Transient rolling friction model for discrete element simulations of sphere assemblies

The rolling resistance between a pair of contacting particles can be modeled with two mechanisms. The first mechanism, already widely addressed in the DEM literature, involves a contact moment between the particles. The second mechanism involves a reduction of the tangential contact force, but without a contact moment. This type of rotational resistance, termed creep-friction, is the subject of the paper. Within the creep-friction literature, the term “creep” does not mean a viscous mechanism, but rather connotes a slight slip that accompanies rolling. Two extremes of particle motions bound the range of creep-friction behaviors: a pure tangential translation is modeled as a Cattaneo–Mindlin interaction, whereas prolonged steady-state rolling corresponds to the traditional wheel–rail problem described by Carter, Poritsky, and others. DEM simulations, however, are dominated by the transient creep-friction rolling conditions that lie between these two extremes. A simplified model is proposed for the three-dimensional transient creep-friction rolling of two spheres. The model is an extension of the work of Dahlberg and Alfredsson, who studied the two-dimensional interactions of disks. The proposed model is applied to two different systems: a pair of spheres and a large dense assembly of spheres. Although creep-friction can reduce the tangential contact force that would otherwise be predicted with Cattaneo–Mindlin theory, a significant force reduction occurs only when the rate of rolling is much greater than the rate of translational sliding and only after a sustained period of rolling. When applied to the deviatoric loading of an assembly of spheres, the proposed creep-friction model has minimal effect on macroscopic strength or stiffness. At the micro-scale of individual contacts, creep-friction does have a modest influence on the incremental contact behavior, although the aggregate effect on the assembly's behavior is minimal.     

Non-slipping adhesive contact between mismatched elastic spheres: A model of adhesion mediated deformation sensor

A generalized JKR model is established for non-slipping adhesive contact between two dissimilar elastic spheres subjected to a pair of pulling forces and a mismatch strain. We discuss the full elastic solution to the problem as well as the so-called non-oscillatory solution in which tension and shear tractions along the contact interface is decoupled from each other. The model indicates that the mismatch strain has significant effect on the contact area and the pull-off process. Under a finite pulling force, a pair of adhering spheres is predicted to break apart spontaneously at a critical mismatch strain. This study suggests an adhesion mediated deformation sensing mechanism by which cells and molecules can detect mechanical signals in the environment via adhesive interactions.     

Non-slipping adhesive contact between mismatched elastic cylinders

We have recently proposed a generalized JKR model for non-slipping adhesive contact between two elastic spheres subjected to a pair of pulling forces and a mismatch strain (Chen, S., Gao, H., 2006c. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54, 1548–1567). Here we extend this model to adhesion between two mismatched elastic cylinders. The attention is focused on how the mismatch strain affects the contact area and the pull-off force. It is found that there exists a critical mismatch strain at which the contact spontaneously dissociates. The analysis suggests possible mechanisms by which mechanical deformation can affect binding between cells and molecules in biology.     

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%.     

Brownian dynamics simulation for suspensions of oblong-particles under shear flow

Computer simulations of the shear flow for the suspensions of oblong-particles were performed using nonequilibrium Brownian Dynamics (BD). The model particle is a rigid body made up of linearly connected spheres with the interparticle potential of a repulsive Lennard-Jones potential. The length-over-width ratios of the oblong-particles used in the present calculations are 5/3 and 3. In the concentrated suspensions high orientation is easily induced by shear at low shear rates. The systems of the oblong-particles exhibit the structural transition that causes the significant change in the rheological properties at high shear rates. Furthermore, the dependence of the length-over-width ratio of the particle is examined. Received: 16 June 1997 Accepted: 3 February 1998     

Application of moment interaction to the construction of a stable model of graphite crystal lattice

