We find that the bubbles follow a zigzag trajectory as they ascend. The bubbles acquire elliptic shapes that oscillate $\pm 45 ^{\circ}$ around their geometrical center, with the largest inclination angle at the turning points of the zigzag motion. Also, the bubbles take a larger eccentricity at the same positions. The Reynolds number of the bubbles is 372 and vortex shedding is observed. All dynamical properties are in quantitative agreement with experimental results. [Preview Abstract] |
Monday, November 22, 2010 4:01PM - 4:14PM |
LR.00003: Evolution of an elastic capsule in two-dimensional Stokes flow Michael Higley, Michael Booty, Michael Siegel We consider an inviscid bubble surrounded by an elastic membrane. In planar Stokes flow, the deformation of the capsule can be described by adapting existing conformal mapping techniques. We present analytical and numerical results for the evolution and steady states of the capsule. These include the effects of different far-field conditions in the flow, resulting in behaviors such as tank-treading and cusp formation. [Preview Abstract] |
Monday, November 22, 2010 4:14PM - 4:27PM |
LR.00004: Numerical Study of Taylor Bubble Dynamics Jing Lou, Shaoping Quan, Changwei Kang Taylor bubble rising is numerically investigated using a front tracking/finite difference method, with systematic studies of bubble shape, the effects of the Reynolds number ($Re_T$), the Weber number ($We_T$), and the Froude number ($Fr$), the thin liquid film thickness ($w$) and the wake length ($l_w$). The effects of density ratio ($\eta$), viscosity ratio ($\lambda$), E\"{o}tv \"{o}s number ($Eo$) and Archimedes number ($Ar$) are examined in detail. The results show that the density ratio and the viscosity ratio have minimal effect on the dynamics of the Taylor bubble. E\"{o}tv\"{o}s number and Archimedes number influence the elongation of the tail and the wake structures, where higher $Eo$ and $Ar$ result in longer $l_w$. A critical value of unity of locally defined Weber number ($We_l$) is found to represent the sudden extension of the bubble tail. The Archimedes number drastically affects the final shape of Taylor bubble, the terminal velocity, the thickness of thin liquid film as well as the wall shear stress. A correlation between thin film thickness ($w/D$) and Archimedes number ($Ar$) is obtained as: $w/D=0.32Ar^{-0.1}$. [Preview Abstract] |
Monday, November 22, 2010 4:27PM - 4:40PM |
LR.00005: Single bubble bouncing on a free surface and effect of the rising velocity and surface tension Toshiyuki Oyama, Shintaro Takeuchi, Shu Takagi, Yoichiro Matsumoto The paper presents a numerical study of bubble bouncing on a free surface with a front tracking method. Contact time is determined as: the duration, within which the length between the mass center of the bubble and the initial position of the free surface is less than the initial bubble radius. The contact time is one of important values in the view of bouncing mechanism predicted by mass-spring modeling. The contact time is relational to the -0.5 power of surface tension coefficient as well as the prediction by mass-spring modeling. This result supports assumption that stored energy due to shape change is dominant to phenomenon of bubble bouncing rather than drainage between films. In the presentation we will refer the relation between the distance of two films between the free surface and the bubble and resolution. [Preview Abstract] |
Monday, November 22, 2010 4:40PM - 4:53PM |
LR.00006: Direct numerical simulation of confined drops and bubbles at low capillary numbers Shahriar Afkhami, Alex Leshansky, Yuriko Renardy The technology of microfluidics and its recent advance in the use of droplets within microchannels lead to the need for the understanding of drop deformation and breakup as a function of flow strength, physical parameters and fluid properties. We perform a combined asymptotic and numerical study of a simplified model for a dispersion which is pumped through a T-junction. The numerical method is based on a height-function formulation for a volume-of-fluid representation of the two liquids. Both the Bretherton and the Richardson bubble are used for benchmarking our code, thus establishing the degree of accuracy and robustness. The viscosity ratio of the drop to matrix liquid is varied to investigate the range of behavior from the presence of a bubble to that of a highly viscous drop. We focus on small Reynolds numbers and the limit of small capillary numbers where prior asymptotic theory of Leshansky and Pismen [Phys. Fluids 21, 023303 (2009) ] has yet to be ascertained with computational results. In this regime, very strong capillary forces combined with confinement contribute to the difficulty in the direct numerical simulations. In particular, more than one mode of drop breakup has been observed in experimental data [Phys. Fluids 21, 072001 (2009)] when a large drop goes through a T-junction. [Preview Abstract] |
Monday, November 22, 2010 4:53PM - 5:06PM |
LR.00007: ABSTRACT WITHDRAWN |
Monday, November 22, 2010 5:06PM - 5:19PM |
LR.00008: The Terminal Velocity of a Bubble in an Oscillating Flow L.A. Romero, A.M. Kraynik, J.R. Torczynski A bubble in an acoustic field experiences a net ``Bjerknes'' force from the nonlinear coupling of its radial oscillations with the oscillating buoyancy force. It is typically assumed that the bubble's net terminal velocity can be found by considering a spherical bubble with the imposed ``Bjerknes stresses''. We have analyzed the motion of such a bubble using a rigorous perturbation approach and found that one must include a term involving an effective mass flux through the bubble that arises from the time average of the second-order nonlinear terms in the kinematic boundary condition. The importance of this term is governed by the dimensionless parameter $\alpha ={R^2\omega } \mathord{\left/ {\vphantom {{R^2\omega } \nu }} \right. \kern-\nulldelimiterspace} \nu $, where $R$ is the bubble radius, $\omega $ is the driving frequency, and $\nu $ is the liquid kinematic viscosity. If $\alpha $ is large, this term is unimportant, but if $\alpha $ is small, this term is the dominant factor in determining the terminal velocity. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, November 22, 2010 5:19PM - 5:32PM |
LR.00009: Simulations of Bubble Motion in an Oscillating Liquid A.M. Kraynik, L.A. Romero, J.R. Torczynski Finite-element simulations are used to investigate the motion of a gas bubble in a liquid undergoing vertical vibration. The effect of bubble compressibility is studied by comparing ``compressible'' bubbles that obey the ideal gas law with ``incompressible'' bubbles that are taken to have constant volume. Compressible bubbles exhibit a net downward motion away from the free surface that does not exist for incompressible bubbles. Net (rectified) velocities are extracted from the simulations and compared with theoretical predictions. The dependence of the rectified velocity on ambient gas pressure, bubble diameter, and bubble depth are in agreement with the theory. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, November 22, 2010 5:32PM - 5:45PM |
LR.00010: Multiscale modeling of bubbles rising in non-Newtonian fluids Arturo Fernandez A multiscale method combining front-tracking with Brownian dynamics simulations is used to examine the dynamics of bubbles rising in a non-Newtonian fluid. Firstly, the evaluation of the material properties for the viscoelastic fluid will be discussed. Then, the results from the computations for a single bubble will be presented. We will discuss how the multiscale methodology is able to capture main features of the system dynamics including the appearance of a negative wake behind the bubble and the discontinuity in the terminal velocity. [Preview Abstract] |
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