Deformation Of Elastic Particles Research Articles

Stochastic model for migration and breakage of detrital and authigenic fines

Mobilisation of attached particles during flow in rocks occurs in geo-energy processes. Particle mobilisation, their migration through rocks and pore plugging yield significant decline in permeability and well injectivity and productivity. While much is currently known about the underlying mechanisms governing the detachment of detrital particles against attracting electrostatic forces, a critical gap exists in the theoretical understanding of detachment by breakage of widely spread authigenic particles, which naturally grow on rock grains during geological times. Previous works derived micro-scale mechanical equilibrium equations for both detrital and authigenic particles, and the upscaling procedure from particle to pore and core scales for detrital fines. In this paper, for the first time we derive a stochastic model for migration and breakage of authigenic fines and authigenic–detrital mixtures. This allows for core-scale transport modelling based on the particle-scale torque balance. We introduce a novel framework for predictive stochastic detachment modelling by particle–rock bond breakage that integrates the beam theory of elastic particle deformation, strength failure criteria and viscous flow around the attached particle. The analytical expressions for stress maxima and stress diagrams for a single particle allow determining the critical failure stresses, breakage points of the beam and breakage flow velocity. The mathematical model describing lab coreflood includes the maximum retention function for both authigenic and detrital fines. The matching laboratory coreflood data under increasing velocity at micro- and core-scales achieved high matching of the experimental data by the model. High matching validates the upscaling and downscaling procedures derived.

Numerical simulation of particle flow behavior in a screw conveyor using the discrete element method

Particle motion in a screw conveyor was simulated with the discrete element method. The particle flow behavior and transport processes at different screw rotating speeds and filling levels were investigated in this study. The spatial distributions of particle velocity were predicted. The predicted mass flow rate increased with increasing screw rotating speed and filling level. The contact forces and granular temperatures of particles were also calculated. The simulation results showed that the translational granular particle temperatures were higher than the rotational granular particle temperatures. In addition, the configurational temperatures of particles were calculated from simulated instantaneous particle overlaps, and results indicated that deformation of elastic particles contributed to the rate of energy dissipation. Good agreement between the numerical simulation and experimental results was achieved in this study.

Elastic particle deformation in rectangular channel flow as a measure of particle stiffness.

In this study, we experimentally observed and characterized soft elastic particle deformation in confined flow in a microchannel with a rectangular cross-section. Hydrogel microparticles of pNIPAM were produced using two different concentrations of crosslinker. This resulted in particles with two different shear moduli of 13.3 ± 5.5 Pa and 32.5 ± 15.7 Pa and compressive moduli of 66 ± 10 Pa and 79 ± 15 Pa, respectively, as measured by capillary micromechanics. Under flow, the particle shapes transitioned from circular to egg, triangular, arrowhead, and ultimately parachute shaped with increasing shear rate. The shape changes were reversible, and deformed particles relaxed back to circular/spherical in the absence of flow. The thresholds for each shape transition were quantified using a non-dimensional radius of curvature at the tip, particle deformation, circularity, and the depth of the concave dimple at the trailing edge. Several of the observed shapes were distinct from those previously reported in the literature for vesicles and capsules; the elastic particles had a narrower leading tip and a lower circularity. Due to variations in the shear moduli between particles within a batch of particles, each flow rate corresponded to a small but finite range of capillary number (Ca) and resulted in a series of shapes. By arranging the images on a plot of Ca versus circularity, a direct correlation was developed between shape and Ca and thus between particle deformation and shear modulus. As the shape was very sensitive to differences in shear modulus, particle deformation in confined flow may allow for better differentiation of microparticle shear modulus than other methods.

