Dynamic simulations of the inhomogeneous sedimentation of rigid fibres

2002 ◽  
Vol 468 ◽  
pp. 205-237 ◽  
Author(s):  
JASON E. BUTLER ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Sedimentation Rate ◽  
Particle Orientation ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Heterogeneous Structure ◽  
Mass Force ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
A Value ◽  
Particle Force

We have simulated the dynamics of suspensions of fibres sedimenting in the limit of zero Reynolds number. In these simulations, the dominant inter-particle force arises from hydrodynamic interactions between the rigid, non-Brownian fibres. The simulation algorithm uses slender-body theory to model the linear and rotational velocities of each fibre. To include far-field interactions between the fibres, the line distribution of force on each fibre is approximated by making a Legendre polynomial expansion of the disturbance velocity on the fibre, where only the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution can be specified completely by a centre-of-mass force, a couple, and a stresslet. Short-range interactions between particles are included using a lubrication approximation, and an infinite suspension is simulated by using periodic boundary conditions. Our numerical results confirm that the sedimentation of these non-spherical, orientable particles differs qualitatively from the sedimentation of spherical particles. The simulations demonstrate that an initially homogeneous, settling suspension develops clusters, or streamers, which are particle rich surrounded by clarified fluid. The instability which causes the heterogeneous structure arises solely from hydrodynamic interactions which couple the particle orientation and the sedimentation rate in particle clusters. Depending upon the concentration and aspect ratio, the formation of clusters of particles can enhance the sedimentation rate of the suspension to a value in excess of the maximum settling speed of an isolated particle. The suspension of fibres tends to orient with gravity during the sedimentation process. The average velocities and orientations, as well as their distributions, compare favourably with previous experimental measurements.

A numerical study of the sedimentation of fibre suspensions

1998 ◽  
Vol 376 ◽  
pp. 149-182 ◽  
Author(s):  
MICHAEL B. MACKAPLOW ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Numerical Study ◽  
Point Particle ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Fibre Suspensions ◽  
The Mean

The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.

Propulsive Efficiency of the Underwater Dolphin Kick in Humans

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Alfred von Loebbecke ◽  
Rajat Mittal ◽  
Frank Fish ◽  
Russell Mark
Keyword(s):  
Fluid Dynamic ◽  
Three Dimensional ◽  
Underwater Video ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Video Footage ◽  
Wide Range ◽  
Dolphin Kick ◽  
Body Theory

Three-dimensional fully unsteady computational fluid dynamic simulations of five Olympic-level swimmers performing the underwater dolphin kick are used to estimate the swimmer’s propulsive efficiencies. These estimates are compared with those of a cetacean performing the dolphin kick. The geometries of the swimmers and the cetacean are based on laser and CT scans, respectively, and the stroke kinematics is based on underwater video footage. The simulations indicate that the propulsive efficiency for human swimmers varies over a relatively wide range from about 11% to 29%. The efficiency of the cetacean is found to be about 56%, which is significantly higher than the human swimmers. The computed efficiency is found not to correlate with either the slender body theory or with the Strouhal number.

scholarly journals MOPSMAP v0.9: A versatile tool for modeling of aerosol optical properties

2018 ◽  
Author(s):  
Josef Gasteiger ◽  
Matthias Wiegner
Keyword(s):  
Remote Sensing ◽  
Optical Properties ◽  
Aerosol Particles ◽  
Particle Orientation ◽  
Spherical Particles ◽  
Refractive Indices ◽  
Hygroscopic Growth ◽  
Web Interface ◽  
Optical Modeling ◽  
Wide Range

Abstract. The spatiotemporal distribution and characterization of aerosol particles are usually determined by remote sensing and optical in-situ measurements. These measurements are indirect with respect to microphysical properties and thus inversion techniques are required to determine the aerosol microphysics. Scattering theory provides the link between microphysical and optical properties; it is not only needed for such inversions but also for radiative budget calculations and climate modeling. However, optical modeling can be very time consuming, in particular if non-spherical particles or complex ensembles are involved. In this paper we present the MOPSMAP package (modeled optical properties of ensembles of aerosol particles) which is computationally fast for optical modeling even in case of complex aerosols. The package consists of a data set of pre-calculated optical properties of single aerosol particles, a Fortran program to calculate the properties of user-defined aerosol ensembles, and a user-friendly web interface for online calculations. Spheres, spheroids, and a small set of irregular particle shapes are considered over a wide range of sizes and refractive indices. MOPSMAP provides the fundamental optical properties assuming random particle orientation, including the scattering matrix for the selected wavelengths. Moreover, the output includes tables of frequently used properties such as the single scattering albedo, the asymmetry parameter or the lidar ratio. To demonstrate the wide range of possible MOPSMAP applications a selection of examples is presented, e.g., dealing with hygroscopic growth, mixtures of absorbing and non-absorbing particles, the relevance of the size equivalence in case of non-spherical particles, and the variability of volcanic ash microphysics. The web interface is designed to be intuitive for expert and non-expert users. To support users a large set of default settings is available, e.g., several wavelength-dependent refractive indices, climatologically representative size distributions, and a parameterization of hygroscopic growth. Calculations are possible for single wavelengths or user-defined sets (e.g., of specific remote sensing application). For expert users more options for the microphysics are available. Plots for immediate visualization of the results are shown. The complete output can be downloaded for further applications. All input parameters and results are stored in the user’s personal folder so that calculations can easily be reproduced. The MOPSMAP package is available on request for offline calculations, e.g., when large numbers of different runs for sensitivity studies shall be made.

