Particle mesh Ewald Stokesian dynamics simulations for suspensions of non-spherical particles

2011 ◽  
Vol 675 ◽  
pp. 297-335 ◽  
Author(s):  
A. KUMAR ◽  
J. J. L. HIGDON
Keyword(s):  
Transport Properties ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Particle Surface ◽  
Spherical Particles ◽  
Stokesian Dynamics ◽  
Volume Fractions ◽  
Particle Mesh Ewald ◽  
The One ◽  
Many Body Interactions

A particle mesh Ewald (PME) Stokesian dynamics algorithm has been developed to model hydrodynamic interactions in suspensions of non-spherical dicolloidal particles. Dicolloids, which have recently been synthesized by a number of independent research groups (Johnson, van Kats & van Blaaderen (Langmuir, vol. 21, 2005, p. 11510), Mocket al. (Langmuir, vol. 22, 2006, p. 4037), Kim, Larsen & Weitz (J. Am. Chem. Soc., vol. 128, 2006, p. 14374)), consist of two intersecting spheres of varying radii and centre-to-centre separation. One-body resistance tensors and disturbance velocity fields are computed for general linear flows using a superposition of Stokes singularities along the symmetry axis of the dicolloid particles. The coefficients and the locations of the singularities are optimized to minimize the norm of the velocity error on the particle surface. The one-body solution provides all coefficients required for the far-field many-body interactions in the Stokesian dynamics algorithm. These generalize the analytical results for spheres employed in the classic algorithm. Modified lubrication interaction tensors are developed for dicolloids for the singular near-field lubrication interactions. Accuracy of the one-body solutions and two-body generalized Stokesian dynamics solutions are validated by comparison with high-precision numerical solutions computed with the spectral boundary element method of Muldowney & Higdon (J. Fluid Mech., vol. 298, 1995, p. 167). The newly developed PME Stokesian dynamics algorithm was used to study transport properties in dicolloidal suspensions over a range of volume fractions (φ ≤ 0.5). The effects of the degree of anisotropy on the properties of the suspension are discussed. For these mildly anisotropic particles, the transport properties remain close to those of spheres, however certain interesting trends emerge, with non-monotonic viscosity dependence as a function of increasing aspect ratio. The minimum viscosity in concentrated suspensions is lower than that for spheres with equal volume fraction over a range of volume fractions.

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

scholarly journals SIMULATION OF THE POLY- AND MONODISPERSED GRANULAR MATERIAL. PART II: THE STABILITY STATE CHARACTERIZATION / DAUGIADISPERSIO IR VIENDISPERSIO DALELIŲ MIŠINIO ELGSENOS TYRIMAS. II DALIS: STABILUMO BŪSENŲ CHARAKTERIZAVIMAS

2012 ◽  
Vol 4 (2) ◽  
pp. 59-66 ◽  
Author(s):  
Gvidas Pocius ◽  
Robertas Balevičius
Keyword(s):  
Volume Fraction ◽  
Particle Surface ◽  
Spherical Particles ◽  
Time Step ◽  
Resonant Effect ◽  
The Stability ◽  
Gravity Acceleration ◽  
Granular Aggregate ◽  
Radius Size

In the Part I of the paper, structure of granular aggregates obtained after compaction of poly- and mono-dispersed spherical particles was characterized in terms of the coordination number, particles contacting forces and volume fraction distributions. This part of investigation deals with characterization of the state of stability under quasistatic conditions of the formed granular aggregate structure. The proposed method is based on visualization of the plane of the particle radius size plotted normally to the particle velocity vector. At the beginning of the compacting process, when the discrete particle drops down under the gravity acceleration (almost free of contact with other particles), the planes plotted the cylinder-like pattern at each time step. At the quasistatic state, when the acceleration of the settled particles tends to negligible values, the plot of these planes represents a certain texture appearing on the particle surface. For the interpretation of these textures, Shilnikov's homoclinic bifurcation theory was discussed and applied. In particular, it was found that textures specifying the quasistatic state mainly resulted from the resonant effect depending on the degree of freedom of the analyzed particles. Santrauka Šioje straipsnio dalyje pagrindinis dėmesys skiriamas viendispersinio ir daugiadispersio sferinių dalelių mišinio mikrobūsenai charakterizuoti, analizuojant atskirų mišinio dalelių stabilumą esant kvazistatiniam būviui. Tiriamos ir vizualizuojamos atskirų dalelių greičio vektorių normalinių plokštumų formuojamos tekstūros, kurios esant kvazistatiniam būviui interpretuojamos kaip tam tikri rezonansinio poveikio dariniai, gaubiantys dalelių paviršių.