Predictions of granular temperatures of particles in a flat bottomed spout bed

The configurational temperature and translational and rotational granular temperatures of particles are simulated using CFD-DEM in a flat bottomed spout bed. The distributions of velocity and volume fraction of particles are obtained in the bed. The translational and rotational granular temperatures are calculated from simulated instantaneous translational and angular velocities of particles. The statistical framework is proposed to define the configurational temperature or compactivity of particles in a flat bottomed spout bed. The configurational temperatures of particles are calculated from simulated instantaneous overlaps of particles. The configurational temperatures are larger at high solids volume fraction than that at low solids volume fractions. The simulated translational and rotational granular temperatures decrease with the increase of solids volume fractions. The predicted configurational temperatures are larger than that translational and rotational granular temperature, indicating that the rate of energy dissipation does contribute by deformation of elastic particles in a flat bottomed spout bed. The lower rotational granular temperature means the translational mechanism dominates the flow behaviors of particles. The influence of air jet velocity on granular temperatures and configurational temperature is analyzed. Increasing air jet velocity, the translational and rotational granular temperatures and configurational temperature are increased.

The Sedimentation of Slim Flexible Particles in Stokes Flow

Background/Objectives: The dynamics of elastic slim particles (filaments) surrounded by fluid flow is a noteworthy topic of study because of its application in natural sciences and industrial processes. When deformation of elastic particle is large many complications arise which needs specific consideration in order to develop an efficient method for modeling the solid-fluid interaction accurately and with acceptable computational cost. Method: In order to study the sedimentation process of filament which is immersed in a quiescent fluid flow, we constitute related governing equations based on nonlocal solid-fluid interaction coupling with slender body theory. The fluid flow governed by Stokes assumptions which allow us to use superposition principle. Also, the extracted equations rearrange by two controller parameters Elasto-gravitation, β, and Slenderness-parameter, ϵ. Findings: A Highly Flexible filament (HF-filament) and a Moderately Flexible filament (MF-filament) have examined by mentioned method. The results show that the HF-filament fall on a periodic motion during the sedimentation process. This periodic motion leads to a set of unbalance forces along the filament which causes a permanent lateral drift. In the other side the MF-filament meets an equilibrium point with a final constant U-shape. Also, in order to validation we compare the outcome data with the results obtained by local and multiple scale analysis methods. Application/Improvements: The approach have been presented by this paper can be used in different fields which there are any necessity to simulating slim particles motion more simple and with less computational cost in compare with conventional methods.

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.

Prediction of configurational and granular temperatures of particles using DEM in reciprocating grates

The configurational temperature and granular temperature of particles are simulated by means of discrete element method (DEM) in the reciprocating grate. Motion of mono-sized particles in the reciprocating grate is predicted with the change of frequency and amplitude of moveable grates. The distributions of velocity and volume fraction of particles are obtained. The granular temperature and configurational temperature of particles are calculated from simulated instantaneous velocities and overlaps of particles in a reciprocating grate. The simulated results show that the granular temperatures of particles increase, reach maximum, and then decrease with the increase of solids volume fractions. While the configurational temperature of particles is monotonously increased with the increase of solids volume fraction, indicating that the rate of energy dissipation contributes by deformation of elastic particles at high solids volume fraction. The influence of amplitude and frequency on granular temperature and configurational temperature is analyzed.

Simulations of configurational and granular temperatures of particles using DEM in roller conveyor

The configurational temperature and translational and rotational granular temperatures of particles are simulated by means of discrete element method (DEM) in the roller conveyor. Motion of particles in the roller conveyor is predicted with the change of rotation speed. The distributions of velocity and volume fraction of particles are obtained along bed height. The translational and rotational granular temperatures are calculated from simulated instantaneous translational and angular velocities of particles. The configurational temperatures of particles are calculated from simulated instantaneous overlaps of particles. The simulated results show that the translational and rotational granular temperatures and configurational temperature of particles decrease with the increase of solids volume fractions. The predicted configurational temperatures are larger than that translational and rotational granular temperature, indicating that the rate of energy dissipation do contributes by sliding and rolling contact deformation of elastic particles in the roller conveyor. The lowest translational granular temperature means that the rotational mechanism dominates in the roller conveyor. The influence of rotation speeds of rollers on granular temperatures and configurational temperature is analyzed.

Stabilization of External Filter Cake by Colloidal Forces in a “Well–Reservoir” System

Growth of an external filter cake with its final stabilization has been widely reported for waterflooding in oilfields, well drilling, fresh water storage, and industrial waste disposal in aquifers. We derive the mechanical equilibrium equation for stabilized cake accounting for electrostatic force and for varying permeate force factor. The main empirical parameter of the model, highly affecting the stabilized cake prediction, is the lever arm ratio for the particle on the cake surface. The lever arm ratio was calculated from laboratory cross-flow filtration experiments and from well injectivity data. It was also determined from Hertz’s theory for the elastic particle deformation on the solid cake surface. Good agreement between the results validates the developed mechanical equilibrium model with the lever arm ratio determined from the elastic particle deformation theory.

