arXiv subjects

F. Candelier

Publications and source records attributed to F. Candelier.

13 recordsLinked to original sources

arXiv2026

Resistance tensors for aggregate particles with Stokesian dynamics

The response of particles to low-Reynolds flow can be compactly predicted with resistance or mobility tensors. However, the difficulty of obtaining accurate values for the elements of these tensors for specific geometries has held back work on particles with complex shapes. Here we show how Stokesian dynamics can be adapted to efficiently compute the resistance and mobility tensors of rigid and flexible aggregates, including confinement by walls. We introduce SHAPES, an implementation of the method, and demonstrate its capabilities for complex geometries including curved fibres, chiral dipoles, interacting aggregates, and active swimmers. Aggregates are represented by assemblies of beads designed to reproduce the geometry and motion of rigid or flexible particles. This coarse-grained description preserves the essential hydrodynamic interactions while substantially reducing computational cost. The method accurately reproduces known exact and approximate solutions, as well as experimental observations. The ability to compute the complete resistance and mobility tensors provides new insight into how aggregate shape controls translation, rotation, and coupling to fluid-velocity gradients. Previous descriptions often relied on simplified models retaining only a few symmetry-allowed couplings. While useful, such reduced descriptions are not always structurally stable under small perturbations of particle shape. Computing the full tensors makes it possible to draw robust conclusions and relate them to shape symmetry and hydrodynamic interactions. In particular, the method allows systematic analysis of non-Jeffery couplings to the strain rate that arise for helicoidal aggregates. SHAPES therefore provides a versatile framework for studying rigid and flexible aggregates in microfluidic, biological, and environmental flows.

physics.flu-dyn↗

arXiv2025

Fluid-inertia torques from particle-shape symmetry

Numerical simulation of particle motion in fluids at low particle Reynolds numbers is often based on empirical force and torque models obtained by fitting force and torque from ab-initio computations for simple particle shapes such as spheres, spheroids, or cylindrical disks and fibres. To do the same for more complex particles shapes, one needs to first know how particle shape constrains the dependence of force and torque on flow velocity, its gradient, and on particle orientation. Here we use symmetry analysis and perturbation theory to determine the form of the hydrodynamic torque on a particle settling in a quiescent fluid at low but non-zero particle Reynolds numbers, for particle shapes with different point-group symmetries. The symmetry conclusions are verified by comparing with explicit calculations for nearly spherical particles.

physics.flu-dyn↗

arXiv2024

Torques on curved atmospheric fibres

Small particles are transported over long distances in the atmosphere, with significant environmental impact. The transport of symmetric particles is well understood, but atmospheric particles, such as curved microplastic fibres or ash particles, are generally asymmetric. This makes the description of their transport properties uncertain. Here, we derive a model for how planar curved fibres settle in quiescent air. The model explains that fluid-inertia torques may align such fibres at oblique angles with gravity as seen in recent laboratory experiments, and shows that inertial alignment is a general and thus important factor for the transport of atmospheric particles.

physics.flu-dyn↗

arXiv2023

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 due to the inhomogeneous solution of the inner problem. We also compute the disturbance flow, illustrating convective and unsteady effects when the particle experiences a sudden start followed by a sudden stop.

physics.flu-dyn↗

arXiv2022

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.

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arXiv2022

Unsteady and inertial dynamics of an active particle in a fluid

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

physics.flu-dyn↗

arXiv2018

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.

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arXiv2016

Angular dynamics of a small particle in turbulence

We compute the angular dynamics of a neutrally buoyant nearly spherical particle immersed in an unsteady fluid. We assume that the particle is small, that its translational slip velocity is negligible, and that unsteady and convective inertia are small perturbations. We derive an approximation for the torque on the particle that determines the first inertial corrections to Jeffery's equation. These corrections arise as a consequence of local vortex stretching, and can be substantial in turbulence where local vortex stretching is strong and closely linked to the irreversibility of turbulence.

physics.flu-dyn↗

arXiv2016

Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number

We analyse the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity $ω$ equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number, for all aspect ratios considered. For the special case of a sphere we find $ω/s = -1/2+0.0540\, \mbox{Re}_\mbox{s}^{3/2}$ where $s$ is the shear rate, and $\mbox{Re}_\mbox{s}$ is the shear Reynolds number. This result differs from that derived by Lin et al. [J. Fluid Mech. 44 (1970) 1] who obtained a numerical coefficient roughly three times larger.

physics.flu-dyn↗

arXiv2015

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.

physics.flu-dyn↗

arXiv2015

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.

physics.flu-dyn↗

arXiv2015

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.

physics.flu-dyn↗

arXiv2015

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.

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