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 RQ: Bubbles V |
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Chair: Jun-Hong Liang, University of California, Los Angeles Room: Long Beach Convention Center 203B |
Tuesday, November 23, 2010 3:05PM - 3:18PM |
RQ.00001: Bubble distributions and dynamics in the far wake of a ship Douglas Schwer, Russell Dahlburg, Jay Boris This research focuses on how to simulate efficiently the dynamics of the bubble size distribution in the far wake of a surface ship with a water jet or conventional propulsion system. In this region, the wake is undergoing turbulent decay and the bubble void fraction is low enough to justify one-way coupling. A particle-tracking method is used to create an ``ideal'' bubbly flow solution within a decaying wake, accounting for buoyancy, agglomeration, dissolution, drag, and convection. These solutions are then compared with multi-group methods for bubble size distributions and dynamics. Multi-group methods are generally much more efficient than particle-tracking methods, but determining appropriate expressions for the different bubble processes described above can be less straight-forward. A comparison of the evolution of the bubble distribution in the far wake between the multi-group and particle-tracking methods shows how well the multi-group methods are able to capture the bubble dynamics in these flow regimes. [Preview Abstract] |
Tuesday, November 23, 2010 3:18PM - 3:31PM |
RQ.00002: Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall Kazuyasu Sugiyama, Fumio Takemura A deformation-induced lateral migration of a nearly spherical bubble rising near a vertical plane wall in a stagnant creeping liquid flow is numerically studied by means of a boundary-fitted finite-difference approach (Sugiyama \& Takemura (2010) J. Fluid Mech. accepted). The migration velocity is obtained using Lorentz's reciprocal theorem as a function of $\varepsilon$, corresponding to a ratio of a bubble-wall gap to the bubble radius. For $\varepsilon\gg 1$, the simulated migration velocities are consistent with an available analytical solution for the wide-gap case (Magnaudet {\it et al.} (2003) J. Fluid Mech. {\bf 476}, 115). With decreasing $\varepsilon$, the lift force is found to be more affected by the high-order deformation modes. The simulation and the lubrication analysis (Hodges {\it et al.} (2004) J. Fluid Mech. {\bf 512}, 95) consistently demonstrate that when $\varepsilon\leq 1$, the lubrication effect makes the migration velocity asymptotically $\mu V_{B1}^2/(25\varepsilon \gamma)$ (here, $V_{B1}$, $\mu$, and $\gamma$ denote the rising velocity, the liquid viscosity, and the surface tension, respectively). However, the experimentally measured migration velocity is considerably higher by a factor of about 3 than the simulated one, implying that unexplored factors may be involved in the system. [Preview Abstract] |
Tuesday, November 23, 2010 3:31PM - 3:44PM |
RQ.00003: Saddle-point dynamics in bubble break-up Lipeng Lai, Wendy W. Zhang Cylindrically-symmetric bubble break-up are unstable against azimuthal perturbations. While most perturbations preempt the symmetric pinch-off singularity by creating a smooth contact, our simulations also show a qualitatively different, non-monotonic evolution for certain narrow ranges of initial conditions. To explore this novel behavior, we simulate the break-up of a bubble in 2D in the presence of an $n=2$ Fourier mode distortion. For this choice of the initial perturbation, the non-monotonic shape evolution proceeds as follows: the neck cross-section collapses into a narrow and long slot shape. The two ends of the ``slot'' initially sharpen rapidly. Then the sharpening slows. Eventually the curvatures of the two ends invert, creating two narrow fingers of water that intrude into the bubble interior. As time goes on, the tip of the intrusion broadens while the finger remains relatively narrow, causing the entire intrusion font to resemble a mushroom on a thin stalk. This sharpen-first-then-broaden sequence is qualitatively consistent with a phase space trajectory controlled by the presence of a saddle point. The maximum end curvature attained during the time evolution appears to diverge as the amplitude or the phase of the initial Fourier mode distortion is tuned towards appropriate threshold values. This suggests that the saddle corresponds to a singular interface shape. [Preview Abstract] |
Tuesday, November 23, 2010 3:44PM - 3:57PM |
