Emmanuel Villermaux

Infotaxis as a strategy for searching without gradients

Chemotactic bacteria rely on local concentration gradients to guide them towards the source of a nutrient. Such local cues pointing towards the location of the source are not always available at macroscopic scales because mixing in a flowing medium breaks up regions of high concentration into random and disconnected patches. Thus, animals sensing odours in air or water detect them only intermittently as patches sweep by on the wind or currents. A macroscopic searcher must devise a strategy of movement based on sporadic cues and partial information. Here we propose a search algorithm, which we call ‘infotaxis’, designed to work under such conditions. Any search process can be thought of as acquisition of information on source location; for infotaxis, information plays a role similar to concentration in chemotaxis. The infotaxis strategy locally maximizes the expected rate of information gain. We demonstrate its efficiency using a computational model of odour plume propagation and experimental data on mixing flows. Infotactic trajectories feature ‘zigzagging’ and ‘casting’ paths similar to those observed in the flight of moths. The proposed search algorithm is relevant to the design of olfactory robots, but the general idea of infotaxis can be applied more broadly in the context of searching with sparse information.

Break-up and atomization of a round water jet by a high-speed annular air jet

The near- and far-field break-up and atomization of a water jet by a high-speed annular air jet are examined by means of high-speed flow visualizations and phase Doppler particle sizing techniques. Visualization of the jets near field and measurements of the frequencies associated with the gas–liquid interfacial instabilities are used to study the underlying physical mechanisms involved in the primary break-up of the water jet. This process is shown to consist of the stripping of water sheets, or ligaments, which subsequently break into smaller lumps or drops. An entrainment model of the near-field stripping of the liquid is proposed, and shown to describe the measured liquid shedding frequencies. This simplified model explains qualitatively the dependence of the shedding frequency on the air/water momentum ratio in both initially laminar and turbulent water jets. The role of the secondary liquid break-up in the far-field atomization of the water jet is also investigated, and an attempt is made to apply the classical concepts of local isotropy to explain qualitatively the measurement of the far-field droplet size distribution and its dependence on the water to air mass and momentum ratios. Models accounting for the effect of the local turbulent dissipation rate in the gas on both the break-up and coalescence of the droplets are developed and compared with the measurements of the variation of the droplet size along the jets centreline. The total flux of kinetic energy supplied by the gas per unit total mass of the spray jet was found to be the primary parameter determining the secondary break-up and coalescence of the droplets in the far field.

Flow regimes of large-velocity-ratio coaxial jets

An investigation of the near-eld flow structure of coaxial jets with large outer to inner velocity ratio ru has been conducted. Since in all cases ru > 1, the outer jet dominates the near-eld flow structure. Two flow regimes are identied depending on whether ru is larger or smaller than a critical value ruc. When ru r uc, the inner potential cone is truncated and is followed by an unsteady recirculation bubble with low-frequency oscillation. The transition from one regime to another is explained by a simple model whose ingredients are the turbulent entrainment rate, governed by the outer-jet mixing layers and mass conservation. This model satisfactorily predicts the dependence of the inner potential cone length on ru and the critical velocity ratio ruc. The recirculation bubble has a wake-type instability. It oscillates at a low frequency and a large amplitude compared to the Kelvin{Helmholtz mode. Angular cross-correlations in the plane parallel to the jet outlet show moreover that this oscillation displays an azimuthal precession such that the rotation time of the phase of the oscillation equals the oscillation period. These salient features are discussed in the framework of the nonlinear delayed saturation (NLDS) model. Coaxial jets are a simple way by which two fluid streams can be mixed and this conguration is used for instance in combustion chambers of rocket engines. Often, one of the jets (the inner one) is in a liquid state and has to be atomized by a high-speed annular gas jet. This process, known as airblast atomization, has received considerable attention (Lefebvre 1989) during the past few decades. Most of the time the experiments have been aimed at characterizing the spray and have not allowed an analysis of the near-eld flow structure and the instabilities in any detail. Leaving aside surface tension eects, the important parameters in this problem are the momentum flux ratio between the two streams M = 2U 2=1U 2 and the ratio of the outer to the inner nozzle diameters = D2=D1. When the fluid densities are the same, the momentum flux ratio reduces to the velocity ratio of the outer to inner jet ru = U2=U1. The near-eld flow structure of coaxial jets in homogeneous fluids is, therefore, expected to be relevant to the understanding of liquid jet atomization. In the coaxial water jets studied here, quantitative flow visualizations can be used which are particularly helpful in the understanding of the interaction of dierent mixing layers present in the near eld. This is well demonstrated by the laser-induced-fluorescence visualizations of coaxial water jets with 0:59 6 ru 6 4:16, performed by Dahm,

Mixing in coaxial jets

The stirring and mixing properties of one-phase coaxial jets, with large outer (annular) to inner velocity ratio r u = u 2 / u 1 are investigated. Mixing is contemplated according to its geometrical, statistical and spectral facets with particular attention paid to determining the relevant timescales of the evolution of, for example, 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 γ = ( u 2 − u 1 )/ e constructed with the velocity difference between the streams and the gap thickness e of the annular jet. The kinetics of evolution of the interface corrugations, and the rate at which the mixture evolves from the initial segregation towards uniformity is prescribed by γ −1 . 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 formula here 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.

