Practically all flows are turbulent in nature and contain some kind of irregularly-shaped particles, e.g. dirt, pollen, or life forms such as bacteria or insects. The effect of the particles on such flows and vice-versa are highly non-trivial and are not completely understood, particularly when the particles are finite-sized. Here we report an experimental study of millimetric fibers in a strongly sheared turbulent flow. We find that the fibers show a preferred orientation of $-0.38π\pm 0.05π$ ($-68 \pm 9^\circ$) with respect to the mean flow direction in high-Reynolds number Taylor-Couette turbulence, for all studied Reynolds numbers, fiber concentrations, and locations. Despite the finite-size of the anisotropic particles, we can explain the preferential alignment by using Jefferey's equation, which provides evidence of the benefit of a simplified point-particle approach. Furthermore, the fiber angular velocity is strongly intermittent, again indicative of point-particle-like behavior in turbulence. Thus large anisotropic particles still can retain signatures of the local flow despite classical spatial and temporal filtering effects.
Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way co…
In this paper we consider a computational model for the motion of thin, rigid fibers in viscous flows based on slender body theory. Slender body theory approximates the fluid velocity field about the fiber as the flow due to a distribution of singular solutions to the Stokes equations along the fiber centerline. The velocity of the fiber itself is often approximated by an asymptotic limit of this expression. Here we investigate the efficacy of simply evaluating the slender body velocity expression on a curve along the surface of the actual 3D fiber, rather than limiting to the fiber centerline…
We investigate the motion of a thin rigid body in Stokes flow and the corresponding slender body approximation used to model sedimenting fibers. In particular, we derive a rigorous error bound comparing the rigid slender body approximation to the classical PDE for rigid motion in the case of a closed loop with constant radius. Our main tool is the slender body PDE framework established by the authors and D. Spirn in [18,19], which we adapt to the rigid setting.
The motion of an assembly of rigid fibers is investigated for different classes of closed streamline flows, steady or time dependent, two dimensional or three dimensional. In our study, the dynamics of the fiber assembly is fully-coupled to the flow field by means of a state-of-the-art immersed boundary method. We show that, for sufficiently small Stokes times of the assembly, the whole flow gradient tensor can be accurately reconstructed by simply tracking the fiber assembly and measuring suitable fiber velocity differences evaluated at the fiber ends. Our results strongly suggest the possibi…
Orientation Dynamics of Rigid Fibers in a Microfluidic Burgers-like Vortex
ESPCI Paris, PSL University, CNRS, Sorbonne University, and Paris Cité University（巴黎高等物理化工学院、巴黎文理研究大学、法国国家科学研究中心、索邦大学、巴黎西岱大学）；CNRS, Ecole Polytechnique, Institut Polytechnique de Paris（法国国家科学研究中心、巴黎综合理工学院、巴黎理工学院）；Institut Universitaire de France（法国高等教育研究院）
The effect of a network of fixed rigid fibers on fluid flow is investigated by means of three-dimensional direct numerical simulations using an immersed boundary method for the fluid-structure coupling. Different flows are considered (i.e., cellular, parallel and homogeneous isotropic turbulent flow) in order to identify the modification of the classic energy budget occurring within canopies or fibrous media, as well as particle-laden flows. First, we investigate the stabilizing effect of the network on the Arnold-Beltrami-Childress (ABC) cellular flow, showing that, the steady configuration o…
Using hybrid Direct Numerical Simulation with Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime for both flexible polymers and rigid fibers. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we identify the rotational orientation time as the unifyi…
We propose a novel integral model describing the motion of curved slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates flow near the fiber using singular solutions of the Stokes equations integrated along the fiber centerline. In contrast to other models based on (singular) SBT, our model yields a smooth integral kernel which incorporates the (possibly varying) fiber radius naturally. The integral operator is provably negative definite in a non-physical idealized …
We develop a novel Moving Particle Simulation (MPS) method to accurately reproduce the motion of fibers floating in sheared liquids. In conventional MPS schemes, if a fiber suspended in a liquid is represented by a one-dimensional array of MPS particles, it is entirely aligned to the flow direction due to the lack of shear stress difference between fiber-liquid interfaces. To address this problem, we employ the micropolar fluid model to introduce rotational degrees of freedom into the MPS particles. The translational motion of liquid and solid particles and the rotation of solid particles are …
Using time-resolved measurements of the orientation of rigid inertial fibers in a turbulence-tank, we investigate the autocorrelation of their tumbling rate. The correlation time ($τ_d$) is well predicted by Kolmogorov inertial-range scaling based on the fiber length (L) when the fiber inertia can be neglected. For inertial fibers, we propose a simple model considering fiber inertia (measured by a tumbling Stokes number) and a viscous torque which accurately predicts both the correlation time and the variance of the tumbling rate.
