Dynamic simulation of arbitrarily shaped particles in shear flow

A new simulation framework was created for modeling the dynamics of arbitrarily shaped particles dispersed in Newtonian fluid. Theoretical complexity usually restricts suspension simulations to those for spheroids. This new simulation is loosely based on the Stokesian Dynamics method including long range hydrodynamic interaction and uses spheres as building components for greater particulates of arbitrary shape. This approach is capable of accurately reproducing the dynamics of an isolated arbitrarily shaped particle. As verification, the simulated results are compared against known results for a rod-like particle. An elongated rod-shaped structure made from linked spheres is shown to reproduce the well-known elongated ellipsoidal particle dynamics described by [Jeffrey Proc R Soc Lond A 102:161–179, 1923]. The predicted orbital period and spin rates for a fiber in shear are reproduced and compare well with theoretical prediction over a wide aspect ratio range. Predicted particle dynamics for other shaped particles are then demonstrated.     

Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibility. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation functions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.     

Mullins effect in elastomers filled with particles aligned by a magnetic field

Magnetorheological elastomers (MRE) are particulate composite materials, whose fillers are structured by a magnetic field during curing. These particles are brought in quasi-contact by the field, in a chain-like unidirectional structure. Due to this organization the local stresses between the particles is high and debonding between particles and elastomer occur at low strain. We have experimentally studied and analytically modeled the progressive breaking of the polymer-to-particle bonds. The two cases of strong and weak bonds between elastomers and particles have been studied. The analytical model correctly reproduces the stress strain curve in the presence of a debonding process although overestimating the size of the debonding cavity which is obtained by comparison between experiments and FEM simulations. The extension of the model to a chain of spheres allows to well explain the Mullins effect on MRE. Furthermore it is shown that the quality of the bonds between the particles and the elastomer does not influence the change of stiffness brought by the application of a magnetic field.     

Dynamic simulation of non-spherical particulate suspensions

Particle-level simulation has been employed to investigate rheology and microstructure of non-spherical particulate suspensions in a simple shear flow. Non-spherical particles in Newtonian fluids are modeled as three-dimensional clusters of neutrally buoyant, non-Brownian spheres linked together by Hookean-type constraint force. Rotne–Prager correction to velocity disturbance has been employed to account for far-field hydrodynamic interactions. An isolated rod-like particle in simple shear flow exhibits a periodic orientation distribution, commonly referred to as Jeffery orbit. Lubrication-like repulsive potential between clusters have been included in simulation of rod-like suspensions at various aspect ratios over dilute to semi-dilute volume fractions. Shear viscosity evaluated by orientation distribution qualitatively agrees with one obtained by direct computation of shear stress.     

Rotational dynamics in dipolar colloidal suspensions: video microscopy experiments and simulations results

The dynamics of field-induced structures in very dilute dipolar colloidal suspensions subject to rotating magnetic fields have been experimentally studied using video microscopy. When a rotating field is imposed the chain-like aggregates rotate with the magnetic field frequency. We found that the size of the induced structures at small rotational frequencies is larger than at zero rotating frequency, i.e. when an uniaxial magnetic field is applied. At higher frequencies, the average size of the aggregates decreases with frequency following a power law with exponent −0.5 as the hydrodynamic friction forces overcome the dipolar magnetic forces, causing the chains break up. A non-thermal molecular dynamics simulations are also reported, showing good agreement with the experiments.     

Simulating orthokinetic heterocoagulation and cluster growth in destabilizing suspensions

Using direct numerical simulation, we investigate the coagulation behavior of non-Brownian colloidal particles as exemplified by Al₂O₃ particles. This yields the so-called capture efficiency, for which we give an analytical expression, as well as other time-dependent variables such as the cluster growth rate. Instead of neglecting or strongly approximating the hydrodynamic interactions between particles, we include hydrodynamic and non-hydrodynamic interactions in a Stokesian dynamics approach and a comprehensive modeling of the interparticle forces. The resulting parallelized simulation framework enables us to investigate the dynamics of polydisperse particle systems composed of several hundred particles at the same high level of modeling we used for a close investigation of the coagulation behavior of two unequal particles in shear flow. Appropriate cluster detection yields all the information about large destabilizing systems, which is needed for models used in flow-sheet simulations. After non-dimensionalization, the results can be generalized and applied to other systems tending to secondary coagulation.     

Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions

Dynamical correlations between colloidal particles, in a quasi-two-dimensional geometry, are measured by optical microscopy. The system consists of charged polystyrene spheres suspended in water and confined between two parallel plates. The long-range electrostatic interaction is screened and the interparticle direct interaction becomes an effective excluded volume interaction. Thus, the observed long-range correlations, between the motion of pairs of particles, are due to the solvent mediated hydrodynamic interactions. Such correlations are observed as a dependence in the interparticle distance of the diffusion coefficients for the normal modes, collective and relative, for which results are presented here for a range of particle concentrations.     

Slow Motion of an Assemblage of Porous Spherical Shells Relative to a Fluid

The body-force-driven motion of a homogeneous distribution of spherically symmetric porous shells in an incompressible Newtonian fluid and the fluid flow through a bed of these shell particles are investigated analytically. The effect of the hydrodynamic interaction among the porous shell particles is taken into account by employing a cell-model representation. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field around a single particle in a unit cell, and the drag force acting on the particle by the fluid is obtained in closed forms. For a suspension of porous spherical shells, the mobility of the particles decreases or the hydrodynamic interaction among the particles increases monotonically with a decrease in the permeability of the porous shells. The effect of particle interactions on the creeping motion of porous spherical shells relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solution describing the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres. The particle-interaction behavior for a suspension of porous spherical shells with a relatively low permeability may be approximated by that of permeable spheres when the porous shells are sufficiently thick.     

Modelling and numerical methods for the dynamics of impurities in a gas

The dynamics of a mixture of impurities in a gas can be represented by a system of linear Boltzmann equations for hard spheres. We assume that the background is in thermodynamic equilibrium and that the polluting particles are sufficiently few (in comparison with the background molecules) to admit that there are no collisions among couples of them. In order to derive non‐trivial hydrodynamic models, we close the Euler system around local Maxwellian's which are not equilibrium states. The kinetic model is solved by using a Monte Carlo method, the hydrodynamic one by implicit–explicit Runge–Kutta schemes with weighted essentially non‐oscillatory reconstruction (J. Sci. Comput. 2005; 25 (1–2):129–155). Several numerical tests are then computed in order to compare the results obtained with the kinetic and the hydrodynamic models. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental Study of Nonlinear Resonances and Anti-Resonances in a Forced,Ordered Granular Chain

We experimentally study a one-dimensional uncompressed granular chain composed of a finite number of identical spherical elastic beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary drive at its left end and has a fixed boundary at its right end. Such ordered granular media represent an interesting new class of nonlinear acoustic metamaterials, since they exhibit essentially nonlinear acoustics and have been designated as “sonic vacua” due to the fact that their corresponding speed of sound (as defined in classical acoustics) is zero. This paves the way for essentially nonlinear and energy-dependent acoustics with no counterparts in linear theory. We experimentally detect time-periodic, strongly nonlinear resonances whereby the particles (beads) of the granular chain respond at integer multiples of the excitation period, and which correspond to local peaks of the maximum transmitted force at the chain’s right, fixed end. In between these resonances we detect a local minimum of the maximum transmitted forces corresponding to an anti-resonance in the stationary-state dynamics. The experimental results of this work confirm previous theoretical predictions, and verify the existence of strongly nonlinear resonance responses in a system with a complete absence of any linear spectrum; as such, the experimentally detected nonlinear resonance spectrum is passively tunable with energy and sensitive to dissipative effects such as internal structural damping in the beads, and friction or plasticity effects. We compare the experimental results with direct numerical simulations of the granular network and deduce satisfactory agreement.     