Simulations of deformable systems in fluids under shear flow using an arbitrary Lagrangian Eulerian technique

An arbitrary Lagrangian Eulerian finite element method based numerical code for viscoelastic fluids using well-known stabilization techniques (SUPG, DEVSS, log-conformation) is adapted to perform a 3D study of soft systems (drops, elastic particles) suspended in Newtonian and viscoelastic fluids under unbounded shear flow. Since the interface between the suspended objects and the matrix needs to be tracked, a finite element method with SUPG stabilization and second-order time discretization is defined on the interface, with the normal velocity of the interface equal to the normal component of the fluid velocity and a tangential velocity such that the elements on the interface are evenly distributed. This allows the mesh to get rid of the tank-treading motion of the particle. Both drops and elastic particles deform because of the flow and attain stationary deformed shape and orientation with respect to the flow direction. The effects of the physical parameters of the system on the phenomenon are investigated. The code is validated for drops and elastic particles in a Newtonian fluid through comparison with data from literature. New results on the deformation of elastic particles in an Upper Convected Maxwell fluid and a Giesekus fluid are presented.

Deformation of elastic particles in viscous shear flow

In this paper, the dynamics of two dimensional elastic particles in a Newtonian viscous shear flow is studied numerically. To describe the elastic deformation, an evolution equation for the Eulerian Almansi strain tensor is derived. A constitutive equation is thus constructed for an incompressible “Neo–Hookean” elastic solid where the extra stress tensor is assumed to be linearly proportional to the Almansi strain tensor. The displacement field does not appear in this formulation. A monolithic finite element solver which uses Arbitrary Lagrangian–Eulerian moving mesh technique is then implemented to solve the velocity, pressure and stress in both fluid and solid phase simultaneously. It is found that the deformation of the particle in the shear flow is governed by two non-dimensional parameters: Reynolds number ( Re) and Capillary number ( Ca, which is defined as the ratio of the viscous force to the elastic force). In the Stokes flow regime and when Ca is small ( Ca < 0.65 ), the particle deforms into an elliptic shape while the material points inside the particle experience a tank-treading like motion with a steady velocity field. The deformation of the elastic particle is observed to vary linearly with Ca, which agrees with theoretical results from a perturbation analysis. Interactions between two particles in a viscous shear flow are also explored. It is observed that after the initial complicated interactions, both particles reach an equilibrium elliptic shape which is consistent with that of a single particle.

Influence of Elastic Deformation of Particles on Heckel Analysis

The Heckel equation is one of the most useful equations for describing the compaction properties of pharmaceutical powders. Important material properties (e.g., yield strength) of powders can be derived using Heckel analysis. Two types of Heckel analysis are in common use. One is the “out-of-die,” or “zero-pressure” method, the other is the “in-die” or “at-pressure” method. Because particles undergo elastic deformation under pressure, which tends to lower the porosity of the powder bed, the “out-of-die” method describes powder consolidation and compaction more accurately than the “in-die” method. However, “in-die” Heckel analysis has been widely used because of the speed and ease of data collection. Using L-lysine monohydrochloride dihydrate as a model compound, this work analyzes quantitatively the effects of elastic deformation on the calculation of porosity of a tablet, and therefore on the Heckel analysis. The effects of a small change in porosity, ε, on Heckel analysis are presented mathematically. It is found that a decrease in porosity of 0.001, when the porosity is lower than 0.05, causes a significant increase in the value of −ln ε. Therefore, data at ε < 0.05 should be interpreted with caution when using Heckel analysis. Elastic deformation causes positive deviations in the Heckel plot, and therefore leads to a yield strength that is lower than the true value. The lower the elastic modulus of the powder, the greater is the deviation from the true value. Therefore, the “in-die” method gives values of yield strength that are significantly lower than the true values for most pharmaceutical powders.

