Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session BJ: Bubbles II: Bubble Deformation and Breakup |
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Chair: Detlef Lohse, University of Twente Room: 101I |
Sunday, November 22, 2009 10:30AM - 10:43AM |
BJ.00001: Viscous irrotational analysis of the deformation and break-up time of a bubble or drop in uniaxial straining flow Juan C. Padrino, Daniel D. Joseph The deformation of a bubble or drop in uniaxial straining flow is modeled by assuming the motion of the viscous fluids to be irrotational. In this approach, viscosity enters the analysis through the balance of normal stresses at the interface. The tracking of the interface motion is achieved by integration of the set of differential equations furnished by the conservation of linear momentum and kinematical conditions, coupled with a boundary-integral formulation along the interface. This methodology is thus employed to investigate the influence of a finite Reynolds number on the time evolution, up to break-up, of the drop or bubble for various Weber numbers. Comparison with results from simulations of the Navier-Stokes motion, which includes rotational effects, are presented and discussed. [Preview Abstract] |
Sunday, November 22, 2009 10:43AM - 10:56AM |
BJ.00002: Bubble deformation, translation, collapse and bursting in a uniform electric field Stephen Shaw, Peter Spelt, Omar Matar We study the dynamics of a bubble in a dielectric fluid subjected to a uniform electric field in the limit of weak viscosity and compressibility. We use a domain perturbation method to derive a set of ordinary differential equations that govern the evolution of the bubble deformation, oscillation and translation; these equations contain second-order interaction terms. Both steady-state and time-dependent solutions are presented. Our analysis of the results indicates that for initially uncharged spherical bubbles, only even shape modes and odd components of the charge density are excited. We show that situations wherein all modes are excited could give rise to an instability over a certain range of parameter values. This instability manifests itself via suddent bubble acceleration and growth, which ultimately renders the theory invalid. [Preview Abstract] |
Sunday, November 22, 2009 10:56AM - 11:09AM |
BJ.00003: Bubble pinch-off in viscous liquids Roc\'Io Bola\~{n}os-Jim\'{e}nez, Alejandro Sevilla, Carlos Mart\'Inez-Baz\'{a}n, Devaraj van der Meer, Jos\'{e} Manuel Gordillo The effect of liquid viscosity on the final instants previous to pinch-off of an air bubble immersed in a stagnant viscous liquid is experimentally and theoretically investigated. Our experiments show that the use of a power-law to describe the collapse dynamics of the bubble is not appropriate in an intermediate range of liquid viscosities, for which a transition from an inviscid to a fully viscous pinch-off takes place. Instead, the instantaneous exponent $\alpha(\tau)$ varies during a single pinch-off event from the typical values of inviscid collapse, $\alpha\simeq 0.58$, to the value corresponding to a fully viscous dynamics, $\alpha\simeq 1$. However, we show that the pinch-off process can be accurately described by the use of a pair of Rayleigh-like differential equations for the time evolution of the minimum radius and the axial curvature evaluated at the minimum radius, $r_1$. This theoretical model is able to describe the smooth transition which takes place from inviscid to viscous-dominated pinch-off in liquids of intermediate viscosity, 10 $\leq\mu\leq$ 100 cP, and accounts for the fact that the axial curvature remains constant when the local Reynolds number becomes small enough, in agreement with our experimental measurements. [Preview Abstract] |
Sunday, November 22, 2009 11:09AM - 11:22AM |
BJ.00004: Evolution and Pinch-off of Axisymmetric Viscous Bubbles in Stokes Flow Shadi Naderi, Monika Nitsche Boundary integral simulations of the evolution of an axisymmetric viscous bubble in an axisymmetric strain field are presented, using the Stokes flow approximation. Previous works have shown the bubble reaches a steady state while the capillary number measuring the strain field stays below a critical value. Above this value no steady state is found. Previous experimental observations and numerical works indicate that a slight increase in the capillary number past this critical value causes an elongation and break-up. We present numerical studies of the evolution of bubbles towards the steady state subject to various capillary numbers and viscosity ratios using the high order method developed by Ceniceros, Karniala and Nitsche (preprint). Steady state results obtained from this method are compared with previous findings. A numerical investigation of pinch-off for a capillary number past this critical value is presented. [Preview Abstract] |
Sunday, November 22, 2009 11:22AM - 11:35AM |
BJ.00005: X-ray Imaging of Memory in Air Bubble Pinch-Off Nathan Keim, Kamel Fezzaa, Sidney Nagel We report on studies of underwater air bubble pinch-off. Previously, we have shown that this pinch-off is a singularity with memory, in which azimuthal symmetry may be broken by tilting the nozzle or by blowing bubbles from a slot-shaped nozzle, and that 2- or 3-lobed perturbations to the pinching neck's cross-section are remembered as small vibrations of the neck shape.\footnote{Keim \& Nagel, DFD 2008 AH.1} This is consistent with the model of Schmidt et al.\footnote{\emph{Nat.\ Phys.}\textbf{5}, 343} Even modest perturbations to the initial bubble shape can cause the neck to develop concavities late in its collapse, as shown by Turitsyn et al.\footnote{arXiv:0902.0393v1} Using high-speed X-ray phase contrast imaging at the Advanced Photon Source, we have observed these concavities, as well as the Worthington jet. Tilting a nozzle by as little as $1^{\circ}$ suppresses jet formation outside of a small region near pinch-off. Further experiments show that placing walls near the bubble also creates azimuthal perturbations, and that the vertical motion and vertical asymmetry of the neck at its minimum radius are due primarily to the neck's impedance of gas flow. [Preview Abstract] |
Sunday, November 22, 2009 11:35AM - 11:48AM |