Fracture of granular materials composed of arbitrary grain shapes: A new cohesive interaction model

Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesive phase lying between the grains. Contact situations are solved according to unilateral contact and Coulomb friction laws. In order to test the developed model, 2D uniaxial compression simulations are performed. Numerical results show the ability of the model to mimic the macroscopic behavior of an aggregate grain subject to axial compression, as well as fracture initiation and propagation. A study of the influence of model and sample parameters provides important information on the ability of the model to reproduce various behaviors.     

The stochastic dynamics of an array of atomic force microscopes in a viscous fluid

We consider the stochastic dynamics of an array of two closely spaced atomic force microscope cantilevers in a viscous fluid for use as a possible biomolecule sensor. The cantilevers are not driven externally, as is common in applications of atomic force microscopy, and we explore the stochastic cantilever dynamics due to the constant buffeting of fluid particles by Brownian motion. The stochastic dynamics of two adjacent cantilevers are correlated due to long range effects of the viscous fluid. Using a recently proposed thermodynamic approach the hydrodynamic correlations are quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available atomic force microscope cantilevers. It is shown that the force on a cantilever due to the fluid correlations with an adjacent cantilever is more than 3 times smaller than the Brownian force on an individual cantilever. Our results indicate that measurements of the correlations in the displacement of an array of atomic force microscopes can detect piconewton forces with microsecond time resolution.     

Motion of a magnetizable liquid in a rotating magnetic field

Moskowitz and Rosensweig [1] describe the drag of a magnetic liquid — a colloidal suspension of ferromagnetic single-domain particles in a liquid carrier — by a rotating magnetic field. Various hydrodynamic models have been proposed [2, 3] to describe the macroscopic behavior of magnetic suspensions. In the model constructed in [2] it was assumed that the intensity of magnetization is always directed along the field so that the body torque is zero. Therefore, this model cannot account for the phenomenon under consideration. We make a number of simplifying assumptions to discuss the steady laminar flow of an incompressible viscous magnetizable liquid with internal rotation of particles moving in an infinitely long cylindrical container in a rotating magnetic field. The physical mechanism setting the liquid in motion is discussed. The importance of unsymmetric stresses and the phenomenon of relaxation of magnetization are emphasized. The solution obtained below is also a solution of the problem of the rotation of a polarizable liquid in a rotating electric field according to the model in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–43, July–August, 1970.     

OBSERVATIONS OF BUBBLE SELF-ORGANIZATION IN LASER-MATTER INTERACTIONS

Bubbles generated in laser–metal interactions (LMI) at the transition from planar-to-volume boiling behave like hard (and soft) spheres. Micrographic analysis indicates that the surface layer of vaporizing metal, which comprises small microscale bubbles, behaves like a two-dimensional granular system. Bubble collision leads to bubble self-organization which changes with laser power density Q_p, and falls into (i) the kinetic regime, (ii) the clustering regime, or (iii) the regime of inelastic collapse (when bubbles form chain-like clusters), in analogy with the results of numerical simulations of hard-sphere dynamics. At a certain power density, shock waves that travel over the surface become strong enough, so that the system of bubbles behaves like horizontally and vertically shaken granular material. Since bubbles in the vibrational process are decelerated, hydrodynamic forces deform them, causing them to stay coalesced after the collision, forming a cluster with plateau borders, which is actually metal foam. The results presented show the existence of various complexity levels in the self-organization of bubbles, their sensitivity to the variation of interaction parameters, and finally, they indicate some universal features of bubble system dynamics.     

Structural instability in the sedimentation of particulate suspensions through viscoelastic fluids

A theory is developed to describe a structural instability that has been observed during the sedimentation of particulate suspensions through viscoelastic fluids. The theory is based on the assumption that the influence of hydrodynamic interactions in viscoelastic fluids, which tend to cause particles to aggregate, is in competition with hydrodynamic dispersion, which acts to maintain a homogeneous microstructure. In keeping with the experimental observations, it predicts that the suspension structure will stratify into vertical columns when a dimensionless stability parameter exceeds a critical value. The column-to-column separation, measured in particle radii, is predicted to be proportional to the square root of the ratio of the dimensionless dispersion coefficient to the product of the particle volume fraction and the Deborah number. The time for the formation of the columns is predicted to scale with the inverse of the average volume fraction. These predictions are in agreement with experimental data reported in the literature.     

