arXiv subjects

Éric Climent

Publications and source records attributed to Éric Climent.

3 recordsLinked to original sources

arXiv2026

Rise regimes of freely rising droplets with a moderate viscosity ratio

The dynamics of buoyant droplets rising freely in a large body of an immiscible liquid is investigated numerically for a moderate drop-to-fluid viscosity ratio $μ^\ast$. We focus on toluene droplets rising in clean water, for which $μ^\ast=0.62$, and vary the radius over $0.5\,\text{mm}\leq R\leq3.0\,\text{mm}$. Direct numerical simulations are performed in imposed axisymmetric and fully three-dimensional configurations. As $R$ increases, the system displays a rich sequence of rise regimes. Starting from steady vertical rise with an axisymmetric disturbance flow, it first undergoes an internal flow instability associated with an azimuthal mode $m=2$, leading to a biplanar-symmetric wake and reduced terminal speed. This state is followed by a steady oblique regime, in which the $m=1$ mode also becomes unstable and coexists with the $m=2$ mode. At larger radii, the path becomes nearly vertical again before the flow enters an $m=2$ rotating-wave regime, where the wake drifts azimuthally at an approximately constant angular velocity. For still larger droplets, persistent shape oscillations and vortex shedding lead to fully three-dimensional chaotic paths. Simulations initialised from finite-amplitude asymmetric states further reveal several multistable size ranges, in which distinct terminal states coexist depending on the initial condition. Taken together, these findings show that the path instability of moderate-viscosity-ratio droplets differs fundamentally from that of bubbles and solid particles: in most regimes encountered here, axisymmetry breaking is initiated within the droplet, highlighting the central role of the internal flow instability in shaping the subsequent wake structure, rise speed and droplet dynamics.

physics.flu-dyn↗

arXiv2025

Flow past a fixed spherical droplet: breaking of axisymmetry by an internal flow bifurcation

Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to determine the parameter range within which the axisymmetric flow becomes unstable. The problem is governed by three dimensionless parameters: the drop-to-fluid dynamic viscosity ratio, $μ^\ast$, and the external and internal Reynolds numbers, $\Rey^e$ and $\Rey^i$, which are defined using the kinematic viscosities of the external and internal fluids, respectively. The present study confirms the existence of a regime at low-to-moderate viscosity ratio where the axisymmetric flow breaks down due to an internal flow instability. In the initial stages of this bifurcation, the external flow remains axisymmetric, while the asymmetry is generated and grows only inside the droplet. As the disturbance propagates outward, the entire flow first transits to a biplanar symmetric flow, characterised by two pairs of counter-rotating streamwise vortices in the wake. A detailed examination of the flow field reveals that the vorticity on the internal side of the droplet interface is driving the flow instability. Specifically, the bifurcation sets in once the maximum internal vorticity exceeds a critical value that decreases with increasing $\Rey^i$. For sufficiently large $\Rey^i$, internal flow bifurcation may occur at viscosity ratios of $μ^\ast = O(10)$, an order of magnitude higher than previously reported values. Finally, we demonstrate that the internal flow bifurcation in the configuration of a fixed droplet in a uniform fluid stream is closely related to the first path instability experienced by a buoyant, deformable droplet of low-to-moderate $μ^\ast$ freely rising in a stagnant liquid.

physics.flu-dyn↗

arXiv2025

Wake instability of a fixed spherical droplet with a high drop-to-fluid viscosity ratio

Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to investigate the parameter range within which the axisymmetric flow becomes unstable due to an external flow bifurcation. The hydrodynamics is governed by three dimensionless numbers: the viscosity ratio, $μ^\ast$, and the external and internal Reynolds numbers, $\Rey^e$ and $\Rey^i$, respectively. The drop-to-fluid density ratio is related to these parameters as $ρ^\ast=μ^\ast \Rey^i/\Rey^e$. This study focuses on highly viscous droplets with $μ^\ast \geq 5$, where wake instability is driven by the vorticity flux transferred from the droplet surface into the surrounding fluid. By analysing the wake structure, we confirm that the onset of the external bifurcation is linked to the tilting of the azimuthal vorticity, $ω_ϕ$, in the wake and that the bifurcation occurs once the isocontours of $ω_ϕ$ align nearly perpendicular to the symmetry axis. We propose an empirical criterion for predicting the onset of the external bifurcation, formulated in terms of the maximum vorticity on the external side of the droplet surface. This criterion is applicable for sufficiently high $\Rey^i$ and holds over a wide range of $μ^\ast$ and $\Rey^e$. Additionally, we examine the bifurcation sequence for two specific external Reynolds numbers, $\Rey^e=300$ and $\Rey^e=500$, and show that, beyond a critical viscosity ratio, the axisymmetric wake first transitions to a steady planar-symmetric state before undergoing a secondary Hopf bifurcation. Finally, we highlight the influence of $\Rey^i$ on external bifurcation and show that, at moderate $\Rey^i$, wake instability may set in at a lower vorticity threshold than predicted by our criterion. These findings provide new insights into the external flow bifurcation of viscous droplets.

physics.flu-dyn↗