arXiv subjects

Aliénor Rivière

Publications and source records attributed to Aliénor Rivière.

7 recordsLinked to original sources

arXiv2025

Deformation and stability of a gas bubble in a biaxial straining flow

Taking advantage of the recently developed L-ALE framework [Sierra-Ausin \textit{et al.}, Phys. Rev. Fluids {\bf{7}}, 113603 (2022)], we characterize the linear dynamics of an incompressible gas bubble immersed in a biaxial straining flow. We show that the system undergoes a saddle-node bifurcation with strongly different equilibrium shapes when varying the Ohnesorge number, $\Oh$, which compares viscous and capillary effects. Equilibrium shapes are found to be oblate for sufficiently large $\Oh$ while, counter-intuitively, they are prolate for low-enough $\Oh$. The bifurcation diagram is found to contain also two sets of disconnected branches that cannot be obtained by continuation starting from a spherical shape. One set corresponds to bubble shapes expected to be unstable, while the second set comprises a wide region exhibiting stable shapes that might be observed in practice. We then characterize the linear stability of the various branches. In addition to the unstable axisymmetric mode arising at the saddle-node bifurcation, two non-oscillating drift modes are also identified, together with a new unstable non-oscillating mode with azimuthal wave number $m=2$. This mode might be responsible for some type of bubble breakup observed in experiments.

physics.flu-dyn↗

arXiv2025

Breakup cascade in gas filament

Despite its importance in both geophysical and industrial contexts, the inertial fragmentation of gas filaments has received much less attention than their liquid counterparts. Yet, gas filaments produce the smallest bubble sizes, which drive gas dissolution, critical to ocean-atmosphere exchange such as carbon dioxide and oxygen, as well as marine aerosols emission, serving as nuclei for cloud condensation and ice particle production. Here, we unravel the fundamental physics governing the splitting of a single filament in a model geometry by combining numerical simulations, laboratory experiments and theory. We show that the splitting of a single filament generates a power-law bubble size distribution following $d^{-3/2}$ with $d$ the volume equivalent bubble diameter, suggesting the existence of a self-similar breakup mechanism, absent in liquid ligament fragmentation. We propose a deterministic model, based on the capillary fragmentation of a filament with power-law shape, which quantitatively captures the bubble size distribution. We demonstrate that the filament shape at breakup sets the size distribution of a first generation of bubbles. This distribution is then reproduced at smaller and smaller scales by latter breakups in a self-similar manner. The $d^{-3/2}$-distribution coincides with the size distribution of small bubbles observed in dilute turbulent flow, such as below breaking waves. We argue that the turbulent bubble size distribution observed in nature arises as the superposition of many individual filament splittings. The turbulence nature of the flow only sets the initial conditions of each splitting dynamics, and play no role in the bubble size selection.

physics.flu-dyn↗

arXiv2025

Bubble breakup probability in turbulent flows

Bubbles drive gas and chemical transfers in various industrial and geophysical contexts, in which flows are typically turbulent. As gas and chemical transfers are bubble size dependent, their quantification requires a prediction of bubble breakup. The most common idea, introduced by Kolmogorov and Hinze, is to consider a sharp limit between breaking and non breaking bubbles, given by $\mathrm{We}_c\approx 1$, where the Weber number $\mathrm{We}$ is the ratio between inertial and capillary forces at the bubble scale. Yet, due to the inherent stochasticity of the flow every bubble might in reality break. In this work, we use a stochastic linear model previously developed to infer the breakup probability of bubbles in turbulence as function of both We and the residence time. This allows us to introduce a definition of the critical Weber number accounting for the time spent by bubbles within a turbulent region. We show that bubble breakup is a memoryless process, whose breakup rate varies exponentially with $\mathrm{We}^{-1}$. The linear model successfully reproduces experimental breakup rates from the literature. We show that the stochastic nature of bubble breakup is central when the residence time of bubbles is smaller than ten correlation times of turbulence at the bubble scale: the transition between breaking and non breaking bubbles is smooth and most bubbles can break. For large residence times, the original vision of Kolmogorov and Hinze is recovered.

physics.flu-dyn↗

arXiv2024

Bubble shape oscillations in a turbulent environment

We investigate bubble deformations in an homogeneous and isotropic turbulent flow by means of direct numerical simulations of a single bubble in turbulence. We examine interface deformations by decomposing the local radius into the spherical harmonics base. We show that the linear dynamics of each mode, (for low Weber number), can be modeled by a forced stochastic linear oscillator. We measure the coefficients of the model directly from the modes' statistics. We find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, dissipation increases by a factor 15 compared to the quiescent case, at $Re_λ= 55$. This enhanced dissipation originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the integration of pressure over the bubble surface, is independent on bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. Eventually, we investigate the pressure modes' statistics in the absence of bubbles and compare them to the effective forcing statistics. We show that both fields share the same pdf, characterized by exponential tails, and a characteristic timescale corresponding to the eddy turnover time at the mode scale.

physics.flu-dyn↗

arXiv2024

Phase transition to turbulence via moving fronts

Directed percolation (DP), a universality class of continuous phase transitions, has recently been established as a possible route to turbulence in subcritical wall-bounded flows. In canonical straight pipe or planar flows, the transition occurs via discrete large-scale turbulent structures, known as puffs in pipe flow or bands in planar flows, which either self-replicate or laminarize. However, these processes might not be universal to all subcritical shear flows. Here, we design a numerical experiment that eliminates discrete structures in plane Couette flow and show that it follows a different, simpler transition scenario: turbulence proliferates via expanding fronts and decays via spontaneous creation of laminar zones. We map this phase transition onto a stochastic one-variable system. The level of turbulent fluctuations dictates whether moving-front transition is discontinuous, or continuous and within the DP universality class, with profound implications for other hydrodynamic systems.

physics.flu-dyn↗

arXiv2022

Experimental observations and modeling of sub-Hinze bubble production by turbulent bubble break-up

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_\mathrm{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_\mathrm{H}$ (probing up to $d_0 / d_\mathrm{H} = 8.3$), the size distribution of bubbles smaller than $d_\mathrm{H}$ 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 ones. 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 $d_0 / d_\mathrm{H}$. 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.

physics.flu-dyn↗

arXiv2021

Bubble deformation by a turbulent flow

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 number (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 number, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale.

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