Life of a smooth liquid sheet

We report on experiments with liquid sheets formed through the impact of a slender jet on a small disc at high Reynolds number. When the interaction with the surrounding air is negligible, the sheet spreads out radially and remains smooth. The study extends over the whole life of the sheet, considering the dynamics of its formation and destruction and paying special attention to the stationary regime, in which the transition from sheet to drops occurs.

Intense vortical structures in grid‐generated turbulence

This paper presents a set of experiments aimed at investigating the features and the statistical frequency of intense vortical structures (sometimes called ‘‘filaments’’, or ‘‘worms’’) as manifested by a migrating bubble technique in a mean shear free, homogeneous, isotropic, stationary turbulence generated by oscillating grids in a water tank for Rλ reaching up to 300. It is found that the nucleation of filaments at the surface of the walls of the tank, where boundary layers are liable to destabilize is much more frequent than in the homogeneous bulk of the tank where one filament is typically detected each hundred large scale turnover time. This distinction between the wall surface and the bulk activity, supplemented with the fact that the size of the filaments and their lifetime compare with the length and time‐scales of the largest structures of the flow leads us to formulate an elementary model explaining the origin and the geometrical features of these intense vortical structures in turbulent flows ...

How vortices mix

The advection of a passive scalar blob in the deformation field of an axisymmetric vortex is a simple mixing protocol for which the advection–diffusion problem is amenable to a near-exact description. The blob rolls up in a spiral which ultimately fades away in the diluting medium. The complete transient concentration field in the spiral is accessible from the Fourier equations in a properly chosen frame. The concentration histogram of the scalar wrapped in the spiral presents unexpected singular transient features and its long time properties are discussed in connection with real mixtures.

On the geometry of turbulent mixing

We investigate the temporal evolution of the geometrical distribution of a passive scalar injected continuously into the far eld of a turbulent water jet at a scale d smaller than the local integral scale of the turbulence. The concentration eld is studied quantitatively by a laser-induced-fluorescence technique on a plane cut containing the jet axis. Global features such as the scalar dispersion from the source, as well as the ne structure of the scalar eld, are analysed. In particular, we dene the volume occupied by the regions whose concentration is larger than a given concentration threshold (support of the scalar eld) and the surface in which this volume is enclosed (boundary of the support). The volume and surface extents, and their respective fractal dimensions are measured as a function of time t, and the concentration threshold is normalized by the initial concentration Cs=C0 for dierent injection sizes d. All of these quantities display a clear dependence on t, d and Cs, and their evolutions rescale with the variable =( ut=d)(Cs=C0), the fractal dimension being, in addition, scale dependent. The surface-to-volume ratio and the fractal dimension of both the volume and the surface tend towards unity at large , reflecting the sheet-like structure of the scalar at small scales. These ndings suggest an original picture of the kinetics of turbulent mixing.

Periodically arranged co-flowing jets

The problem of a periodic planar arrangement of a large number of co-flowing, interacting jets is investigated. It is shown that this interaction gives rise to strong nearfield oscillations of large-scale spatial coherence and to far-field inhomogeneities. In the experiments performed, the jets were produced behind a flat plate perforated by holes arranged in a square or triangular periodic pattern and placed perpendicular to a uniform flow. At moderate Reynolds numbers, the interaction results in a remarkable low-frequency oscillation of the merging distance of the jets downstream of the plate. A detailed description of the recirculating flow in the cavities between the jets emphasizes the role of the backflow in the cavities on the oscillatory behaviour. This description is supported by measurements of the local fluctuating velocity and pressure, two-point correlation measurements and quantitative flow visualizations. These experimental observations suggest a new formulation for the instability dynamics of such unstable recirculating flows. This formulation, based on the nonlinear delayed saturation of the jets shear layer instability (NLDS model) predicts successfully the dependence of the oscillation of the merging distance on the jet Reynolds number and on the local geometrical features of the confinement of the jets. Furthermore, it is shown that the diffusion of mass coming from one jet, seeded with an inert dye, gives rise to an exponential diffusion front over a distance corresponding to a few mesh sizes indicating a strong local coupling of the jets. At the scale of the whole jet assembly, the oscillations are organized as large-scale travelling waves, propagating from the boundaries of the domain to its centre. This symmetry-breaking property is discussed and supplemented by a spatio-temporal simulation of an array of coupled oscillators.

Mixing by random stirring in confined mixtures

We study the relaxation of initially segregated scalar mixtures in randomly stirred media, aiming to describe the overall concentration distribution of the mixture, its shape and rate of deformation as it evolves towards uniformity. A stirred scalar mixture can be viewed as a collection of stretched sheets, possibly interacting with each other. We consider a situation in which the interaction between the sheets is enforced by confinement and is the key factor ruling its evolution. It consists of following a mixture relaxing towards uniformity around a fixed average concentration while flowing along a constant cross-section channel. The interaction between the sheets is found to be of a random addition nature in concentration space, leading to concentration distributions that are stable by self-convolution. The resulting scalar field is naturally coarsened at a scale much larger than the dissipation scale. Consequences on the mixture entropy and scalar rate of dissipation are also examined.