arXiv subjects

Bruno Andreotti

Publications and source records attributed to Bruno Andreotti.

50 records · Page 3Linked to original sources

arXiv2012

Numerical simulation of turbulent sediment transport, from bed load to saltation

Sediment transport is studied as a function of the grain to fluid density ratio using two phase numerical sim- ulations based on a discrete element method (DEM) for particles coupled to a continuum Reynolds averaged description of hydrodynamics. At a density ratio close to unity (typically under water), vertical velocities are so small that sediment transport occurs in a thin layer at the surface of the static bed, and is called bed load. Steady, or 'saturated' transport is reached when the fluid borne shear stress at the interface between the mobile grains and the static grains is reduced to its threshold value. The number of grains transported per unit surface is therefore limited by the flux of horizontal momentum towards the surface. However, the fluid velocity in the transport layer remains almost undisturbed so that the mean grain velocity scales with the shear velocity u\ast. At large density ratio (typically in air), the vertical velocities are large enough to make the transport layer wide and dilute. Sediment transport is then called saltation. In this case, particles are able to eject others when they collide with the granular bed, a process called splash. The number of grains transported per unit surface is selected by the balance between erosion and deposition and saturation is reached when one grain is statistically replaced by exactly one grain after a collision, which has the consequence that the mean grain velocity remains independent of u\ast. The influence of the density ratio is systematically studied to reveal the transition between these two transport regimes. Based on the mechanisms identified in the steady case, we discuss the transient of saturation of sediment transport and in particular the saturation time and length. Finally, we investigate the exchange of particles between the mobile and static phases and we determine the exchange time of particles.

cond-mat.soft↗

arXiv2012

Contact angles on a soft solid: from Young's law to Neumann's law

The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles different from that predicted by Neumann's law, which applies when the drop is floating on another liquid. Here we derive an elasto-capillary model for contact angles on a soft solid, by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of vanishing elastic modulus yields Neumann's law or a slight variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit (Young) to the soft limit (Neumann) appears when the length scale defined by the ratio of surface tension to elastic modulus $γ/E$ reaches a few molecular sizes.

physics.flu-dyn↗

arXiv2012

Capillary Pressure and Contact Line Force on a Soft Solid

The surface free energy, or surface tension, of a liquid interface gives rise to a pressure jump when the interface is curved. Here we show that a similar capillary pressure arises at the interface of soft solids. We present experimental evidence that immersion of a thin elastomeric wire into a liquid induces a substantial elastic compression due to the solid capillary pressure at the bottom. We quantitatively determine the effective surface tension from the elastic displacement field, and find a value comparable to the liquid-vapor surface tension. Most importantly, these results also reveal the way the liquid pulls on the solid close to the contact line: the capillary force is not oriented along the liquid-air interface, nor perpendicularly to the solid surface, as previously hypothesized, but towards the interior of the liquid.

physics.flu-dyn↗

arXiv2011

Air Entrainment by Viscous Contact Lines

The entrainment of air by advancing contact lines is studied by plunging a solid plate into a very viscous liquid. Above a threshold velocity, we observe the formation of an extended air film, typically 10 microns thick, which subsequently decays into air bubbles. Exploring a large range of viscous liquids, we find an unexpectedly weak dependence of entrainment speed on liquid viscosity, pointing towards a crucial role of the flow inside the air film. This induces a striking asymmetry between wetting and dewetting: while the breakup of the air film strongly resembles the dewetting of a liquid film, the wetting speeds are larger by orders of magnitude.

physics.flu-dyn↗

arXiv2011

Elastocapillary instability under partial wetting conditions: bending versus buckling

The elastocapillary instability of a flexible plate plunged in a liquid bath is analysed theoretically. We show that the plate can bend due to two separate destabilizing mechanisms, when the liquid is partially wetting the solid. For contact angles $θ_e > π/2$, the capillary forces acting tangential to the surface are compressing the plate and can induce a classical buckling instability. However, a second mechanism appears due to capillary forces normal to surface. These induce a destabilizing torque that tends to bend the plate for any value of the contact angle $θ_e > 0$. We denote these mechanisms as "buckling" and "bending" respectively and identify the two corresponding dimensionless parameters that govern the elastocapillary stability. The onset of instability is determined analytically and the different bifurcation scenarios are worked out for experimentally relevant conditions.

physics.flu-dyn↗

arXiv2011

Elastic deformation due to tangential capillary forces

A sessile liquid drop can deform the substrate on which it rests if the solid is sufficiently "soft". In this paper we compute the detailed spatial structure of the capillary forces exerted by the drop on the solid substrate using a model based on Density Functional Theory. We show that, in addition to the normal forces, the drop exerts a previously unaccounted tangential force. The resultant effect on the solid is a pulling force near the contact line directed towards the interior of the drop, i.e. not along the interface. The resulting elastic deformations of the solid are worked out and illustrate the importance of the tangential forces.

