Motion of elongated particles in shear is studied. In applications where particles are much heavier than the carrying fluid, e.g. aerosols, the influence of particle inertia dominates the particle dynamics. Assuming that the particle only experiences a local linear velocity profile, its rotational and translational motion are independent. However, we show that quadratic terms of the local velocity profile combined with particle inertia cause a lateral drift of prolate spheroidal particles. We find that this drift is maximal when particle inertial forces are of the same order of magnitude as viscous forces, and that both extremely light and extremely heavy particles have negligible drift. In the non-inertial case, the particle rotates according to the local linear velocity profile, with each instantaneous orientation corresponding to a velocity that gives zero force on the particle. This results in a translational motion in the flow direction with periodic velocity fluctuations. With added particle inertia, the particle is slow to react to the surrounding fluid motion and the particle will switch between slower and faster rotation compared to the zero-force solution. The final motion that gives zero integrated force over a rotational period, is a motion with a lateral drift. We show that this drift is purely an effect of the non-sphericity of the particle and its translational inertia, while rotational inertia is negligible. Finally, although this inertial drift will contribute to the lateral motion of heavy elongated particles in channel flow, sedimentation due to gravity will dominate in any practical application on earth.
Sorting prolate and oblate spheroids with a diatomic gas in a magnetic field
Institute for Theoretical Physics, University of Amsterdam（阿姆斯特丹大学理论物理研究所）；Dutch Institute for Emergent Phenomena (DIEP), University of Amsterdam（阿姆斯特丹大学荷兰涌现现象研究所）；Institute for Advanced Study, University of Amsterdam（阿姆斯特丹大学高等研究院）
We investigate the instabilities, bifurcations and transition in the wake behind a 45-degree inclined 6:1 prolate spheroid, through a series of direct numerical simulations (DNS) over a wide range of Reynolds numbers (Re) from 10 to 3000. We provide a detailed picture of how the originally symmetric and steady laminar wake at low Re gradually looses its symmetry and turns unsteady as Re is gradually increased. Several fascinating flow features have first been revealed and subsequently analysed, e.g. an asymmetric time-averaged flow field, a surprisingly strong side force etc. As the wake parti…
The swimming of a spheroid immersed in a viscous fluid and performing surface deformations periodically in time is studied on the basis of Stokes equations of low Reynolds number hydrodynamics. The average over a period of time of the swimming velocity and the rate of dissipation are given by integral expressions of second order in the amplitude of surface deformations. The first order flow velocity and pressure, as functions of spheroidal coordinates, are expressed as sums of basic solutions of Stokes equations. Sets of superposition coefficients of these solutions which optimize the mean swi…
Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids
Phytoplankton are the foundation of aquatic food webs. Through photosynthesis, phytoplankton draw down CO2 at magnitudes equivalent to forests and other terrestrial plants and convert it to organic material that is then consumed by other organisms of phytoplankton in higher trophic levels. Mechanisms that affect local concentrations and velocities are of primary significance to many encounter-based processes in the plankton including prey-predator interactions, fertilization and aggregate formation. We report results from simulations of sinking phytoplankton, considered as elongated spheroids,…
We investigate Brownian noise effects on magnetic focusing of prolate and oblate spheroids carrying permanent magnetic dipoles in channel (Poiseuille) flow subject to a uniform magnetic field. The focusing is effected by the low-Reynolds-number wall-induced hydrodynamic lift which can be tuned via tilt angle of the field relative to the flow direction. This mechanism is incorporated in a steady-state Smoluchowski equation that we solve numerically to analyze the noise effects through the joint position-orientation probability distribution function of spheroids within the channel. The results f…
Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow
International Centre for Theoretical Sciences（国际理论科学中心）；Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究工程力学组）
We discuss an inertial migration of oblate spheroids in a plane channel, where steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius $a$. By analysing the inertial lift force we argue that this force is proportional to $a^3b$, where $b$ is the polar radius, and conclude that the dime…
