arXiv subjects

Christophe Josserand

Publications and source records attributed to Christophe Josserand.

At least 19 recordsLinked to original sources

arXiv2026

Superflows around corners

We investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, we focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, we show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. For both wall and well configurations, we identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding an excellent agreement between the theory and our numerical simulations. Our results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features and are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems.

cond-mat.quant-gas↗

arXiv2026

Morphology of ice structures induced by a freezing rivulet

We investigate the solidification of a water rivulet flowing over a cold inclined substrate and the resulting formation of three-dimensional ice structures. Using a controlled hydraulic and thermal setup, combined with spatiotemporal phase-shifting profilometry and infrared thermography, we characterize both the transient evolution and the final morphology of the ice. We show that a typical experiment proceeds through three stages: formation of a straight ice ridge that stabilizes the rivulet, destabilization and lateral excursions of the flow leading to rapid transverse spreading of the ice structure, and progressive thickening and smoothing of the ice block. Across a wide range of flow rates, inclinations and thermal conditions, the final morphology comprises an upstream triangular lateral envelope, followed by a downstream region of nearly constant width once the substrate edges are reached. Infrared measurements reveal that the rivulet residence time on the substrate follows a Gaussian distribution in the azimuthal angle, implying that the central region of the structure is visited far more frequently than its lateral edges. Focusing on the domain where the height has converged at the end of the experiments, we develop a two-dimensional theoretical model that couples a hydrodynamic model for the rivulet geometry with heat transport in both liquid and solid phases. In the large Péclet number limit, the model predicts an exponential increase of the stationary ice height along the flow direction and it shows an excellent agreement with the experimental height field. We further show how the combination of the stationary height profile and the non-uniform residence time distribution controls the angular convergence of the ice cross-sections.

physics.flu-dyn↗

arXiv2025

Birth of a bubble: Drop impact onto a thin liquid film for an immiscible three-fluid system

When a drop impacts a solid substrate or a thin liquid film, a thin gas disc is entrapped due to surface tension, the gas disc retracts into one or several bubbles. While the evolution of the gas disc for impact on solid substrate or film of the same fluid as the drop have been largely studied, little is known on how it varies when the liquid of the film is different that of the drop. We study numerically the latter unexplored area, focussing on the contact between the drop and the film, leading to the formation of the air bubble. The volume of fluid method was adapted to three fluids in the framework of Basilisk solver. The numerical simulations show that the deformation of the liquid film due to the air cushioning plays a crucial role in the bubble entrapment. A new model for the contact time and the entrapment geometry was deduced from the case of the impact on a solid substrate. This was done by considering the deformation of the thin immiscible liquid layer during impact depending mainly on its thickness and viscosity. The lubrication of the gas layer was found to be the major effect governing the bubble entrapment. However the film viscosity was also identified as having a critical role in bubble formation and evolution; the magnitude of its influence was also quantified.

physics.flu-dyn↗

arXiv2025

Geometry-driven jets underlie dispersal of plants and fungi by raindrops

The impact of droplets on concave surfaces is poorly understood, although it is relevant to a mode of dispersal that has evolved independently in several species of plants and fungi. This mode relies on splash-cups, specialized organs that use raindrops to disperse reproductive units away from the parent organism. We investigated the impact of droplets on conical cavities that mimic splash-cups and we found that such impact may lead to the formation of two types of jets, which appear essential for dispersal in nature. We built a minimal kinematic model that explains jet formation, involving the motion of fluid particles along geodesics (shortest paths) on the cone surface and we predicted cone angles that optimize jet formation, consistent with the geometries of natural splash-cups

physics.flu-dyn↗

arXiv2025

Crystal growth at a liquid-liquid interface upon drop impact

The crystallisation that occurs when a drop is placed in contact with a cold surface is a particularly challenging phenomenon to capture experimentally and describe theoretically. The situation of a liquid-liquid interface, where crystals appear on a mobile interface is scarcely studied although it provides a defect-free interface. In this paper, we quantify the dynamics of crystals appearing upon the impact of a drop on a cool liquid bath. We rationalize our observations with a model considering that crystals appear at a constant rate depending on the thermal shock on the expanding interface. This model provides dimensionless curves on the number and the surface area of crystals that we compare to our experimental measurements.

physics.flu-dyn↗

arXiv2025

Free surface topography of capillary flows using spatiotemporal phase shifting profilometry

We present a novel experimental technique to characterize the free surface of capillary flows adapted from the Spatio-Temporal Phase Shifting Profilometry (ST-PSP) method introduced by Ri et al. (Journal of Optics, 2019) for solid bodies. The present study is focused on various regimes of capillary flows over inclined surfaces, including drops, rivulets, meanders, and braided films. A calibration process is carried out using a solid wedge to determine the optical distances required for the phase-to-height relationship. The optimal dye concentration necessary for accurately reconstructing the free surface of a dyed water flow is explored. The ST-PSP method is then applied to profile different liquid flows and objects, achieving large signal-to-noise ratios across all experiments. Notably, the analysis of a sessile droplet shows a promising correlation between the ST-PSP results and side-view visualizations, as evidenced by the accurate recovery of its apparent contact angle. Furthermore, free surface reconstructions of rivulet flows exhibit good agreement with the theoretical predictions of Duffy and Moffatt (The Chemical Engineering Journal and the Biochemical Engineering Journal, 1995). These results suggest that the ST-PSP method is highly effective for obtaining accurate height maps of capillary flows and objects, making it a valuable tool for validating theoretical models in the future.

