Settling of an asymmetric dumbbell in a quiescent fluid

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal then fluid inertia causes the dumbbell to settle in a horizontal orientation.Comment: 11 pages, 1 figure, as publishe

Effect of weak fluid inertia upon Jeffery orbits

We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyse how the linear stability of the \lq log-rolling\rq{} orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general both unsteady and non-linear terms in the Navier-Stokes equations are important.Comment: 5 pages, 2 figure

Super-diffusion around the rigidity transition: Levy and the Lilliputians

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.Comment: 7 pages, 6 figure

Rotation of a spheroid in a simple shear at small Reynolds number

We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show how inertial effects lift the degeneracy of the Jeffery orbits and determine the stabilities of the log-rolling and tumbling orbits at infinitesimal shear Reynolds numbers. For prolate spheroids we find stable tumbling in the shear plane, log-rolling is unstable. For oblate particles, by contrast, log-rolling is stable and tumbling is unstable provided that the aspect ratio is larger than a critical value. When the aspect ratio is smaller than this value tumbling turns stable, and an unstable limit cycle is born.Comment: 25 pages, 5 figure

Inertial torque on a squirmer

A small spheroid settling in a quiescent fluid experiences an inertial torque that aligns it so that it settles with its broad side first. Here we show that an active particle experiences such a torque too, as it settles in a fluid at rest. For a spherical squirmer, the torque is $\boldsymbol{T}^\prime = -{\tfrac{9}{8}} m_f (\boldsymbol{v}_s^{(0)} \wedge \boldsymbol{v}_g^{(0)})$ where $\boldsymbol{v}_s^{(0)}$ is the swimming velocity, $\boldsymbol{v}_g^{(0)}$ is the settling velocity in the Stokes approximation, and $m_f$ is the equivalent fluid mass. This torque aligns the swimming direction against gravity: swimming up is stable, swimming down is unstable.Comment: 10 pages, 3 figure

Hydrodynamic force on a small squirmer moving with a time-dependent velocity at small Reynolds numbers

We calculate the hydrodynamic force on a small spherical, unsteady squirmer moving with a time-dependent velocity in a fluid at rest, taking into account convective and unsteady fluid-inertia effects in perturbation theory. Our results generalise those of Lovalenti and Brady (1993) from passive to active spherical particles. We find that convective inertia changes the history contribution to the hydrodynamic force, as it does for passive particles. We determine how the hydrodynamic force depends on the swimming gait of the unsteady squirmer. Since swimming breaks the spherical symmetry of the problem, the force is not completely determined by the outer solution of the asymptotic-matching problem, as it is for passive spheres. There are additional contributions brought by the inhomogeneous solution of the inner problem. We also compute the disturbance flow, illustrating convective and unsteady fluid-inertia effects for a sudden start of the centre-of-mass motion, and for swimming with a periodic gait. We discuss the implications of our findings for small motile organisms in a marine environment.Comment: 16 pages, 4 figure

The role of inertia for the rotation of a nearly spherical particle in a general linear flow

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur

The features of the lateral flow in the cross-section slice of an elongated body : experimental approach

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.The aim of this work is to identify experimentally the features of the lateral flow in a cross-section slice of an elongated body during locomotion. We use an experimen- tal approach in the context of the undulatory swimming of an elongated body. For that, two kinematic parameters of the fish’s body are taking into account, the body’s cur- vature and the cross-section diameter. We examine the lateral flow field for different elliptical cylinder-shape, and we perform the experiments using particle image velocime- try (PIV) technique.dc201

Inertial drag on a sphere settling in a stratified fluid

We compute the drag force on a sphere settling slowly in a quiescent, linearly stratified fluid. Stratification can significantly enhance the drag experienced by the settling particle. The magnitude of this effect depends on whether fluid-density transport around the settling particle is due to diffusion, to advection by the disturbance flow caused by the particle, or due to both. It therefore matters how efficiently the fluid disturbance is convected away from the particle by fluid-inertial terms. When these terms dominate, the Oseen drag force must be recovered. We compute by perturbation theory how the Oseen drag is modified by diffusion and stratification. Our results are in good agreement with recent direct-numerical simulation studies of the problem at small Reynolds numbers and large (but not too large) Froude numbers.Comment: 10 pages, 1 figur

Density, extractives and decay resistance variabilities within branch wood from four agroforestry hardwood species

Agroforestry practices like pruning trees to control the light flux to crops produce every year a large volume of branches which is valorized by farmers as mulching or energy fuel. However, according to the literature, the wood of branches shows higher rates of polyphenols than stem wood and this can open some new perspectives for branch exploitation. In this study, the wood properties (density, mechanical properties, extractive content and decay resistance) were determined on branches of different sizes from oak, chestnut, poplar and walnut trees collected in two agroforestry systems. These properties were evaluated according to the wood age and the sampling position along the radial and longitudinal axes of the branch. All samples were analyzed by NIR-Spectroscopy and a predicting model aimed to assess the branch wood properties has been developed. Wood characteristics largely vary between species and do not exactly follow the same trends from one species to another. Overall, hardwood density of branches is similar to that of trunks, the content in wood extractives follows similar evolutions, and the decay resistance of branch wood does not seem to be really impacted by its position along the branch. Reliable NIRS models were built to easily predict the wood density and extractives content of agroforestry branches. The extractives content and the decay resistance of branch hardwood appear to be substantially lower than those of trunks, which suggests a non-suitability of branch wood for developing highvalued green chemistry