We study the rotational dynamics of {\it inertial} disks and rods in three-dimensional, homogeneous isotropic turbulence. In particular, we show how the alignment and the decorrelation time-scales of such spheroids depend, critically, on both the level of inertia and the aspect ratio of these particles. These results illustrate the effect of inertia---which leads to a preferential sampling of the local flow geometry---on the statistics of both disks and rods in a turbulent flow. Our results are important for a variety of natural and industrial settings where the turbulent transport of asymmetr…
Previous studies on nonspherical particle-fluid interaction were mostly confined to elongated fiber-like particles, which were observed to induce turbulence drag reduction. However, with the presence of tiny disk-like particles how wall turbulence is modulated and whether drag reduction occurs are still unknown. Motivated by those open questions, we performed two-way coupled direct numerical simulations of inertialess spheroids in turbulent channel flow by an Eulerian-Lagrangian approach. The additional stress accounts for the feedback from inertialess spheroids on the fluid phase. The results…
We study the translational and rotational dynamics of neutrally-buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which is reflected in distinct axi…
Particles in inertialess flows of shear thinning fluids are a model representation for several systems in biology, ecology, and micro-fluidics.In this paper, we analyze the motion of a spheroid in a pressure driven flow of a shear thinning fluid.The shear thinning rheology is characterized by the Carreau model.We use a combination of perturbative techniques and the reciprocal theorem to delineate the kinematics of prolate and oblate spheroids.There are two perturbative strategies adopted, one near the zero shear Newtonian plateau and the other near the infinite shear Newtonian plateau.In both …
We study the cross-stream inertial migration of a torque-free neutrally buoyant spheroid, of an arbitrary aspect ratio $κ$, in wall-bounded plane Poiseuille flow for small particle Reynolds numbers\,($Re_p\ll1$) and confinement ratios\,($λ\ll1$), with the channel Reynolds number, $Re_c = Re_p/λ^2$, assumed to be arbitrary; here, $λ=L/H$ where $L$ is the semi-major axis of the spheroid and $H$ denotes the separation between the channel walls. In the Stokes limit\,($Re_p =0)$ and for $λ\ll 1$, a spheroid rotates along any of an infinite number of Jeffery orbits parameterized by an orbit constant…
In a shear flow particles migrate to their equilibrium positions in the microchannel. Here we demonstrate theoretically that if particles are inertial, this equilibrium can become unstable due to the Saffman lift force. We derive an expression for the critical Stokes number that determines the onset of instable equilibrium. We also present results of lattice Boltzmann simulations for spherical particles and prolate spheroids to validate the analysis. Our work provides a simple explanation of several unusual phenomena observed in earlier experiments and computer simulations, but never interpret…
How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio $λ= 1/6$) to prolate ($λ= 6$), and we consider low and moderate particle Reynolds numbers (${\rm Re} \le 50$). We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers remains qualitatively correct for Reynolds numbers up to ${\rm Re} \sim 10$. The amplitude…
We experimentally investigate the effect of geometrical anisotropy for buoyant ellipsoidal particles rising in a still fluid. All other parameters, such as the Galileo number $Ga \approx 6000$ and the particle density ratio $Γ\approx 0.53$ are kept constant. The geometrical aspect ratio, $χ$, of the particle is varied systematically from $χ$ = 0.2 (oblate) to 5 (prolate). Based on tracking all degrees of particle motion, we identify six regimes characterised by distinct rise dynamics. Firstly, for $0.83 \le χ\le 1.20$, increased rotational dynamics are observed and the particle flips over semi…
The gravity-driven motion of rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion where…
We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneous isotropic turbulence using direct numerical simulations and theory. The gravity-induced inertial torque acting on sub-Kolmogorov spheroids leads to pronouncedly non-Gaussian orientation distributions localized about the broadside-on(to gravity) orientation. Orientation distributions and average settling velocities are obtained over a wide range of spheroid aspect ratios, Stokes and Froude numbers. Orientational moments from the simulations compare well with analytical predictions in the inertiale…
