Papers by emmanuel villermaux
HAL (Le Centre pour la Communication Scientifique Directe), Sep 13, 2016
International audienc
Bulletin of the American Physical Society, Nov 20, 2017
Liquid rims collisions and the formation of fines BAPTISTE N ÉEL,
Bulletin of the American Physical Society, Nov 19, 2012
Richardson Dispersion in Brownian Motion EMMANUEL VILLER-MAUX, Aix Marseille University, JEROME D... more Richardson Dispersion in Brownian Motion EMMANUEL VILLER-MAUX, Aix Marseille University, JEROME DUPLAT, Universite Joseph Fourier -Since Langevin, the Brownian motion of a microscopic particle explicitly accounts for a short-time correlated "thermal" force. The motion is ballistic, x 2 ∼ t 2 at short time scales, and diffusive x 2 ∼ t at long time scales, where x is the displacement of the particle during time t, and the average is taken over the thermal distribution of initial conditions. High Reynolds number turbulence is known to exhibit a régime called Richardson dispersion, in which the relative separation δx of material particles grows super-diffusively. Namely, δx 2 ∼ t 3 , with the average taken over many particles released from the same initial conditions. We show that Richardson dispersion is indeed property of Brownian motion, under the condition that the initial velocity is fixed rather than distributed thermally. We analyze the motion of an optically trapped particle in air, and indeed find t 3 dispersion. This super-diffusive régime, unveiled here, is the direct proof of the existence of the random, rapidly varying force imagined by Langevin, and reveals a profound similarity between molecular diffusion at microscopic scales and turbulent diffusion at much larger scales.
Journal of Fluid Mechanics, Nov 10, 2022
The advection-diffusion of a small surface element of scalar in three dimensions (or of a small l... more The advection-diffusion of a small surface element of scalar in three dimensions (or of a small line element in two dimensions) is solved analytically thanks to the Ranz transform (Ranz,
APS Division of Fluid Dynamics Meeting Abstracts, Nov 1, 1999
The stirring and mixing properties of one phase coaxial jets, with large outer (annular) to inner... more The stirring and mixing properties of one phase coaxial jets, with large outer (annular) to inner velocity ratio ru = u_2/u1 are investigated. Mixing is contemplated according to its geometrical, statistical and spectral facets with a particular attention paid at determining the relevant timescales of the evolution of e.g. the interface area generation between the streams, the emergence of its scale-dependent (fractal) properties and of the mixture composition after the mixing transition. The two key quantities are the vorticity thickness of the outer, fast stream velocity profile which determines the primary shear instability wavelength and the initial size of the lamellar structures peeled-off from the slow jet, and the elongation rate gamma = u_2-u_1\overe constructed with the velocity difference between the streams and the gap thickness e of the annular jet. The mixing time t_s, that is the time needed to bring the initial scalar lamellae down to a transverse size where molecular diffusion becomes effective, and the corresponding dissipation scale s(t_s) are ts ~ Sc^1/5\overgamma and s(t_s) ~ eRe-1/2Sc-2/5, where Re and Sc denote the gap Reynolds number and the Schmidt number, respectively. The persistence of the large scale straining motion is also apparent from the spectra of the scalar fluctuations which exhibit a k-1 shape on the inertial range of scales.
HAL (Le Centre pour la Communication Scientifique Directe), 2019
International audienc
Bulletin of the American Physical Society, Nov 22, 2015
Mixing in sheared suspensions REGIS TURUBAN, HENRI LHUISSIER, BLOEN METZGER, IUSTI CNRS UMR 7343 ... more Mixing in sheared suspensions REGIS TURUBAN, HENRI LHUISSIER, BLOEN METZGER, IUSTI CNRS UMR 7343 Marseille France, GEP TEAM -Mixing occurs spontaneously in sheared suspensions even at low Reynolds number. The presence of particles induces disorder which lead to exponential elongations within the fluid: concentration levels thus quickly spread and decay. We experimentally characterize the evolution of the concentration PDFs of a blob of fluorescent dye initially injected in an index-matched suspension. High precision optical imaging technics reveal for the first time the finnest spatial details of the concentration field possibly generated by this chaotic flow (Batchelor scales). We find that at short times, the evolution of the concentration PDFs are correctly predicted by a model based solely on the stretching kinematics. At longer times, we show that to predict the experimental observations, the model should also include the effect of coalescence between adjacent lamellae of dye.