Micromechanical analysis for transverse thermal conductivity of composites

2010 ◽  
Vol 45 (11) ◽  
pp. 1245-1255 ◽  
Author(s):  
Sangwook Sihn ◽  
Ajit K. Roy
Keyword(s):  
Thermal Conductivity ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Numerical Models ◽  
Matrix Material ◽  
Analytic Solutions ◽  
Fiber Distribution ◽  
Fiber Volume ◽  
Volume Fractions ◽  
Transverse Thermal Conductivity

Micromechanical analyses were conducted for the prediction of transverse thermal conductivity of laminated composites. We reproduced and reinvestigated both analytic and numerical models with regular and randomly distributed fibers in matrix material. A parametric study was conducted for wide ranges of fiber volume fractions and fiber-to-matrix thermal conductivity ratios. The numerical solutions using finite element (FE) analysis were compared with various analytic solutions from simple and enhanced rule or mixtures and an effective inclusion method (EIM). It was found that the EIM yields a reasonably agreeable solution with the FE solution using a hexagonal-array of regular fiber distribution for wide ranges of fiber volume fraction and fiber-to-matrix thermal conductivity ratios, which makes the EIM a useful method in predicting various multiphysical transverse properties of composites. Comparison of the results from the regular- and random-fiber models indicates that the transverse thermal conductivity of composites can significantly be affected by the random fiber distributions, especially at high fiber volume fractions. A similar conclusion was made for the foams with random pore distribution. It was shown that the predictions with the random fiber distribution agree well with the experimental data.

scholarly journals Propagation of a strong shock over a random bed of spherical particles

2018 ◽  
Vol 839 ◽  
pp. 157-197 ◽  
Author(s):  
Y. Mehta ◽  
C. Neal ◽  
K. Salari ◽  
T. L. Jackson ◽  
S. Balachandar ◽  
...  
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Wave Dynamics ◽  
Volume Fractions ◽  
Reflected Shock ◽  
Complex Wave ◽  
The Mean ◽  
Particle Bed

Propagation of a strong incident shock through a bed of particles results in complex wave dynamics such as a reflected shock, a transmitted shock, and highly unsteady flow inside the particle bed. In this paper we present three-dimensional numerical simulations of shock propagation in air over a random bed of particles. We assume the flow is inviscid and governed by the Euler equations of gas dynamics. Simulations are carried out by varying the volume fraction of the particle bed at a fixed shock Mach number. We compute the unsteady inviscid streamwise and transverse drag coefficients as a function of time for each particle in the random bed for different volume fractions. We show that (i) there are significant variations in the peak drag for the particles in the bed, (ii) the mean peak drag as a function of streamwise distance through the bed decreases with a slope that increases as the volume fraction increases, and (iii) the deviation from the mean peak drag does not correlate with local volume fraction. We also present the local Mach number and pressure contours for the different volume fractions to explain the various observed complex physical mechanisms occurring during the shock–particle interactions. Since the shock interaction with the random bed of particles leads to transmitted and reflected waves, we compute the average flow properties to characterize the strength of the transmitted and reflected shock waves and quantify the energy dissipation inside the particle bed. Finally, to better understand the complex wave dynamics in a random bed, we consider a simpler approximation of a planar shock propagating in a duct with a sudden area change. We obtain Riemann solutions to this problem, which are used to compare with fully resolved numerical simulations.