physics.flu-dyn↗

arXiv2011

Origin of line tension for a Lennard-Jones nanodroplet

The existence and origin of line tension has remained controversial in literature. To address this issue we compute the shape of Lennard-Jones nanodrops using molecular dynamics and compare them to density functional theory in the approximation of the sharp kink interface. We show that the deviation from Young's law is very small and would correspond to a typical line tension length scale (defined as line tension divided by surface tension) similar to the molecular size and decreasing with Young's angle. We propose an alternative interpretation based on the geometry of the interface at the molecular scale.

physics.flu-dyn↗

arXiv2008

A microscopic view on contact angle selection

We discuss the equilibrium condition for a liquid that partially wets a solid on the level of intermolecular forces. Using a mean field continuum description, we generalize the capillary pressure from variation of the free energy and show at what length scale the equilibrium contact angle is selected. After recovering Young's law for homogeneous substrates, it is shown how hysteresis of the contact angle can be incorporated in a self-consistent fashion. In all cases the liquid-vapor interface takes a nontrivial shape, which is compared to models using a disjoining pressure.

physics.flu-dyn↗

arXiv2007

Barchan dune corridors: field characterization and investigation of control parameters

The structure of the barchan field located between Tarfaya and Laayoune (Atlantic Sahara, Morocco) is quantitatively investigated and compared to that in La Pampa de la Joya (Arequipa, Peru). On the basis of field measurements, we show how the volume, the velocity and the output sand flux of a dune can be computed from the value of its body and horn widths. The dune size distribution is obtained from the analysis of aerial photographs. It shows that these fields are in a statistically homogeneous state along the wind direction and present a `corridor' structure in the transverse direction, in which the dunes have a rather well selected size. Investigating the possible external parameters controlling these corridors, we demonstrate that none among topography, granulometry, wind and sand flux is relevant. We finally discuss the dynamical processes at work in these fields (collisions and wind fluctuations), and investigate the way they could regulate the size of the dunes. Furthermore we show that the overall sand flux transported by a dune field is smaller than the maximum transport that could be reached in the absence of dunes, i.e. in saltation over the solid ground.

cond-mat.soft↗

arXiv2007

Spreading of a granular droplet

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment. We study experimentally a thin granular film spreading under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the``granular droplet'') and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective dynamic friction coefficients between the base and the granular layer under sustained and controlled vibrations. We derive an empirical friction law involving external driving parameters and the layer height to represent our data.

cond-mat.soft↗

arXiv2006

A scaling law for aeolian dunes on Mars, Venus, Earth, and for subaqueous ripples

The linear stability analysis of the equations governing the evolution of a flat sand bed submitted to a turbulent shear flow predicts that the wavelength $λ$ at which the bed destabilises to form dunes should scale with the drag length $L_{\rm drag} = \frac{ρ_s}{ρ_f} d$. This scaling law is tested using existing and new measurements performed in water (subaqueous ripples), in air (aeolian dunes and fresh snow dunes), in a high pressure CO$_2$ wind tunnel reproducing conditions close to the Venus atmosphere and in the low pressure CO$_2$ martian atmosphere (martian dunes). A difficulty is to determine the diameter of saltating grains on Mars. A first estimate comes from photographs of aeolian ripples taken by the rovers Opportunity and Spirit, showing grains whose diameters are smaller than on Earth dunes. In addition we calculate the effect of cohesion and viscosity on the dynamic and static transport thresholds. It confirms that the small grains visualised by the rovers should be grains experiencing saltation. Finally, we show that, within error bars, the scaling of $λ$ with $L_{\rm drag}$ holds over almost five decades. We conclude with a discussion on the time scales and velocities at which these bed instabilities develop and propagate on Mars.

cond-mat.soft↗

arXiv2005

Aeolian sans ripples: experimental study of saturated states

We report an experimental investigation of aeolian sand ripples, performed both in a wind tunnel and on stoss slopes of dunes. Starting from a flat bed, we can identify three regimes: appearance of an initial wavelength, coarsening of the pattern and finally saturation of the ripples. We show that both initial and final wavelengths, as well as the propagative speed of the ripples, are linear functions of the wind velocity. Investigating the evolution of an initially corrugated bed, we exhibit non-linear stable solutions for a finite range of wavelengths, which demonstrates the existence of a saturation in amplitude. These results contradict most of the models.

cond-mat.soft↗

arXiv2002

Selection of dune shapes and velocities. Part 1: Dynamics of sand, wind and barchans

Almost fifty years of investigations of barchan dunes morphology and dynamics is reviewed, with emphasis on the physical understanding of these objects. The characteristics measured on the field (shape, size, velocity) and the physical problems they rise are presented. Then, we review the dynamical mechanisms explaining the formation and the propagation of dunes. In particular a complete and original approach of the sand transport over a flat sand bed is proposed and discussed. We conclude on open problems by outlining future research directions.

cond-mat↗

arXiv2002

Selection of dune shapes and velocities. Part 2: A two-dimensional modelling

We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes, which, by contrast to the former, do not show avalanche slip face. Their shape and velocity can be predicted as a function of their size. We recover in particular that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no stable dune exists. However, the linear stability analysis of a flat sand sheet shows that it is unstable at large wavelengths and suggests a mechanism of dune initiation.

cond-mat↗