arXiv subjects

Dominique Legendre

Publications and source records attributed to Dominique Legendre.

9 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 $\mu^\ast$. We focus on toluene droplets rising in clean water, for which $\mu^\ast=0.62$, 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, $\mu^\ast$, 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 $\mu^\ast = O(10)$, 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 $\mu^\ast$ 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, $\mu^\ast$, 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 $\rho^\ast=\mu^\ast \Rey^i/\Rey^e$. This study focuses on highly viscous droplets with $\mu^\ast \geq 5$, 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, $\omega_\phi$, in the wake and that the bifurcation occurs once the isocontours of $\omega_\phi$ 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 $\mu^\ast$ 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↗

arXiv2025

Gas bubble dynamics

The study of gas bubble dynamics in liquids is justified by the numerous applications and natural phenomena where this two-phase flow is encountered. Gas bubbles move as forces are applied to them; their dynamics are full of nuances that need to be addressed carefully. Since the mass of gas bubbles is practically negligible, in comparison to that of the surrounding liquid, their reaction to the fluid is controlled by the added mass acceleration and is thus impacted by all the forces arising from the fluid action. Furthermore, since their surface can be deformed by the same forces acting on them, their shape may change leading to changes in their resistance to move, the drag force, and therefore affecting their speed and their interaction with the surrounding flow which is often turbulent. The liquid rheology, as well as its surfactant content can also affect the bubble shape and motion as well. Understanding these issues, in addition to the effect of interactions with other bubbles, walls, and non-uniform flows, provides sufficient elements to model and predict bubble behavior through the solution of dynamic equations. In this review, we cover the key aspects of non-condensable gas bubble dynamics. We survey classical references on the subject and provide an overview of the main findings in the past 20 years. We conclude with a scope and suggestions for future research directions, with special attention to the dynamics of bubble in turbulence, in non-Newtonian fluid and/or in the presence of electrolytes.

physics.flu-dyn↗

arXiv2022

The presence of surfactants controls the stability of bubble chains in carbonated drinks

Bubbles appear when a carbonated drink is poured in a glass. Very stable bubble chains are clearly observed in champagne, showing an almost straight line from microscopic nucleation sites from which they are continuously formed. In some other drinks such as soda, such chains are not straight (not stable). Considering pair interactions for spherical clean bubbles, bubble chains should not be stable which contradicts these observations. The aim of this work is to explain the conditions for bubble chain stability. For this purpose, experiments and direct numerical simulation are conducted. The bubble size as well as the level of interface contamination are varied, to match the range of parameters in typical drinks. Both factors are shown to affect the bubble chain stability. The transition from stable to ustable behavior results from the reversal of the lift force, which is induced by the bubble wake. A criteria based on the production of vorticity at the bubble surface is proposed to identify the conditions of transition from stable to unstable bubble chains. Beyond carbonated drinks, understanding bubble clustering has impact in many two-phase problems of current importance.

physics.flu-dyn↗

arXiv2022

How does gravity influence freezing dynamics of drops on a solid surface

Water droplet freezing is a common phenomenon in our daily life. In both natural scenarios and industrial production, different surface inclinations bring distinctive deformation and freezing dynamics to frozen droplets. We explore the freezing of pendent and sessile droplets at different Bond number regimes. The effect of gravity on the droplet freezing process is analyzed by considering droplet morphology, freezing front dynamics, and freezing time. It is found that gravity can significantly influence droplet freezing processes via shaping the initial droplet, resulting in the flattening or elongation of pendent and sessile droplets, respectively. We show that the droplet initial geometry is the most important parameter and it completely controls the droplet freezing. Despite the significant difference in the initial droplet shape several remarkable similarities have been found for pendent and sessile droplets at small and large Bond numbers. The final height of a frozen droplet is found to be linearly proportional to its initial height. The time evolution of the ice-liquid-air contact line is found to reproduce the power-law $t^{0.5}$, but noticeably faster than the Stefan 1-D icing front propagation. As a consequence, the time to freeze a droplet is faster than predicted by the Stefan model and it is found to be dependent on the initial droplet height and base radius through a simple power-law.

physics.flu-dyn↗

arXiv2021

How molecular effects affect solutal Marangoni convection

Interfacial tension gradients drive flow along liquid-liquid interfaces in a process known as the Marangoni effect. Such gradients can be caused by surfactants, which has been extensively studied in the literature. Less is known of its nanoscale properties, where molecular interfaces display properties separate from bulk liquid matter such as interfacial viscosity. In this report we study the molecular solutal Marangoni effect using molecular dynamics simulations. We show that molecular interfacial effects are important and should be accounted for in nanofluidic regimes. Hydrodynamic models can be extended with effective terms which include them.

physics.flu-dyn↗

arXiv2016

Van der Waals interaction between a moving nano-cylinder and a liquid thin film

We study the static and dynamic interaction between a horizontal cylindrical nano-probe and a thin liquid film. The effects of the physical and geometrical parameters, with a special focus on the film thickness, the probe speed, and the distance between the probe and the free surface are analyzed. Deformation profiles have been computed numerically from a Reynolds lubrication equation, coupled to a modified Young-Laplace equation, which takes into account the probe/liquid and the liquid/substrate non-retarded van der Waals interactions. We have found that the film thickness and the probe speed have a significant effect on the threshold separation distance below which the jump-to-contact instability is triggered. These results encourage the use of horizontal cylindrical nano-probes to scan thin liquid films, in order to determine either the physical or geometrical properties of the latter, through the measurement of interaction forces.

cond-mat.mes-hall↗

arXiv2009

Influence of slip on the dynamics of two-dimensional wakes

We study numerically the two-dimensional flow past a circular cylinder as a prototypical transitional flow, and investigate the influence of a generic slip boundary condition on the wake dynamics. We show that slip significantly delays the onset of recirculation and shedding in the wake behind the cylinder. As expected, the drag on the cylinder decreases with slip, with an increased drag sensitivity for large Reynolds numbers. We also show that past the critical shedding Reynolds number, slip decreases the vorticity intensity in the wake, as well as the lift forces on the cylinder, but increases the shedding frequency. We further provide evidence that the shedding transition can be interpreted as a critical accumulation of surface vorticity, similarly to related studies on wake instability of axisymmetric bodies. Finally, we propose that our results could be used as a passive method to infer the effective friction properties of slipping surfaces.

physics.flu-dyn↗