physics.flu-dyn↗

arXiv2025

A mixing length model for arbitrary geometry: the case of parallel flows

We present a phenomenological model for the mixing length used in turbulence models. It has the advantage of naturally accounting for the object's geometry while satisfying the standard symmetries of the Navier-Stokes equations. We employ the model to study channel flow and pipe flow. We calibrate the three model parameters to recover the damping in the viscous sub-layer, the log-law of the wall, and the outer region behaviors. Our model compares favorably to friction factor measurements in the pipe flow at high Reynolds numbers and gives analytical predictions of the mixing length for several canonical flows.

physics.flu-dyn↗

arXiv2024

On the shape of ice stalagmites

The growth of ice stalagmites obtained by the solidification of impacting droplets on a cooled substrate ($-50^{\circ}$C to $-140^{\circ}$C) is investigated experimentally. It is shown that for any combination of substrate temperature and drop discharge, there is a critical height above which unfrozen water accumulates at the stalagmite's tip, drips and develops into fingers that give a star-shape to the stalagmite. Both the vertical growth and the radial growth of the stalagmite are discussed through the Stefan problem and mass scaling arguments respectively. Finally, a phase diagram that presents the stalagmite aspect ratio in function of the main control parameters is proposed.

physics.flu-dyn↗

arXiv2024

Role of melting and solidification in the spreading of an impacting water drop

The present study reports experiments of water droplet impacting on ice or on a cold metallic substrate, with the aim of understanding the effect of phase change on the impingement process. Both liquid and substrate temperatures are varied, as well as the height of fall. The dimensionless maximum spreading diameter, $β_m$, is found to increase with both temperatures as well as with the impact velocity. Furthermore, $β_m$ is reduced when solidification, which enhances dissipation, is present, whereas fusion favours the liquid film spreading. These observations are rationalized by extending an existing model of effective viscosity, in which phase change alters the size and shape of the developing viscous boundary layer, thereby modifying the value of $β_m$. The use of this correction allows to adapt a scaling law existing for isothermal drop impacts to propose a universal law giving the maximum diameter of an impacting water droplet in the presence of melting or solidification.

physics.flu-dyn↗

arXiv2024

Flat-cupped transition in freezing drop impacts

We present an experimental study on the freezing of alkane drops impacted on a liquid bath. More specifically, for drops of hexadecane and tetradecane on brine, we found a morphological transition of the solid between a flat disk and a cupped shape. We show that this transition depends mainly on melting temperature and thermal shock, and varies weakly with impact velocity. We observed that the impact dynamics does not depend on the thermal shock before the drop starts to solid ify, which allows a rationalization of the solid size by models established for impact without phase change. Finally, we show that the relevant timescale setting the onset of solidification is associated with the formation of a thin solid layer between the drop and the bath, a timescale much shorter than the total solidification time. These findings offer the possibility to collapse the data for both liquids in a single phase diagram.

cond-mat.soft↗

arXiv2024

Freezing receding contact lines

We investigate experimentally the receding of a contact line when a Peltier module is pulled out of a water bath at constant speed, while a ice layer is also growing at constant speed on the Peltier module. A steady regime is therefore reached for all the parameters used in this studied, corresponding to a dynamical stationnary meniscus. We show that the height of the meniscus provides most of the properties of the flow. For high pulling rate, it is related to the amount of liquid of the equivalent Landau-Levich (LL) film that would be extracted from the bath, which is eventually freezing as the plate is lifted upward. For smaller velocity, so that no LL film would be formed without freezing, the meniscus height is directly linked to the contact angle of water on ice in these conditions. Solving numerically the meniscus equation taking into account the solidifcation of water, our results suggest that the contact angle of water on ice should be around $6^\circ$.

physics.flu-dyn↗

arXiv2024

A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor-Couette test case. To impose the boundary condition when the fluid-fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.

physics.flu-dyn↗

arXiv2023

Three-dimensional flow around and through a porous screen

We investigate the three-dimensional flow around and through a porous screen for various porosities at high Reynolds number Re = O(10000). Historically, the study of this problem was focused on two-dimensional cases and for a screen spanning completely or partially a channel. Since many recent problems have involved a porous object in a three-dimensional free flow, we present a three-dimensional model for porous screens, initially based on Koo & James (1973) and Steiros & Hultmark (2018), accounting for viscous effects at the vicinity of the screen, from which we can derive velocities, pressure distribution as well as aerodynamic forces. We then characterize experimentally the aerodynamic drag coefficient for a porous square screen, composed of fibers, immersed in a laminar air flow with different angles of attack. We test various fiber diameters to explore the effect of the space between the pores on the drag force. The drag prediction from the model is in good agreement with our experimental results. Our theoretical and experimental results suggest that for high solidity, a homogeneous porous screens composed of fibers can have a higher drag coefficient than a flat plate with the same dimensions. We also show that local viscous effects are important: at the same solidity and with the same air flow, the drag coefficient strongly depends on the Reynolds number based on the fiber diameter. The model, taking into account three-dimensional effects and the shape of the porous screen, may have many applications including the prediction of water collection efficiency for fog harvesters.

