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Microplastics are globally ubiquitous in marine environments, and their concentration is expected to continue rising at significant rates as a result of human activity. They present a major ecological problem with well-documented environmental harm. Sea spray from bubble bursting can transport salt and biological material from the ocean into the atmosphere, and there is a need to quantify the amount of microplastic that can be emitted from the ocean by this mechanism. We present a mechanistic study of bursting bubbles transporting microplastics. We demonstrate and quantify that jet drops are efficient at emitting microplastics up to 280μm in diameter and are thus expected to dominate the emitted mass of microplastic. The results are integrated to provide a global microplastic emission model which depends on bubble scavenging and bursting physics; local wind and sea state; and oceanic microplastic concentration. We test multiple possible microplastic concentration maps to find annual emissions ranging from 0.02 to 7.4—with a best guess of 0.1—mega metric tons per year and demonstrate that while we significantly reduce the uncertainty associated with the bursting physics, the limited knowledge and measurements on the mass concentration and size distribution of microplastic at the ocean surface leaves large uncertainties on the amount of microplastic ejected.

 

We 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. 

Breaking waves modulate the transfer of energy, momentum, and mass between the ocean and atmosphere, controlling processes critical to the climate system, from gas exchange of carbon dioxide and oxygen to the generation of sea spray aerosols that can be transported in the atmosphere and serve as cloud condensation nuclei. The smallest components, i.e., drops and bubbles generated by breaking waves, play an outsize role. This fascinating problem is characterized by a wide range of length scales, from wind forcing the wave field at scales of [Formula: see text](1 km–0.1 m) to the dynamics of wave breaking at [Formula: see text](10–0.1 m); air bubble entrainment, dynamics, and dissolution in the water column at [Formula: see text](1 m–10 μm); and bubbles bursting at [Formula: see text](10 mm–1 μm), generating sea spray droplets at [Formula: see text](0.5 mm–0.5 μm) that are ejected into atmospheric turbulent boundary layers. I discuss recent progress to bridge these length scales, identifying the controlling processes and proposing a path toward mechanistic parameterizations of air–sea mass exchange that naturally accounts for sea state effects. 

We investigate how turbulence in liquid affects the rising speed of gas bubbles within the inertial range. Experimentally, we employ stereoscopic tracking of bubbles rising through water turbulence created by the convergence of turbulent jets and characterized with particle image velocimetry performed throughout the measurement volume. We use the spatially varying, time-averaged mean water velocity field to consider the physically relevant bubble slip velocity relative to the mean flow. Over a range of bubble sizes within the inertial range, we find that the bubble mean rise velocity $\left \langle v_z \right \rangle$ decreases with the intensity of the turbulence as characterized by its root-mean-square fluctuation velocity, $u'$ . Non-dimensionalized by the quiescent rise velocity $v_{q}$ , the average rise speed follows $\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ at high ${\textit {Fr}}$ , where ${\textit {Fr}}=u'/\sqrt {dg}$ is a Froude number comparing the intensity of the turbulence to the bubble buoyancy, with $d$ the bubble diameter and $g$ the acceleration due to gravity. We complement these results by performing numerical integration of the Maxey–Riley equation for a point bubble experiencing nonlinear drag in three-dimensional, homogeneous and isotropic turbulence. These simulations reproduce the slowdown observed experimentally, and show that the mean magnitude of the slip velocity is proportional to the large-scale fluctuations of the flow velocity. Combining the numerical estimate of the slip velocity magnitude with a simple theoretical model, we show that the scaling $\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ originates from a combination of the nonlinear drag and the nearly isotropic behaviour of the slip velocity at large ${\textit {Fr}}$ that drastically reduces the mean rise speed. 

Bubble-mediated gas exchange in turbulent flow is critical in bubble column chemical reactors as well as for ocean–atmosphere gas exchange related to air entrained by breaking waves. Understanding the transfer rate from a single bubble in turbulence at large Péclet numbers (defined as the ratio between the rate of advection and diffusion of gas) is important as it can be used for improving models on a larger scale. We characterize the mass transfer of dilute gases from a single bubble in a homogeneous isotropic turbulent flow in the limit of negligible bubble volume variations. We show that the mass transfer occurs within a thin diffusive boundary layer at the bubble–liquid interface, whose thickness decreases with an increase in turbulent Péclet number, $\widetilde {{Pe}}$ . We propose a suitable time scale $\theta$ for Higbie ( Trans. AIChE , vol. 31, 1935, pp. 365–389) penetration theory, $\theta = d_0/\tilde {u}$ , based on $d_0$ the bubble diameter and $\tilde {u}$ a characteristic turbulent velocity, here $\tilde {u}=\sqrt {3}\,u_{{rms}}$ , where $u_{{rms}}$ is the large-scale turbulence fluctuations. This leads to a non-dimensional transfer rate ${Sh} = 2(3)^{1/4}\sqrt {\widetilde {{Pe}}/{\rm \pi} }$ from the bubble in the isotropic turbulent flow. The theoretical prediction is verified by direct numerical simulations of mass transfer of dilute gas from a bubble in homogeneous and isotropic turbulence, and very good agreement is observed as long as the thin boundary layer is properly resolved. 

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. 

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.