The aim of the present paper is to construct and study a model of pair moment interaction between carbon atoms in the two-dimensional graphite lattice. The carbon atom is modeled by a structure consisting of three rigidly connected mass points located at the vertices of an equilateral triangle. The interaction between mass points is described by a pair force potential, but the total interatomic interaction contains moment components owing to the finite size of the structure modeling the atom. We compute rank 4 tensors characterizing the elastic properties of the graphite crystal lattice constructed on the basis of our model. We determine lattice stability criteria depending on the number of coordination spheres taken into account. We show that this model permits one to ensure stability of the graphite lattice but significantly underestimates the transverse-to-longitudinal interatomic coupling rigidity ratio. We construct a generalized moment potential that permits one to obtain a rigidity ratio consistent with experimental data.     

Steady shear rheology of dilute polystyrene particle gels

This paper describes an experimental study on dispersions of monodisperse polystyrene (PS) spheres with a typical radius of 1 μm, dispersed in an electrolyte at high ionic strength, screening the electrostatic repulsion. These suspensions gelate at rest even at low volume fractions of PS particles. The density of the particles is matched with the solvent by using deuterium oxide for volume fractions φ≤0.117. Steady-state flow curves, viscosity as a function of shear rate, are measured and reported for 0.014<φ<0.322. The measured flow curves are analyzed on the basis of two models: 1. In the giant floc model (van Diemen and Stein 1983, 1984; Schreuder et al. 1986, 1987; Laven et al. 1988), at low shear rates, the shear is not distributed homogeneously but is limited to certain shear planes; the energy dissipation during steady flow is due primarily to overcoming the viscous drag on the suspended particles during motion caused by encounters of particles in the shear planes. Though this model was developed for higher solid volume fractions (0.35–0.425), we found that it also describes the rheology of dilute particle gels for 0.15≤φ≤0.3, using the same values for the parameters in the model as in the high solid volume fraction region. For φ<0.15, the model also describes the data if the fraction of distance by which a moving particle entrains its neighbors, is assumed to increase in this φ region. 2. The model of de Rooij (de Rooij et al. 1993, 1994) considers aggregates in shear flow to be monodisperse impermeable spheres with a fractal structure. The permeability is taken into account by considering a hydrodynamic radius smaller than the gyration radius in the Krieger-Dougherty expression for the hydrodynamic contribution to the viscosity. Through the use of a yield criterion the aggregate radius is modeled as a function of shear rate. We found that the model describes our experimental results, with a combination of parameter values used already by de Rooij, but only for φ<0.15. Received: 7 May 1998 Accepted: 22 December 1998     

On the viscosity of a concentrated suspension of solid spheres

Explanations of the very high viscosities of concentrated suspensions of spheres based on the dissipation in squeezing flow between particles pairs are shown to be in error. The dissipation in pair interactions is always of the order of that generated by shearing motions, and this dissipation is of too low an order in concentration for single pair interactions to explain the observed viscosities.     

Dynamics of the flow around colliding spheres

An investigation of the flow resulting from the collision of two spheres at low Reynolds numbers is presented. Each sphere starts from rest and traverses a distance of 5 sphere diameters to the point of contact. Experimental and numerical results are compared for a symmetric collision; that is, a collision between two spheres of the same diameter and travelling with the same velocity. The flow consists of two axisymmetric recirculation zones which become a pair of colliding vortex rings, expanding radially from the collision point. Several examples of unbalanced collisions are also presented numerically, with one or both of the velocity and diameter of the spheres altered. These collisions break the symmetry, altering the post-collision expansion of the vortex rings.     

