Session G36: Particle-Laden Flows: Non-Spherical Particles

Measurements of Inertial Torques on Sedimenting Fibers

Stokes flow solutions predict that ellipsoids sedimenting in quiescent fluid keep their initial orientation. However, preferential alignment in low Reynolds number sedimentation is easily observed. For example, sun dogs form from alignment of sedimenting ice crystals. The cause of this preferential alignment is a torque due to non-zero fluid inertia that aligns particles with a long axis in the horizontal direction. These torques are predicted analytically for slender fibers with low Reynolds number based on the fiber diameter ($Re_D$) by Khayat and Cox (JFM 209:435, 1989). Despite increasingly widespread use of these expressions, we did not find experimental measurements of these inertial torques at parameters where the theory was valid, so we performed a set of sedimentation experiments using fore-aft symmetric cylinders and asymmetric cylinders with their center of mass offset from their center of drag. Measured rotation rates as a function of orientation using carefully prepared glass capillaries in silicon oil show good agreement with the theory. We quantify the effect of finite tank size and compare with other experiments in water where the low $Re_D$ condition is not met.   

Statistical model for the orientation of non-spherical particles settling in turbulence

To understand the dynamics of small particles suspended in turbulent flows is important to shed light on many problems in Natural Sciences and in technology. Using direct numerical simulations and a statistical model, we study the dynamics of small, heavy, spheroidal particles falling in a turbulent aerosol. In the statistical model we replace the flow by a random velocity field which is smooth in both space and time. In this model we can solve the dynamics analytically, allowing us to find the functional dependence of statistical quantities on the relevant particle parameters. Rotational symmetry in the problem is broken due to gravity and due to the non-spherical shape of the particles. We study how this affects the settling velocity and orientational distribution of the particles.   

Size effects in the turbulent tumbling of thin rods and large particles

We present experimental, numerical, and theoretical results on rotation of finite-sized, neutrally buoyant, anisotropic particles in isotropic turbulence. By using particles of different shapes and sizes, we explore the effects of particle length scales on rotation. Previous results showed that the leading-order determinant of particle rotation is particle volume (at least for low-aspect-ratio particles) suggesting that shape does not affect the lower order statistics. We offer a possible explanation for this, based on the postulate that the particles’ finite-size effects allow them to be stable with respect to Lagrangian turbulent flow structures which would otherwise align them with coarse-grained vorticity and strain-rate. We test this hypothesis by comparing experimental data with results from computations of inertialess particles forced with a stochastically-generated time series of the velocity gradient tensor based on random flow, which accounts for the particle filtering effect. A second approach to understanding the dynamics is to quantify the alignment statistics between large thin rods and the coarse-grained velocity tensor, which quantifies the way in which the alignment between fluid vorticity and particles’ long axes evolves with particle length scale.   

Shape effects in the turbulent tumbling of large particles

We present laboratory results on rotation of finite-sized, neutrally buoyant, anisotropic particles in isotropic turbulence. The isotropic turbulent flow is generated using a randomly-actuated synthetic jet array that minimizes tank scale circulation and measurements are made with stereoscopic particle image velocimetry. By using particles of different shapes, we explore the effects that symmetries have on particle rotation. We add to previous data collected for spheres cylinders and ellipsoids by performing new measurements on cubes, cuboids and cones. The measurement technique and results on mean-square particle rotation will be presented. Preliminary results, at the time of writing this abstract, indicate that symmetry breaking increases the rate of particle rotation. More complete quantitative results will be presented.   

Rotation rate of inertial fibers in turbulence

Since 2010 more and more studies in Lagrangian turbulence are devoted to anisotropic particles. Our work is motivated by two recent studies from Parsa and Voth [1] and Bordoloi and Variano [2]. They observed two different scalings for the tumbling rate of fiber-like particles. The first one, with thin particles, depends only on the fiber length and is in agreement with slender body approximation [1]. The other, with thick particles, find the same scaling for the length but needs to introduce the particle aspect ratio [2]. The aim of our study is to study the transition from thick to thin particles. For this purpose, we measure the rotation of cylindrical fibers in a turbulent flow generated by the rotation of eight motors located at each corner of a cubic tank. To characterize the transition from thick to thin particles, both the length and the diameter of the fiber is varied and compared to the prediction from slender body theory.\\ [1] S. Parsa and G.A. Voth, \textbf{Inertial Range Scaling in Rotations of Long Rods in Turbulence}, \textit{Phys. Rev. Lett.}, \textbf{112}, 024501 (2014). [2] A. K. Bordoloi and E. Variano, \textbf{Rotational kinematics of large cylindrical particles in turbulence}, \textit{J. Fluid Mech.}, \textbf{815}, 199-22 (2017).   