BJ.00006: Diffraction: wave dynamics near the break-up of an underwater bubble Lipeng Lai, Samuel D. Oberdick, Wendy W. Zhang Recent studies show that the final form of bubble break-up is dominated by a memory of initial asymmetries, in contrast to the idea that the break-up dynamics inevitably evolves towards a universal form independent of boundary and initial conditions. Specifically, when the neck of the submerged bubble is distorted from cylindrical symmetry, vibrations in the neck cross-section about the average contraction are excited. These vibrations, which correspond to standing waves on the air-water interface, persist until break-up. As a result, the break-up dynamics is both asymmetric and dependent on the initial distortion. Previous works analyzed the situation where the initial distortion is dominated by a single vibrational mode. They found that the final dynamics continues to be dominated by the initial mode. Nonlinear interactions, which create new modes and change the relative amplitudes of the different modes present, are expected to have a more pronounced role in the diffraction limit, when many vibrational modes are present. Here we examine the break-up dynamics when a large number of vibrational modes are present. We use a boundary integral simulation to track the how the cross-section of the bubble neck evolves over time. The results are compared against predictions from linear stability. [Preview Abstract] |
Sunday, November 22, 2009 11:48AM - 12:01PM |
BJ.00007: Effect of vertical flow on the break-up of an underwater bubble Daniel C. Herbst, Wendy W. Zhang Previously, the break-up of a fluid drop was believed to evolve towards a universal singularity, with little dependence on initial or boundary conditions. Recent studies reveal that the break-up of a bubble while it is immersed in another liquid follows a different scenario, one preserving detailed information about the initial state. When the bubble neck is nearly cylindrical, the leading-order dynamics has a simple two-dimensional form: the initial shape is advected inwards by a focusing flow in the exterior until break-up. Asymptotic analysis indicates that such a memory-preserving evolution is possible only when the vertical flow out of the minimum remains far weaker than the focusing flow within a horizontal plane. Here we explore what happens to this memory-preserving dynamics when the vertical flow becomes comparable with the horizontal flow. An axisymmetric boundary integral code is used to track the shape evolution. We alter the surface profile at break-up, in particular the upper and lower cone angles, by changing the initial neck shape. For large angles, the vertical momentum flux becomes significant and the velocity evolution is strongly coupled to the surface evolution. We also study the effect of an up-down asymmetry in the initial shape on the final break-up. [Preview Abstract] |
Sunday, November 22, 2009 12:01PM - 12:14PM |
BJ.00008: Combinations of neck vibrations in bubble break-up Samuel D. Oberdick, Lipeng Lai, Konstantin S. Turitsyn, Wendy W. Zhang When an air bubble pinches off inside a liquid, the final dynamics is controlled by the initial shape asymmetries, via vibrations in the neck cross-section. Previously, we showed that, when the break-up is dominated by 1 vibrational mode, the initial shape asymmetry evolves into a smooth contact that divides the cross-section shape into side lobes. The lines of symmetry remain static over time and the average size of the side lobes decreases in discrete steps as the initial distortion size is reduced. Here we use analytics and simulation to study the contact dynamics obtained by combining 2 vibrational modes. A wide variety of intricate contact shapes are possible. When incommensurate modes are present, the lines of symmetry are destroyed. The contact shape becomes askew, i.e. the surface on opposite sides of the contact have different curvature values. When the modes are commensurate, some symmetry lines are preserved. Interference between the different vibration frequencies causes the surface distortion to vary irregularly over time. As a result, the average size of the side lobes decreases in irregular steps as the initial distortion size is reduced. [Preview Abstract] |
Sunday, November 22, 2009 12:14PM - 12:27PM |
BJ.00009: Non-axisymmetric collapse of cylindrical cavities Ivo Peters, Oscar R. Enriquez Paz Y Puente, Stephan Gekle, Laura E. Schmidt, Devaraj van der Meer, Detlef Lohse Upon the impact of a circular disk on a water surface an expanding cylindrical cavity is created which collapses under the influence of the hydrostatic pressure. We experimentally observe small disturbances in the azimuthal direction that tend to grow towards the pinch-off. To quantitatively investigate the growth of specific mode-numbers, we use disks with a harmonic disturbance applied to their round shapes and study the collapse of the disturbed cavity using high-speed imaging. We performed experiments using disturbances up to mode number $m=6$, with varying strength from 1\% to 25\% of the radius of the undisturbed circular disk. For the smallest disturbances we compare the experimental results to a linear stability analysis, following Schmidt \emph{et al.}, Nat. Phys. 5, 343-346 (2009). Larger disturbances become non-linear in an early stage, showing a wealth of complex phenomena like secondary collapses and jets, during which the initial symmetry corresponding to the mode number $m$ always remains preserved. [Preview Abstract] |
Sunday, November 22, 2009 12:27PM - 12:40PM |
BJ.00010: Collapse of cylindrical vapor cavities in a compressible fluid Derrick Treichler, Ken Kiger The collapse of infinitely long cylindrical vapor cavities in water is studied computationally using Gemini, a compressible hydrocode developed by NSWC/IHD. Simulation results are compared to dynamics given by the cylindrical analogue of the Rayleigh-Plesset equation for spherical bubble dynamics. The results of the incompressible solution~are known to depend on size of the domain due to a logarithmic dependance in the governing equation. ~Compressibility is shown to be a controlling factor in the dynamics of the cavity collapse, both as a means to limit the amount of fluid mass to be accelerated and as a source of radiated energy. As a result, the compressible case reaches an invariant collapse time for fluid domains large enough that acoustic waves traveling outward from the cavity wall are unable to return to the bubble before collapse. Analytical results predict a monotonically increasing collapse time with increasing fluid domain size. Thus, for sufficiently large fluid domains, the analytical solution greatly over-predicts the cavity collapse time given by the computational results. [Preview Abstract] |
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