Drag forces of interacting spheres in power-law fluids

Drag forces of interacting particles suspended in power-law fluid flows were investigated in this study. The drag forces of interacting spheres were directly measured by using a micro-force measuring system. The tested particles include a pair of interacting spheres in tandem and individual spheres in a cubic matrix of multi-sphere in flows with the particle Reynolds number from 0.7 to 23. Aqueous carboxymethycellulose (CMC) solutions and glycerin solutions were used as the fluid media in which the interacting spheres were suspended. The range of power-law index varied from 0.6 to 1.0. In conjunction to the drag force measurements, the flow patterns and velocity fields of power-law flows over a pair of interacting spheres were also obtained from the laser assisted flow visualization and numerical simulation.

Both experimental and computational results suggest that, while the drag force of an isolated sphere depends on the power-index, the drag coefficient ratio of an interacting sphere is independent from the power-law index but strongly depends on the separation distance and the particle Reynolds number. Our study also shows that the drag force of a particle in an assemblage is strongly positions dependent, with a maximum difference up to 38%.     

Hydrodynamic interactions in squirmer motion: Swimming with a neighbour and close to a wall

We analyze the hydrodynamic coupling of pairs of squirmers and the impact it has on their short and long-time behavior. The study combines an analytic analysis of the hydrodynamic interactions between pairs of squirmers with computer simulations to elucidate the quantitative capabilities of the theoretical approach. The numerical study allows us to address the motion of simple geometries of squirmers on long times and perform a complete discussion of the effective repulsive interactions in squirmer ensembles. The contrast between analytic and numerical results identifies the features of active motion responsible for such effective interactions. The framework developed also allows for an analysis of the hydrodynamic coupling between a squirmer and a solid wall and shows the possibility of bounded motion next to a solid wall.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment

The rheological behavior of stable slurries is shown to be characterized by a bimodal model that represents a slurry as made up of a coarse fraction and a colloidal size fine fraction. According to the model, the two fractions behave independently of each other, and the non-Newtonian behavior of the viscosity is solely caused by the colloidal fraction, while the coarse fraction increases the viscosity level through hydrodynamic interactions. Data from experiments run with colloidal coal particles of about 2–3 µm average size dispersed in water show the viscosity of these colloidal suspensions to exhibit a highly shearrate-dependent behavior and, in the high shear limit, to match very closely the viscosity of suspensions of uniform size rigid spheres although the coal volume fraction must be determined semi-empirically. Different amounts of coarse coal particles are added to the colloidal suspension and the viscosity of the truly bimodal slurries measured as a function of shear rate. In agreement with the bimodal model, the measured shear viscosities show the coarse fraction to behave independently of the colloidal fraction and its contribution to the viscosity rise to be independent of the shear rate. It is shown that the shear rate exerted on the colloidal fraction is higher than that applied by the viscometer as a result of hydrodynamic interactions between the coarse particles, and that it is this effective higher shear rate which is necessary to apply in the correlations. For determining the coal volume fraction a relatively simple and quite accurate measurement technique is developed for determining the density and void fraction of coarse porous particles; the technique directly relates volume fraction to mass fraction.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

Stokes flow past an assemblage of axisymmetric porous spherical shell-in-cell models: effect of stress jump condition

The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of porous concentric spherical shell-in-cell model is studied. Boundary conditions on the cell surface that correspond to the Happel, Kuwabara, Kvashnin and Cunningham/Mehta-Morse models are considered. At the fluid-porous interfaces, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid are used. The hydrodynamic drag force acting on the porous shell by the external fluid in each of the four boundary conditions on the cell surface is evaluated. It is found that the normalized mobility of the particles (the hydrodynamic interaction among the porous shell particles) depends not only on the permeability of the porous shells and volume fraction of the porous shell particles, but also on the stress jump coefficient. As a limiting case, the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres with jump.