RQ.00004: Complex fluid pinch-off in bubble rafts Chin-Cahng Kuo, Sheryll Nery, Mike Arciniaga, Michael Dennin Pinch-off processes have been investigated in two and three dimensional liquid systems. A common element of pinch-off is the existence of a well-defined scaling regime in which the minimum radius of the system decreases as a power-law in time. The exact value for the power-law depends on the dominant mechanism in the material and the dimensionality. For complex fluids, the dynamics are strongly dependent on the applied stress, rate of strain, and the inner structure of the material, which lead to interesting pinch-off behavior. Here we present the experimental results for pinch-off in bubble rafts pulled by two parallel plates on a liquid surface. Power-law behavior is observed, and we will report on the impact of pulling speed and composition on the value of the power-law exponents. [Preview Abstract] |
Tuesday, November 23, 2010 3:57PM - 4:10PM |
RQ.00005: Pinch-off of axisymmetric squashed underwater bubbles Daniel C. Herbst, Wendy W. Zhang Up until now, theoretical and computational studies of bubble pinch-off have assumed for simplification that the neck near break-up is nearly cylindrical, and that the surrounding water flows inwards radially. In this regime, azimuthal perturbations, however small initially, give rise to vibrations that dominate the collapse. Here we use a boundary integral simulation to investigate the surface evolution starting from initial states in the opposite limit, where the neck shape is composed of two cones with large opening angle. We also compare simulation results near the minimum against predictions from a leading-order expansion that is valid for strongly squashed neck shapes, in contrast to previous slender-neck expansions. We derive the instantaneous condition that the exterior flow must satisfy in order for the shape to evolve without changing the opening angle. The simulation shows that this condition is unstable. The small component of vertical flow present initially grows in magnitude and always acts to make the neck more slender. Thus all initial states evolve towards a dynamics that supports memory-encoding vibrations. [Preview Abstract] |
Tuesday, November 23, 2010 4:10PM - 4:23PM |
RQ.00006: Role of up-down asymmetry in the break-up of an underwater bubble Monte Rinebold, Daniel C. Herbst, Wendy W. Zhang We examine the effect of up-down asymmetry on the axisymmetric break-up of an underwater bubble. Previous works have assumed that the neck shape is always symmetric about the minimum. However, because of hydrostatic pressure, a slight initial up-down asymmetry is in practice always present. In addition, recent experiments by Keim \& Nagel show that the evolution of this asymmetry exhibits complex variations over time and with respect to the gas composition. Our simulations show that, in the idealized regime where the interior flow is negligible, an initial up-down asymmetry, however large, decays rapidly. As an example, starting with an initial neck shape comprised of an upper cone with an opening angle of $60^\circ$ joined smoothly onto a lower cone with an opening angle of $150^\circ$, the magnitude of the asymmetry reduces $20$ fold as the minimum radius decreases by a factor of $10$. This reduction proceeds in a distinctive form: the vertex region of the large cone sharpens while the small cone persists without significant change. As a result, the final up-down symmetric profile retains a memory of the small initial angle but not the large one. Since our simulation tracks only the effect of the exterior flow, this result also suggests that the complex variation observed is created by an interplay of interior gas flow at late times and exterior flow at early times. [Preview Abstract] |
Tuesday, November 23, 2010 4:23PM - 4:36PM |
RQ.00007: Bubble formation in planar co-flowing air-water sheets C. Guti\'errez-Montes, R. Bola\~{n}os-Jim\'enez, E. Sanmiguel-Rojas, C. Mart\'Inez-Baz\'an, A. Sevilla The dynamics of a plane air sheet surrounded by a co-flowing water sheet, discharging into stagnant air, has been investigated by means of experiments and numerical simulations with the aim at proposing new geometrical configurations for air bubble generation. In this case, the problem is governed by the Weber number, $We = \rho_w\,u_w^2\,h_a/\sigma$, and the water-to-air velocity ratio, $\Lambda = u_w/u_a$, being $u_w$ and $u_a$ the mean velocities of the water and air sheets respectively, $\rho_w$ the water density and $h_a$ the half-thickness of the air sheet at the exit. For a fixed liquid-to-gas thickness ratio, $a = h_w/h_a = 5.52$, and a constant Weber number, two different flow regimes have been observed, i.e. a jetting and a bubbling regime. High-speed video images have been used to determine experimentally the transition curve from a jetting regime to a bubbling regime in the $We - \Lambda$ parameter space, as well as to measure several relevant parameters in the bubbling regime, such as the bubbling frequency and the size of the bubbles formed. In addition, direct numerical simulations have been performed by means of the Volume of Fluid technique (VoF), and the results compared with the experimental measurements. [Preview Abstract] |
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