The drag and lift of different non-spherical particles from low to high Re

The present work investigates a simplified drag and lift model that can be used for different non-spherical particles. The flow around different non-spherical particles is studied using a multi-relaxation-time lattice Boltzmann method. We compute the mean drag coefficient $C_{D,\phi}$ at different incident angles $\phi$ for a wide range of Reynolds numbers ($Re$). We show that the sine-squared drag law $C_{D,\phi} = C_{D,\phi=0^{\circ}}+(C_{D,\phi=90^{\circ}}-C_{D,\phi=0^{\circ}})\sin^2\phi$ holds up to large Reynolds numbers $Re=2000$. The sine-squared dependence of $C_D$ occurs at Stokes flow (very low $Re$) due to linearity of the flow fields. We explore the physical origin behind the sine-squared law at high $Re$, and reveal that surprisingly, this does not occur due to linearity of flow fields. Instead, it occurs due to an interesting pattern of pressure distribution contributing to the drag, at higher $Re$, for different incident angles. Similarly, we find that the equivalent theoretical equation of lift coefficient $C_L$ can provide a decent approximation, even at high $Re$, for elongated particles. Such a drag and lift law valid at high $Re$ is very much useful for Euler-Lagrangian fluidization simulations of the non-spherical particles.   

Tuning the shear viscosity of a dilute suspension using particle shapes that inhibit rotation

We show that a suspension of slender, rigid-particles that attain an equilibrium orientation in a simple shear flow have a much smaller intrinsic viscosity relative to a suspension of tumbling particles with the same aspect ratio. An axisymmetric particle, such as a ring or a fiber, with certain cross-sections can attain an equilibrium orientation in a low Reynolds number simple shear flow without application of external forces (Singh et al., \textit{J. Fluid Mech.}, 2013; Bretherton, \textit{J. Fluid Mech.}, 1962 a). These particles align such that the slender dimension(s) of the particle is/are almost perpendicular to the velocity gradient direction of the simple shear flow and thus they have much smaller stresslets compared to the time averaged stresslet of a rotating slender particle. While slender fibers, also remain aligned in a similar state for a long time, the major contribution to the average stresslet occurs when the fiber is flipping. Using slender body theory and boundary element method calculations we demonstrate that particle alignment could significantly reduce the intrinsic viscosity of the suspension relative to a suspension of rotating particles. By choosing particle shapes that can be fabricated using manufacturing techniques such as photolithography or 3-D printing, our results open new pathways to control the rheological properties of a particle suspension by altering the shape of the particle.   

Shear-induced migration and orientation of rigid fibers

The spatial and orientation distributions are measured for a suspension of fibers during pressure-driven flow. The fibers are rigid and non-colloidal, and two aspect ratios (length to diameter ratios) of 12 and 24 were tested; the suspending fluid is viscous, Newtonian, and density matched to the particles. As with the migration of spheres in parabolic flows, the fibers migrate toward the centerline of the channel if the concentration is sufficiently high. Migration is not observed for concentrations below a volume fraction of 0.035 for aspect ratio 24 and 0.07 for aspect ratio 12. The orientation distribution of the fibers is spatially dependent. Fibers near the center of the channel align closely with the flow direction, but fibers near the wall are observed to preferentially align in the vorticity (perpendicular to the flow and gradient) direction.   

A framework for simulating particle-particle particle-wall interactions in suspensions with irregular particles

An efficient direct numerical simulation method is developed to study the sedimentation of non-spherical particles in an incompressible Newtonian fluid. A new strategy is presented to model wall-particle collision based on 3D dynamics of a rigid particle, which complements the particle-particle collision model developed for low Stokes number flows. For non-spherical particles, contrary to spherical particles, upon the collision of a particle with a~wall, particle's orientation needs to be determined.~ In the presented method, kinematics of an arbitrary-shaped particle is solved considering particle's inertia and hydrodynamic forces. This model is used to simulate sedimentation of many particles in a vertical channel as well as suspensions of non-spherical particles under simple shear flow.   

Dynamics of anisotropic particles under waves

We present results on anisotropic particles in wavy flows in order to gain insight into the transport and mixing of microplastic particles in the near-shore environment. From theory and numerical simulations, we find that the rate of alignment of the particles is not constant and depends strongly on their initial orientation; thus, variations in initial particle orientation result in dispersion of anisotropic-particle plumes.~~We find that this dispersion is a function of the particle's eccentricity and the ratio of the settling and wave time scales.~Experiments in which non-spherical particles of various shapes are released under surface gravity waves were also performed. Our main goal is to explore the effects of particle shape under various wave scenarios.~ We vary the aspect ratio of the particle in our experiments while holding other variables constant. Our results demonstrate that particle shape can be important when predicting transport.