Bulletin of the American Physical Society, Nov 22, 2015
Bulletin of the American Physical Society, Nov 19, 2012
Mixing properties of stationary flows in porous media MIHKEL KREE, EMMANUEL VILLERMAUX, Aix Marse... more Mixing properties of stationary flows in porous media MIHKEL KREE, EMMANUEL VILLERMAUX, Aix Marseille University -The interplay between stretching of fluid particles and molecular diffusion leads to enhanced mixing of scalar concentration fields, like in random, turbulent flows. Similarly, the flow in a porous medium develops high strain rates due to the no-slip boundary condition at solid surfaces, altering substantially molecular mixing. We report here on experiments of mixing by a stationary flows in a three-dimensional random stack of solid spheres. Two distinctive fluorescent dyes (with concentrations C 1 and C 2 ) are injected from separate sources and their evolution through the medium is directly observed, this being made possible by matching the refractive indices of the spheres and of the flowing liquid. We quantify the dispersion, concentration distributions, and correlation between the two fields as a function of downstream distance. The value of initially negative correlation coefficient asymptotically reaches zero, meaning that the overall field C 1 + C 2 is a random superposition of the individual fields. The relevant time (distances) scales for mixing are identified.
Many transport processes occurring in fluid flows depend on concentration gradients, including a ... more Many transport processes occurring in fluid flows depend on concentration gradients, including a wide range of chemical reactions, such as mixing-driven precipitation, and biological processes, such as chemotaxis. A general framework for predicting the distribution of concentration gradients in heterogeneous flow fields is proposed based on a disaggregation theory. The evolution of concentration fields under the combined action of heterogeneous advection and diffusion is quantified from the analysis of the development and aggregation of elementary lamellar structures, which naturally form under the stretching action of flow fields. Therefore spatial correlations in concentrations can be estimated based on the understanding of the lamellae aggregation process that determine the concentration levels at neighboring spatial locations. Using this principle we quantify the temporal evolution of the concentration gradient Probability Density Functions in heterogeneous Darcy fields for arbitrary Peclet numbers. This approach is shown to provide accurate predictions of concentration gradient distributions for a range of flow systems, including turbulent flows and low Reynolds number porous media flows, for confined and dispersing mixtures.
Bulletin of the American Physical Society, Nov 24, 2015
The lifetime of evaporating dense sprays ALOIS DE RIVAS, EM-MANUEL VILLERMAUX, Aix-Marseille Univ... more The lifetime of evaporating dense sprays ALOIS DE RIVAS, EM-MANUEL VILLERMAUX, Aix-Marseille University -We study the processes by which a set of nearby liquid droplets (a spray) evaporates in a gas phase whose relative humidity (vapor concentration) is controlled at will. A dense spray of micronsized water droplets is formed in air by a pneumatic atomizer and conveyed through a nozzle in a closed chamber whose vapor concentration has been pre-set to a controlled value. The resulting plume extension depends on the relative humidity of the diluting medium. When the spray plume is straight and laminar, droplets evaporate at its edge where the vapor is saturated, and diffuses through a boundary layer developing around the plume. We quantify the shape and length of the plume as a function of the injecting, vapor diffusion, thermodynamic and environment parameters. For higher injection Reynolds numbers, standard shear instabilities distort the plume into stretched lamellae, thus enhancing the diffusion of vapor from their boundary towards the diluting medium. These lamellae vanish in a finite time depending on the intensity of the stretching, and relative humidity of the environment, with a lifetime diverging close to the equilibrium limit, when the plume develops in an medium saturated in vapor. The dependences are described quantitatively.
Bulletin of the American Physical Society, Nov 21, 2016
The American Physical Society How a laser impact fragments a liquid drop HANNEKE GELDERBLOM, ALEX... more The American Physical Society How a laser impact fragments a liquid drop HANNEKE GELDERBLOM, ALEXANDER L. KLEIN
Fluid mechanics and its applications, 1996
A new flow pattern transition is observed in the near field of high Reynolds number coaxial jets.... more A new flow pattern transition is observed in the near field of high Reynolds number coaxial jets. The configuration consists of a central jet of velocity u1 surrounded by an annular jet of velocity u2, and the study focuses on the limit of large velocity ratios r u = u2/u1. For moderate velocity ratios (i.e. for r u < r uc = 5 typically), the fast annular jet which dominates the near flow field development pinches the central slow jet at the end of the inner potential core at a frequency corresponding to the outer Strouhal jet mode (St = fD2/u2 = 0.35). The structure of the near flow field is strongly dependent on r u . It is observed experimentally that above the critical velocity ratio r uc , the inner core breaks down into an unsteady recirculation bubble. The size of the recirculation region corresponds to the inner jet diameter D1 and the velocity of the reverse flow is proportional to u2 (figure 1). The transition mechanism is explained by a simple model wdiose ingredients are the turbulent entrainment rate, governed by the outer jet, and mass conservation. This model satisfactorily predicts r uc . The transition to this recirculating regime results a wake type instability. The recirculation bubble oscillates periodically at a low frequency (St = fD1/u2 = 0.035) and a large amplitude relatively to Strouhal fundamental mocde (figure 2). This low frequency mode persists until x/D1 ≈ 3 downstream.