physics.flu-dyn↗

arXiv2022

Rheotaxis of chiral bacteria: from single-cell behavior to a population-level description

Due to their morphology, the dynamics of bacteria suspended in media can exhibit complex behaviors. In the presence of a shear, swimming bacteria experience a drift perpendicular to the shear plane. This drift, termed rheotaxis, is studied here semi-analytically, numerically and experimentally. We find the dependency of bacterial orientation and bacterial speed on the shear rate, in the presence of rotational diffusion. This enables us to show that the drift speed of bacteria perpendicular to the shear is predominantly due to bacterial propulsion, and not rheotactic forces. Comparing the drift speed of bacteria and diffusion leads to the definition of a Péclet number. The rheotactic effect increases with the shear, reaching a plateau at very large Péclet numbers, in good agreement with experiments of rheotaxis performed in microfluidic droplets.

cond-mat.soft↗

arXiv2021

Singular jets in compound drop impact

Compound drop impacting on a solid surface is of considerable importance in industrial applications, such as combustion, food industry, and drug encapsulation. An intriguing phenomenon associated with this process is the occurrence of singular jets that are up to dozens of times faster than the impact velocity. These jets break into micro-droplets, which can produce aerosols and affect the quality of printing technologies. Here, we investigate experimentally and numerically the jetting process after a coaxial water-in-oil compound drop impacts on a glass substrate with different releasing heights and volumetric ratios. After impact, the water core spreads and retracts, giving rise to a vertical jet initially made of oil. For certain values of the impacting velocity, high speed and very thin jets are observed, the so-called singular jets. Depending on the volumetric ratio, one or two velocity peaks can be observed when varying the impact velocity, triggered by the contraction dynamics of a deep and cylindrical cavity. The self-similar time-evolution of the collapse for the first singularity regime follows a 1/2 power law in time, which can be derived from bubble pinch-off. In contrast, the collapse at the second peak follows a 2/3 power law, which can be accounted for by a balance between inertial and capillary forces.

physics.flu-dyn↗

arXiv2020

Freezing-damped impact of a water drop

We experimentally investigate the effect of freezing on the spreading of a water drop. Whenever a water drop impacts a cold surface, whose temperature is lower than 0°C, a thin layer of ice grows during the spreading. This freezing has a notable effect on the impact: at given Reynolds and Weber numbers, we show that lowering the surface temperature reduces the drop maximal extent. Using an analogy between this ice layer and the viscous boundary layer, which also grows during the spreading, we are able to model the effect of freezing as an effective viscosity. The scaling laws designed for viscous drop impact can therefore be applied to such a solidification problem, avoiding the recourse to a full and complex modelling of the thermal dynamics.

physics.flu-dyn↗

arXiv2020

Dimple drainage before the coalescence of a droplet deposited on a smooth substrate

Thin liquid or gas films are everywhere in nature, from foams to submillimetric bubbles at a free surface, and their rupture leaves a collection of small drops and bubbles. However, the mechanisms at play responsible for the bursting of these films is still in debate. The present study thus aims at understanding the drainage dynamics of the thin air film squeezed by gravity between a millimetric droplet and a smooth solid or a liquid thin film. Solving coupled lubrication equations and analyzing the dominant terms in the solid and liquid film cases, we explain why the drainage is much faster in the liquid film case, leading often to a shorter coalescence time, as observed in recent experiments.

physics.flu-dyn↗

arXiv2020

Solidification of a rivulet: shape and temperature fields

The freezing of a water rivulet begins with a water thread flowing over a very cold surface, is naturally followed by the growth of an ice layer and ends up with a water rivulet flowing on a static thin ice wall. The structure of this final ice layer presents a surprising linear shape that thickens with the distance. This paper presents a theoretical model and experimental characterisation of the ice growth dynamics, the final ice shape and the temperature fields. In a first part, we establish a 2D model, based on the advection-diffusion heat equations, that allows us to predict the shape of the ice structure and the temperature fields in both the water and the ice. Then, we study experimentally the formation of the ice layer and we show that both the transient dynamics and the final shape are well captured by the model. In a last part, we characterise experimentally the temperature fields in the ice and in the water, using an infrared camera. The model shows an excellent agreement with the experimental fields. In particular, it predicts well the linear decrease of the water surface temperature observed along the plane, confirming that the final ice shape is a consequence of the interaction between the thermal boundary layer and the free surface.

physics.flu-dyn↗