Small flexible fibers in a turbulent flow are found to be most of the time as straight as stiff rods. This is due to the cooperative action of flexural rigidity and fluid stretching. However, fibers might bend and buckle when they tumble and experience a strong-enough local compressive shear. Such events are similar to an activation process, where the role of temperature is played by the inverse of Young's modulus. Numerical simulations show that buckling occurs very intermittently in time. This results from unexpected long-range Lagrangian correlations of the turbulent shear.
We investigate the trajectories of rigid fibers as they are transported in a pressure-driven flow, at low Reynolds number, in shallow Hele Shaw cells. The transverse confinement and the resulting viscous friction on these elongated objects, as well as the lateral confinement (i.e. the presence of lateral walls), lead to complex fibers trajectories that we characterize with a combination of microfluidic experiments and simulations using modified Brinkman equations. We show that the transported fiber behaves as an oscillator for which we obtain and analyze a complete state diagram.
The back-reaction of dispersed rigid fibers to turbulence is analyzed by means of a state-of-the-art fully-coupled immersed boundary method. The following universal scenario is identified: turbulence at large scales looses a consistent part of its kinetic energy (via a Darcy friction term), which partially re-appears at small scales where a new range of energy-containing scales does emerge. Large-scale mixing is thus depleted in favor of a new mixing mechanism arising at the smallest scales. Anchored fibers cause the same back-reaction to turbulence as moving fibers of large inertia. Our resul…
The flapping states of a flexible fiber fully coupled to a three-dimensional turbulent flow are investigated via state-of-the-art numerical methods. Two distinct flapping regimes are predicted by the phenomenological theory recently proposed by Rosti et al. [Phys. Rev. Lett. 121, 044501, 2018]: the under-damped regime, where the elasticity strongly affects the fiber dynamics, and the over-damped regime, where the elastic effects are strongly inhibited. In both cases we can identify a critical value of the bending rigidity of the fiber by a resonance condition, which further provides a distinct…
When transported in confined geometries rigid fibers show interesting transport dynamics induced by friction with the top and bottom walls. Fiber flexibility causes an additional coupling between fiber deformation and transport and is expected to lead to more complex dynamics. A first crucial step for their understanding is the characterization of the deformed fiber shape. Here we characterize this shape for a fiber transported in a confined plug flow perpendicular to the flow direction using a combination of microfluidic experiments and numerical simulations. In the experiments, size, initial…
We report experiments on the deformation and transport of an elastic fiber in a viscous cellular flow, namely a lattice of counter-rotative vortices. We show that the fiber can buckle when approaching a stagnation point. By tuning either the flow or fiber properties, we measure the onset of this buckling instability. The buckling threshold is determined by the relative intensity of viscous and elastic forces, the elasto-viscous number Sp. Moreover we show that flexible fibers escape faster from a vortex (formed by closed streamlines) compared to rigid fibers. As a consequence, the deformation …
We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question whether the fiber can spontaneously knot itself. Using a 1D Cosserat model, a simple local viscous drag model and discrete contact forces, we explore the probability of finding knots at any given time when the fiber is interacting with the ABC class of flows. The bending rigidity is shown to have a marginal effect compared to that of increasing the fiber length. Complex knots are formed up to 11 crossings, but some knots are more probable than others. The finite-time Lya…