Non-Spheric Colloidal Suspensions in Three-Dimensional Space

1997 ◽  
Vol 08 (04) ◽  
pp. 985-997 ◽  
Author(s):  
Dewei Qi
Keyword(s):  
Reynolds Number ◽  
Dimensional Space ◽  
Low Reynolds Number ◽  
Paper Industry ◽  
Three Dimensional ◽  
Colloidal Suspensions ◽  
Solid Particles ◽  
Spherical Particles ◽  
Dynamic Simulations ◽  
Low Reynolds

The translation and rotation of non-spherical particles, such as ellipsoidal, cylindric or disk-like pigment particles, in a Couette flow system similar to a blade coating system in the paper industry6 have been successfully simulated by using the lattice-Boltzmann method combined with Newtonian dynamic simulations. Hydrodynamic forces and torques are obtained by the use of boundary conditions which match the moving surface of solid particles. Then Euler equations have been integrated to include three-dimensional rotations of the suspensions by using four quaternion parameters as generalized coordinates. The three-dimensional rotations have been clearly observed. Consequently, the motion of the particles suspended in fluids of both low-Reynolds-number and finite-Reynolds-number, up to several hundreds, has been studied. It appears that the 3D translation and rotation of the non-spherical particles are more clearly observed in a high-Reynolds-number fluid than in a low-Reynolds-number fluid.

Effects of Particle Concentration on the Partitioning of Suspensions at Small Divergent Bifurcations

1996 ◽  
Vol 118 (3) ◽  
pp. 287-294 ◽  
Author(s):  
R. Ditchfield ◽  
W. L. Olbricht
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Diameter ◽  
Circular Cross Section ◽  
Experimental Results ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Straight Tube ◽  
Particle Volume ◽  
Reynolds Number Flow

Experimental results are reported for the low Reynolds number flow of a suspension of spherical particles through a divergent capillary bifurcation consisting of a straight tube of circular cross-section that splits to form two tubes of equal diameter. The partitioning of particles between the downstream branches of the bifurcation is measured as a function of the partitioning of total volume (particles + suspending fluid) between the branches. Two bifurcation geometries are examined: a symmetric Y-shaped bifurcation and a nonsymmetric T-shaped bifurcation. This experiment focuses on the role of hydrodynamic interactions between particles on the partitioning of particles at the bifurcation. The particle diameter, made dimensionless with respect to the diameter of the branch tubes, ranges from 0.4 to 0.8. Results show that hydrodynamic interactions among the particles are significant at the bifurcation, even for conditions where interactions are unimportant in the straight branches away from the bifurcation. As a result of hydrodynamic interactions among particles at the bifurcation, the partitioning of particles between the branches is affected for particle volume fractions as small as 2 percent. The experimental results show that the effect of particle volume fraction is to diminish the inhomogeneity of particle partitioning at the bifurcation. However, the magnitude of this effect depends strongly on the overall shape of the bifurcation geometry, and, in particular on the angles between the branches.

The instability of a dispersion of sedimenting spheroids

1989 ◽  
Vol 209 ◽  
pp. 521-542 ◽  
Author(s):  
Donald L. Koch ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Particle Number ◽  
Particle Density ◽  
Particle Number Density ◽  
Density Fluctuations ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Inertial Effects ◽  
Number Density ◽  
Characteristic Particle ◽  
Particle Length

It is shown that hydrodynamic interactions between non-Brownian, non-spherical, sedimenting particles give rise to an increase in the number of neighbouring particles in the vicinity of any given particle. This result suggests that the suspension is unstable to particle density fluctuations even in the absence of inertia; a linear stability analysis confirms this inference. It is argued that the instability will lead to convection on a lengthscale (nl)−½, where l is a characteristic particle length and n is the particle number density. Sedimenting suspensions of spherical particles are shown to be stable in the absence of inertial effects.

scholarly journals The collective dynamics of self-propelled particles

2008 ◽  
Vol 595 ◽  
pp. 239-264 ◽  
Author(s):  
VISHWAJEET MEHANDIA ◽  
PRABHU R. NOTT
Keyword(s):  
Particle Concentration ◽  
Near Field ◽  
Continuous Process ◽  
Pair Correlation ◽  
Fluid Motion ◽  
Finite Size ◽  
Two Dimensions ◽  
Creeping Flow ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations

We propose a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We propose a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector p, whose locomotion is driven by the action of a force dipole Sp of constant magnitude S0 at a point slightly displaced from its centre. To simplify the calculation, we place the dipole at the centre of the particle, and introduce a virtual propulsion force Fp to effect propulsion. The magnitude F0 of this force is proportional to S0. The directions of Sp and Fp are determined by p. In isolation, a self-propelled particle moves at a constant velocity u0p, with the speed u0 determined by S0. When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, quantified by the area fraction φa. We find several interesting features in the microstructure and statistics. We find that particles tend to swim in clusters wherein they are in close proximity. Consequently, incorporating the finite size of the particles and the near-field hydrodynamic interactions is of the essence. There is a continuous process of breakage and formation of the clusters. We find that the distributions of particle velocity at low and high φa are qualitatively different; it is close to the normal distribution at high φa, in agreement with experimental measurements. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing φa. The pair correlation function shows a large anisotropic build-up near contact, which decays rapidly with separation. There is also an anisotropic orientation correlation near contact, which decays more slowly with separation. Movies are available with the online version of the paper.

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