When punctured, a uniform liquid sheet is known, since Taylor and Culick, to recess at a constant... more When punctured, a uniform liquid sheet is known, since Taylor and Culick, to recess at a constant speed, balancing surface tension and inertia. For planar soap films, this steady solution holds until the initially smooth receding rim is violently destabilized, exhibiting deep indentations from which droplets are ejected. A surprising new three-dimensional mechanism explaining this destabilization and resulting wavelength has been demonstrated: because of the shear between the still outer medium and the receding liquid, the film flaps through a Kelvin-Helmholtz instability, itself inducing an acceleration perpendicular to the film, which intensifies with the flapping amplitude. To this acceleration is associated a classical Rayleigh-Taylor mechanism, promoting the rim indentations.
Bulletin of the American Physical Society, Nov 22, 2015
When Marangoni meets Savart: The distant interaction of a drop with a liquid sheet BAPTISTE N ÉEL... more When Marangoni meets Savart: The distant interaction of a drop with a liquid sheet BAPTISTE N ÉEL, EMMANUEL VILLERMAUX, Aix-Marseille University -The interaction of a radially expanding water sheet (Savart) with an ethanol droplet evaporating at a short distance from it is investigated. The millimetric pendant droplet is positioned a few millimeters above a horizontal sheet, whose thickness is typically a few tens of microns. Although the droplet and the sheet are not in contact, the sheet radius is abruptly reduced downstream of the drop. We infer that the introduction of a few molecules of ethanol vapor emanating from the drop into the water sheet decreases its thickness, via a localized surface tension deficit. The corresponding Marangoni stresses induce a flow which progressively digs the sheet, hastening its rupture. A quantitative mechanism is proposed to represent all these observations, whose relevance to the puzzling problem of thin films (in the micron range) stability is underlined.
Bulletin of the American Physical Society, Nov 24, 2014
Mixing at low Reynolds number by shearing suspensions MATH-IEU SOUZY, BLOEN METZGER, CHERIFA ABID... more Mixing at low Reynolds number by shearing suspensions MATH-IEU SOUZY, BLOEN METZGER, CHERIFA ABID, IUSTI, EMMANUEL VILLERMAUX, IRPHE, XIAOLONG YIN, Colorado School of Mines -Sheared suspensions provide a unique system where mixing spontaneously occurs even under low Reynolds numbers conditions. Under flow, particles within the fluid experience frequent collisions with one another, and are thus deviated from their laminar streamlines. Particles can be thought of as many "stirrers" inducing disturbances in the fluid phase, which produce an efficient mixing. Using index matching and laser induced fluorescence, we investigate experimentally the evolution of the concentration profiles of a layer of dye initially applied on the outer wall of a cylindrical Couette cell, in a sheared suspension of neutrally buoyant, non-Brownian particles. Close to the walls, although the particle-translational-diffusive motion is frustrated, particle rotation significantly enhances the rate of mass transfer, which is found to propagate across the gap super-diffusively. The fine-scale mixing properties of this disordered flow are investigated as well. The stretching laws of isolated scalar blobs are measured and used to infer the probability density function of the concentration in the medium.
Proceedings of the National Academy of Sciences of the United States of America, Dec 30, 2021
Significance Bubble bursting aerosols play a critical role in forming clouds, scattering sunlight... more Significance Bubble bursting aerosols play a critical role in forming clouds, scattering sunlight, and transporting pathogens from water to the air. Most of them are produced from the fragmentation of bubble cap film. They usually have a diameter below 1 μm. However, their physical production mechanism has remained unknown. In this work, we discovered that these drops are probably generated from flapping bubble cap film (like a flapping flag). It explains the mysterious relation between bubble size and number of drops produced per bubble, providing a fundamental framework for understanding the production flux of bubble bursting aerosols, such as sea spray aerosol, and substance transfer through the air–water interface during drop ejection.
Cambridge University Press eBooks, Jan 12, 2004
The collision of a droplet with a solid surface The photographs displayed above show the impact, ... more The collision of a droplet with a solid surface The photographs displayed above show the impact, spreading, and boiling history of n -heptane droplets on a stainless steel surface. The impact velocity, Weber number, and initial droplet diameter are constant (values of 1 m/s, 43 and 1.5 mm respectively), and the view is looking down on the surface at an angle of about 30°. The photographs were taken using a spark flash method and the flash duration was 0.5 μs. The dynamic behavior illustrated in the photographs is a consequence of varying the initial surface temperature. The effect of surface temperature on droplet shape may be seen by reading across any row; the evolution of droplet shape at various temperatures may be seen by reading down any column. An entrapped air bubble can be seen in the drop when the surface temperature is 24°C. At higher temperatures vigorous bubbling, rather like that of a droplet sizzling on a frying pan, is seen (the boiling point of n -heptane is 98°C) but the bubbles disappear as the Leidenfrost temperature of n-heptane (about 200°C) is exceeded because the droplet become levitated above a cushion of its own vapor and does not make direct contact with the surface. The droplet shape is unaffected by surface temperature in the early stage of the impact process (t≤0.8 ms) but is affected by temperature at later time (cf. t≥ 1.6 ms) because of the progressive influence of intermittent solid-liquid contact as temperature is increased.
Cambridge University Press eBooks, Jan 12, 2004
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Papers by emmanuel villermaux