Eric Lajeunesse

Bio: Eric Lajeunesse is an academic researcher from Institut de Physique du Globe de Paris. The author has contributed to research in topics: Sediment transport & Bed load. The author has an hindex of 30, co-authored 75 publications receiving 2850 citations. Previous affiliations of Eric Lajeunesse include Paris Diderot University & IPG Photonics.

Bed load transport in turbulent flow at the grain scale: Experiments and modeling

Abstract: [1] We report an experimental investigation of the motion of bed load particles under steady and spatially uniform turbulent flow above a flat sediment bed of uniform grain size. Using a high-speed video imaging system, we recorded the trajectories of the moving particles and measured their velocity and the length and duration of their flights, as well as the surface density of the moving particles. Our observations show that entrained particles exhibit intermittent motion composed of the succession of periods of “flight” and periods of rest. During one flight, a particle may go through phases of reptation, during which it moves in nearly persistent contact with the rough bed, and phases of saltation, during which it travels sufficiently high above the bed to reach high velocities. The distributions of longitudinal and transverse particle velocities obey a decreasing exponential and a Gaussian law, respectively. Interestingly, these observations are similar to those previously reported for viscous flows. The experimental results presented here support the erosion-deposition model of Charru (2006) and allow the calibration of the involved coefficients. In particular, noting τ*, the Shields number, and τ*c, the threshold Shields number, we find that (1) the surface density of moving particles increases linearly with τ* − τ*c; (2) the average particle velocity increases linearly with τ*1/2 − τ*c1/2, with a finite nonzero value at the threshold; (3) the flight duration scales with a characteristic settling time with no significant dependence on either τ* or the settling Reynolds number; and (4) the flight length increases linearly with τ*1/2 − τ*c1/2. The results presented in this paper should provide a valuable physical framework to describe bed form development in turbulent flows.

Spreading of a granular mass on a horizontal plane

Abstract: The transient surface flow occurring when a cylindrical pile of dry granular material is suddenly allowed to spread on a horizontal plane is investigated experimentally as a function of the released mass M, the initial aspect ratio a of the granular cylinder pile, the properties of the underlying substrate (smooth or rough, rigid or erodible) and the bead size. Two different flow regimes leading to three different deposit morphologies are observed as a function of the initial aspect ratio a, whatever the substrate properties and the bead size. For a≲3, the granular mass spreads through an avalanche on its flanks producing either truncated cone or conical deposits. For a≳3, the upper part of the column descends conserving its shape while the foot of the pile propagates radially outward. The obtained deposit looks like a “Mexican hat” and the slope angle at the foot of the deposit is observed to saturate at a value of the order of 5°. For a given ground and bead size, the flow dynamics and the deposit morph...

Granular slumping on a horizontal surface

Abstract: We report the results of an experimental investigation of the flow induced by the collapse of a column of granular material (glass beads of diameter d) over a horizontal surface. Two different setups are used, namely, a rectangular channel and a semicircular tube, allowing us to compare two-dimensional and axisymmetric flows, with particular focus on the internal flow structure. In both geometries the flow dynamics and the deposit morphologies are observed to depend primarily on the initial aspect ratio of the granular column a=Hi∕Li, where Hi is the height of the initial granular column and Li its length along the flow direction. Two distinct regimes are observed depending on a: an avalanche of the column flanks producing truncated deposits for small a and a column free fall leading to conical deposits for large a. In both geometries the characteristic time scale is the free fall of the granular column τc=Hi∕g. The flow initiated by Coulomb-like failure never involves the whole granular heap but remains localized in a surface layer whose size and shape depend on a and vary in both space and time. Except in the vicinity of the pile foot where the flow is pluglike, velocity profiles measured at the side wall are identical to those commonly observed in steady granular surface flows: the velocity varies linearly with depth in the flowing layer and decreases exponentially with depth in the static layer. Moreover, the shear rate is constant, γ=0.3g∕d, independent of the initial aspect ratio, the flow geometry, position along the heap, or time. Despite the rather complex flow dynamics, the scaled deposit height Hf∕Li and runout distance ΔL∕Li both exhibit simple power laws whose exponents depend on a and on the flow geometry. We show that the physical origin of these power laws can be understood on the basis of a dynamic balance between acceleration, pressure gradient, and friction forces at the foot of the granular pile. Two asymptotic behaviors can be distinguished: the flow is dominated by friction forces at small a and by pressure forces at large a. The effect of the flow geometry is determined primarily by mass conservation and becomes important only for large a.

On the use of Saint Venant equations to simulate the spreading of a granular mass

Abstract: [1] Cliff collapse is an active geomorphological process acting at the surface of the Earth and telluric planets. Recent laboratory studies have investigated the collapse of an initially cylindrical granular mass along a rough horizontal plane for different initial aspect ratios a = Hi/Ri, where Hi and Ri are the initial height and radius, respectively. A numerical simulation of these experiments is performed using a minimal depth-integrated model based on a long-wave approximation. A dimensional analysis of the equations shows that such a model exhibits the scaling laws observed experimentally. Generic solutions are independent of gravity and depend only on the initial aspect ratio a and an effective friction angle. In terms of dynamics, the numerical simulations are consistent with the experiments for a ≤ 1. The experimentally observed saturation of the final height of the deposit, when normalized with respect to the initial radius of the cylinder, is accurately reproduced numerically. Analysis of the results sheds light on the correlation between the area overrun by the granular mass and its initial potential energy. The extent of the deposit, the final height, and the arrest time of the front can be directly estimated from the “generic solution” of the model for terrestrial and extraterrestrial avalanches. The effective friction, a parameter classically used to describe the mobility of gravitational flows, is shown to depend on the initial aspect ratio a. This dependence should be taken into account when interpreting the high mobility of large volume events.

Miscible displacement in a Hele-Shaw cell at high rates

Abstract: We study experimentally and theoretically the downward vertical displacement of one miscible fluid by another lighter one in the gap of a Hele-Shaw cell at sufficiently high velocities for diffusive effects to be negligible. Under certain conditions on the viscosity ratio, M , and the normalized flow rate, U , this results in the formation of a two-dimensional tongue of the injected fluid, which is symmetric with respect to the midplane. Thresholds in flow rate and viscosity ratio exist above which the two- dimensional flow destabilizes, giving rise to a three-dimensional pattern. We describe in detail the two-dimensional regime using a kinematic wave theory similar to Yang & Yortsos (1997) and we delineate in the ( M , U )-plane three different domains, characterized respectively by the absence of a shock, the presence of an internal shock and the presence of a frontal shock. Theoretical and experimental results are compared and found to be in good agreement for the first two domains, but not for the third domain, where the frontal shock is not of the contact type. An analogous treatment is also applied to the case of axisymmetric displacement in a cylindrical tube.

Microfluidics: Fluid physics at the nanoliter scale

Abstract: Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

On dense granular flows.

Abstract: The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divises (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

The Structure of Turbulent Shear Flow

Abstract: The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.