arXiv subjects

G. Voth

Publications and source records attributed to G. Voth.

6 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↗

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.

physics.flu-dyn↗

arXiv2017

Passive directors in turbulence

In experiments and numerical simulations we measured angles between the symmetry axes of small spheroids advected in turbulence ("passive directors"). Since turbulent strains tend to align nearby spheroids, one might think that their relative angles are quite small. We show that this intuition fails in general because angles between the symmetry axes of nearby particles are anomalously large. We identify two mechanisms that cause this phenomenon. First, the dynamics evolves to a fractal attractor despite the fact that the fluid velocity is spatially smooth at small scales. Second, this fractal forms steps akin to scar lines observed in the director patterns for random or chaotic two-dimensional maps.

physics.flu-dyn↗

arXiv2014

Shape-dependence of particle rotation in isotropic turbulence

We consider the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence. Using laboratory experiments as well as numerical and analytical calculations, we explore how particle rotation depends upon particle shape. We find that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity. Previous work has shown that shape significantly affects the variance of the tumbling rate of axisymmetric particles. It follows that shape affects the spinning rate in a way that is, on average, complementary to the shape-dependence of the tumbling rate. We confirm this relationship using direct numerical simulations, showing how tumbling rate and spinning rate variances show complementary trends for rod-shaped and disk-shaped particles. We also consider a random but non-turbulent flow. This allows us to explore which of the features observed for rotation in turbulent flow are due to the effects of particle alignment in vortex tubes.

physics.flu-dyn↗

arXiv2001

Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.

nlin.CD↗