Uniaxial deformation of a random packing of particles

Summary Mechanical behavior of dense packing spheres with small irregularities is investigated in this paper. A generalization of the hertzian contact model for surfaces of the form x ^k yields a normal contact force F _n , which is proportional to ζ^{1+1/ k} , with the normal displacement ζ. For oblique forces, the frictional force can be calculated, [10]. Different load cases are explained in detail. It is shown that the stress-strain curve during initial loading of the packing is identical with the force-displacement relation at the contact point, using an appropriate constant. The results for uniaxial loading, unloading and reloading are illustrated. As experimentally observed, the axial pressure in unloading is smaller than during loading, while the lateral pressure increases. The stress-strain relation is compared with well-known empirical relations of rock and soil mechanics, and the wave velocity for spherical irregularities agrees with earlier geomechanical theories for random packing of smooth spheres. Received 19 July 1998; accepted for publication 19 October 1998     

Investigation of transonic and supersonic flow past a pair of bodies

Transonic and supersonic flows past a pair of bodies have been experimentally investigated. The leading bodies were spheres, cylinders, and cones, while the trailing bodies were flat-ended circular cylinders. The leading and trailing bodies were joined by cylindrical rods of various lengths, aligned with the axis of symmetry. For these models, the pattern of flow between the bodies and the Mach number dependence of the drag coefficientC _x were determined in the acceleration and deceleration flow regimes in a wind tunnel. The experimental results are used to analyze the properties of the flow between the bodies and the variation of the aerodynamic coefficients of the models. The reasons for the hysteresis in the behavior of the coefficients in the acceleration and deceleration stages are discussed. The influence of the shape and dimensions of the leading body on the modelC _x is evaluated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 158–164, March–April, 1998.     

Method of fundamental solutions for multidimensional Stokes equations by the dual-potential formulation

A simple and accurate boundary-type meshless method of fundamental solutions (MFS) is applied to solve both 2D and 3D Stokes flows based on the dual-potential formulation of velocity potential and stream function vector. Using the dual-potential concept, the solutions of both 2D and 3D Stokes flows are obtained by combining the much simpler fundamental solutions of Laplace (potential) and bi-harmonic equations without using the complicated singular fundamental solutions such as Stokeslets and their derivatives as well as source doublet hypersingularity. The developed algorithm is used to test five numerical experiments for 2D flows: (1) circular cavity, (2) wave-shaped bottom cavity and (3) circular cavity with eccentric rotating cylinder; and for 3D flows: (4) a uniform flow passing a sphere and (5) a uniform flow passing a pair of spheres. Good results are obtained as comparing with solutions of analytical and numerical methods such as FEM, BEM and other meshfree schemes.     

Digital particle image accelerometry

A high-resolution video-based technique for obtaining two-dimensional fluid acceleration field data has been developed. The algorithm uses a combination of cross-correlations and autocorrelations on doubly exposed images of particle-seeded flows. Autocorrelations of individual video frames in an image pair yield two instantaneous velocity fields from which accelerations can be computed. Cross-correlations between successive images in the pair are used to resolve directional ambiguity associated with the autocorrelation. Time intervals are made arbitrarily small through the use of a laser sheet generator circuit which is synchronized with the framing rate of the camera. The technique is validated using a fluid-filled Petri dish subject to a known periodic motion. Ongoing development, uncertainties, and limitations of the technique are discussed. Received: 22 October 1998/Accepted: 27 September 2000     

The adhesive contact of viscoelastic spheres

We have formulated the restricted self-consistent model for the adhesive contact of linear viscoelastic spheres. This model is a generalization of both the Ting (J. Appl. Mech. 33 (1966) 845) approach to the viscoelastic contact of adhesionless spheres and the restricted self-consistent model for adhesive axisymmetric bodies. We also show how the model can be used in practice by giving a few examples of numerical solutions.     