Stress relaxation of compacts produced from viscoelastic materials

Stress relaxation of tablets is a phenomenon that is known to be related to elastic deformation of particles. Expressions of stress relaxation are tablet expansion and capping. It has been shown that there is a direct relation between the changes in volume of the tablet and the amount of stored energy, calculated from the elastic modulus and the yield strength of the material. The relations are, however, different for the different materials. On the basis of the assumption that the increase in tablet volume is an expression of stress relaxation and stored energy is the driving force for it, there should be a counteracting force that prevents a compact from expansion. This paper shows that the counteracting force is determined by particle bonding, quantified by the Ryshkewitch-Duckworth relation and friction of the tablet with the die wall, quantified by the ejection pressure. The data presented here suggest that the final tablet porosity is unequivocally determined by stored energy, particle attraction and friction of the tablet with the die wall. All tablets that were capped showed both high stored energies and large particle bonding. From this observation it is concluded that porous and capped tablets suffer from the same problem, but the expression stress relaxation is different for the different materials.

特集 粉末の成形・加工 粒子系モデルによる銅の３次元圧縮解析

Simulation of compaction of copper powder is carried out in three-dimensions based on a particulate modeling. Besides elastic deformation of particles, a model of plastic deformation is introduced based on micro-compression of spherical particles ; since the pressure required to achieve certain density by simulation without taking account of plastic deformation of particles is much higher than the experimentally derived one, it is concluded that it is necessary to introduce its effect. Simulations of closed-die compaction, isostatic compaction and three-dimensional compaction, where powder is capable of being compacted with arbitrary strain ratios, are performed for powders of copper particles. It is thus shown that relationship between pressures and density ratio and also constitutive behavior during compaction obtained by the simulation agree qualitatively well with experimental results. Quantitatively, however, the pressure for a particular density ratio is about a half of the experimentally derived one. The reasons are discussed and technical issues for overcoming the problems are suggested.

Coagulation of Particles in Shear Flow: Applications to Biological Cells

A simplified model is developed which makes it possible to describe the shear-induced coagulation of particles with different types of attractive interactions. In this model the trajectories of particles are calculated without taking into account any nonhydrodynamic interactions, while the hydrodynamic interaction is described in terms of the lubrication theory. Coagulation is assumed to occur if the hydrodynamic stretching force exerted on the doublet of particles is smaller than the attractive force binding the particles together. If the nonhydrodynamic interaction is reduced to the Van der Waals forces of molecular attraction, calculations of capture efficiency in terms of our simplified analysis are shown to be in good agreement with those carried out by other authors on the basis of analysis of numerically calculated trajectories. Further applications of our model deal with the coagulation of some biological cells, namely blood platelets, which are responsible for thrombous formation. In the first approximation activated platelets can be described as spherical elastic particles interacting via the superposition of Van der Waals attraction and biochemically specific interactions, which are attributed to receptor-coreceptor bonds between cells. The specific interactions are considered to result from the interplay of two subsystems, chemical and mechanical ones. The analysis of the kinetics of formation of intercellular bonds is carried out, yielding a simple analytic representation for the force of biospecific interaction. The biospecific interaction is shown to affect the capture efficiency, ϵ, at intermediate range of shear rate G , so that a plateau appears in the curve ϵ( G), while beyond this range coagulation is governed by Van der Waals attraction and ϵ is a decreasing function of G. This type of dependence is in qualitative agreement with that observed for blood platelet aggregation. Quantitative agreement is achieved with reasonable choice of parameters of interaction. Our approach also makes it possible to take into account the perturbation of particles' trajectories and the corrections to the force of Van der Waals and biospecific interactions due to elastic deformation of particles, which is shown to increase the capture efficiency at low shear rates and decrease it at high shear rates.

Elastic aftereffect of iron-graphite compacts in cold pressing

1. The results are presented of an investigation of the elastic aftereffect exhibited during pressing by iron-graphite materials containing from 3 to 30 wt.% of graphite. 2. An equation has been derived expressing the elastic aftereffect in terms of compaction pressure and amount of the second component. The hypothesis is put forward that the elastic deformation of particles in their contact zone may be described by Hertz' theory.