We study bubble break-up in homogeneous and isotropic turbulence by direct numerical simulations of the two-phase incompressible Navier–Stokes equations. We create the turbulence by forcing in physical space and introduce the bubble once a statistically stationary state is reached. We perform a large ensemble of simulations to investigate the effect of the Weber number (the ratio of turbulent and surface tension forces) on bubble break-up dynamics and statistics, including the child bubble size distribution, and discuss the numerical requirements to obtain results independent of grid size. We characterize the critical Weber number below which no break-up occurs and the associated Hinze scale $d_h$ . At Weber number close to stable conditions (initial bubble sizes $d_0\approx d_h$ ), we observe binary and tertiary break-ups, leading to bubbles mostly between $0.5d_h$ and $d_h$ , a signature of a production process local in scale. For large Weber numbers ( $d_0> 3d_h$ ), we observe the creation of a wide range of bubble radii, with numerous child bubbles between $0.1d_h$ and $0.3d_h$ , an order of magnitude smaller than the parent bubble. The separation of scales between the parent and child bubble is a signature of a production process non-local in scale. The formation mechanism of these sub-Hinze scale bubbles relates to rapid large deformation and successive break-ups: the first break-up in a sequence leaves highly deformed bubbles which will break again, without recovering a spherical shape and creating an array of much smaller bubbles. We discuss the application of this scenario to the production of sub-Hinze bubbles under breaking waves.
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Simultaneous measurements of deforming Hinze-scale bubbles with surrounding turbulence
We experimentally investigate the breakup mechanisms and probability of Hinze-scale bubbles in turbulence. The Hinze scale is defined as the critical bubble size based on the critical mean Weber number, across which the bubble breakup probability was believed to have an abrupt transition from being dominated by turbulence stresses to being suppressed completely by the surface tension. In this work, to quantify the breakup probability of bubbles with sizes close to the Hinze scale and to examine different breakup mechanisms, both bubbles and their surrounding tracer particles were simultaneously tracked. From the experimental results, two Weber numbers, one calculated from the slip velocity between the two phases and the other acquired from local velocity gradients, are separated and fitted with models that can be linked back to turbulence characteristics. Moreover, we also provide an empirical model to link bubble deformation to the two Weber numbers by extending the relationship obtained from potential flow theory. The proposed relationship between bubble aspect ratio and the Weber numbers seems to work consistently well for a range of bubble sizes. Furthermore, the time traces of bubble aspect ratio and the two Weber numbers are connected using the linear forced oscillator model. Finally, having access to the distributions of these two Weber numbers provides a unique way to extract the breakup probability of bubbles with sizes close to the Hinze scale.
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- NSF-PAR ID:
- 10212191
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 910
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract From air-sea gas exchange, oil pollution, to bioreactors, the ubiquitous fragmentation of bubbles/drops in turbulence has been modeled by relying on the classical Kolmogorov-Hinze paradigm since the 1950s. This framework hypothesizes that bubbles/drops are broken solely by eddies of the same size, even though turbulence is well known for its wide spectrum of scales. Here, by designing an experiment that can physically and cleanly disentangle eddies of various sizes, we report the experimental evidence to challenge this hypothesis and show that bubbles are preferentially broken by the sub-bubble-scale eddies. Our work also highlights that fragmentation cannot be quantified solely by the stress criterion or the Weber number; The competition between different time scales is equally important. Instead of being elongated slowly and persistently by flows at their own scales, bubbles are fragmented in turbulence by small eddies via a burst of intense local deformation within a short time.
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We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier–Stokes equations, considering a low-density bubble in the high-density turbulent flow at various Weber numbers (the ratio of turbulent and surface tension forces) using the air–water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber numbers, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale.more » « less
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We experimentally investigate the rise velocity of finite-sized bubbles in turbulence with a high energy dissipation rate of $\unicode[STIX]{x1D716}\gtrsim 0.5~\text{m}^{2}~\text{s}^{-3}$ . In contrast to a 30–40 % reduction in rise velocity previously reported in weak turbulence (the Weber number ( $We$ ) is much smaller than the Eötvös number ( $Eo$ ); $We\ll 1We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_{H}$ , the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_{H}$ (probing up to $d_0/d_{H} = 8.3$ ), the size distribution of bubbles smaller than $d_{H}$ follows $N(d) \propto d^{-3/2}$ , with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0/d_{H}$ . Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.933
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