Application of solvent evaporation technique for pure drug crystal spheres preparation

An innovative application of the solvent evaporation technique was suggested. Solvent evaporation technique is a technique for drug encapsulation and nanosphere preparation. The widely used technique is also facing the problem of low actual drug entrapment percent, which is not economic from the industrial view. The goal of this work is trying to use the advantage of this technique concerning the product sphericity and the ability to control particle size, to prepare a drug as pure crystals spheres. Ibuprofen is selected as a model drug. The spheres are formed by using Polyvinyl pyrrolidone (PVP) or Polyethylene glycol (PEG) as an anti-aggregating agent but not formed on using tween or span. Particle size and actual drug content depend on the concentrations the anti-aggregating agent used. Surfaces of the drug crystal spheres are porous with empty sphere internal structure on using PVP but spongy and rough on using PEG. The drug has its identity chemical form in the drug crystal spheres. IR scan of spheres prepared on using PEG showed a characteristic ether peak. DSC showed melting endothermic peak of PEG, but X-ray showed minor change in the drug crystal patterns. Drug release profiles from crystal spheres prepared with the same anti-aggregating agent are close to each other. The drug release profiles from drug crystal spheres prepared by using PEG are more controlled than that prepared by using PVP. The drug release mechanism is diffusion. It was concluded that, the same technique could be suggested for preparation of other biomedical material in pure crystals spheres with controlled particle size. These properties may encourage to prepare very small particles with spherical shape for inhalation or injection as an innovative particle technology application for the widely used technique.     

Modeling of the unsteady force for shock–particle interaction

The interaction between a particle and a shock wave leads to unsteady forces that can be an order of magnitude larger than the quasi-steady force in the flow field behind the shock wave. Simple models for the unsteady force have so far not been proposed because of the complicated flow field during the interaction. Here, a simple model is presented based on the work of Parmar et al. (Phil Trans R Soc A 366:2161–2175, 2008). Comparisons with experimental and computational data for both stationary spheres and spheres set in motion by shock waves show good agreement in terms of the magnitude of the peak and the duration of the unsteady force.      

Rheology of concentrated suspensions containing mixtures of spheres and fibres

Optimising flow properties of concentrated suspensions is an important issue common for many industries. The rheology of concentrated suspensions has therefore been studied intensively both experimentally and theoretically. Most studies have focused on monodisperse and polydisperse suspensions of either spheres or fibres. In practice, most suspensions contain particles that are polydisperse both in size and shape. A mixing rule for such systems is expected to be a powerful tool for engineers and product designers. Therefore in this work, suspensions of spheres, fibres and mixtures thereof were characterised using rotational shear rheometry and in-line image analyses. Thereby, total solids volume concentration and fibre fraction was varied. Results from transient and steady-state shear rheometry are discussed with respect to concentration, fibre fraction, and shear induced microstructure. Experimentally obtained viscosity data were accurately fitted using the model proposed by Farris (T Soc Rheol 12:281, 1968) for mixtures of monodisperse non-interacting spheres of different sizes.Originally presented at the Annual European Rheology Conference 2003, AERC 2003     

Rheology of polymer blends: linear model for viscoelastic emulsions

 Kerner's model for flow of composite elastic media is extended to an emulsion of viscoelastic phases with interfacial tension undergoing deformations of small amplitude. A privileged internal structure inside the suspended drops is discussed in terms of fluid circulation across the interface. It is shown that for usual drop radius and interfacial tension values of emulsions, the rheological behavior predicted by the model, with very simple expression for the complex shear modulus, is quantitatively similar to that predicted by Palierne's model. Predictions of the model are compared with experimental data obtained on a polystyrene/polyethylene blend sheared in a small-amplitude oscillatory mode. Received: 10 August 1998 Accepted: 18 December 1998     

A capillary force model for interactions between two spheres

Based on the method of energy principle, an analytical approach for computing the capillary force for sphere/sphere geometry is presented in this paper. In modeling the capillary force, we consider spheres with both equal and non-equal radii, for both symmetric and asymmetric configurations at liquid/solid interfaces. We use numerical analysis to investigate the validity and efficiency of the derived model. The effect of various parameters including humidity, distance between two spheres, radii of spheres and contact angles on the meniscus force are investigated. Finally the results obtained from the model are compared with experimental measurements, and the accuracy and precision of the presented approach is verified.