The effective conductivity of random suspensions of spherical particles

1991 ◽  
Vol 432 (1886) ◽  
pp. 445-465 ◽  
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Effective Conductivity ◽  
Near Field ◽  
Theoretical Work ◽  
Spherical Particles ◽  
Volume Fractions ◽  
Cubic Lattices ◽  
Field Effects ◽  
Infinite Particle

The effective conductivity of an infinite, random, mono-disperse, hard-sphere suspension is reported for particle to matrix conductivity ratios of ∞, 10 and 0.01 for sphere volume fractions, c , up to 0.6. The conductivities are computed with a method previously described by the authors, which includes both far- and near-field interactions, and the particle configurations are generated via a Monte Carlo method. The results are consistent with the previous theoretical work of D. J. Jeffrey to O ( c 2 ) and the bounds computed by S. Torquato and F. Lado. It is also found that the Clausius-Mosotti equation is reasonably accurate for conductivity ratios of 10 or less all the way up to 60% (by volume). The calculated conductivities compare very well with those of experiments. In addition, percolation-like numerical experiments are performed on periodically replicated cubic lattices of N nearly touching spheres with an infinite particle to matrix conductivity ratio where the conductivity is computed as spheres are removed one by one from the lattice. Under suitable normalization of the conductivity and volume fraction, it is found that the initial volume fraction must be extremely close to maximum packing in order to observe a percolation transition, indicating that the near-field effects must be very large relative to far-field effects. These percolation transitions occur at the accepted values for simple (SC), body-centred (BCC) and face-centred (FCC) cubic lattices. Also, the vulnerability of the lattices computed here are exactly those of previous investigators. Due to limited data above the percolation threshold, we could not correlate the conductivity with a power law near the threshold ; however, it can be correlated with a power law for large normalized volume fractions. In this case the exponents are found to be 1.70, 1.75 and 1.79 for SC, BCC and FCC lattices respectively.

scholarly journals Surfactant stabilized bubbles flowing in a Newtonian fluid

2019 ◽  
Vol 24 (12) ◽  
pp. 3823-3842 ◽  
Author(s):  
Eilis Rosenbaum ◽  
Mehrdad Massoudi ◽  
Kaushik Dayal
Keyword(s):  
Newtonian Fluid ◽  
Base Fluid ◽  
Volume Fraction ◽  
Bubble Surface ◽  
Pairwise Interaction ◽  
Spherical Particles ◽  
Prior Work ◽  
Stokesian Dynamics ◽  
Current Application ◽  
A Current

Bubbles suspended in a fluid cause the suspension to have different rheological properties than the base fluid. In general, the viscosity of the suspension increases as the volume fraction of the bubbles is increased. A current application, and motivation for this study, is in wellbore cements used for hydrocarbon extraction and carbon sequestration. In these settings, the gas bubbles are dispersed into the cement to reduce the density as well as improve the properties for specific conditions or wellbore issues. In this paper, we use Stokesian dynamics to numerically simulate the behavior of a large number of bubbles suspended in a Newtonian fluid. Going beyond prior work on simulating particles in suspension, we account for the nature of bubbles by allowing for slip on the bubble surface, the deflection on the bubble surface, and a bubble–bubble pairwise interaction that represents the surfactant physics; we do not account for bubble compressibility. We incorporate these interactions and simulate bubble suspensions of monodisperse size at several volume fractions. We find that the bubbles remain better dispersed compared with hard spherical particles that show a greater tendency to structure or cluster.

A numerical study of granular shear flows of rod-like particles using the discrete element method

2012 ◽  
Vol 713 ◽  
pp. 1-26 ◽  
Author(s):  
Y. Guo ◽  
C. Wassgren ◽  
W. Ketterhagen ◽  
B. Hancock ◽  
B. James ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Flow Direction ◽  
Particle Surface ◽  
Granular Flows ◽  
Spherical Particles ◽  
Surface Geometry ◽  
High Solid ◽  
Volume Fractions ◽  
Aspect Ratios ◽  
Particle Aspect Ratio

AbstractThe effect of particle aspect ratio and surface geometry on granular flows is assessed by performing numerical simulations of rod-like particles in simple shear flows using the discrete element method (DEM). The effect of particle surface geometry is explored by adopting two types of particles: glued-spheres particles and true cylindrical particles. The particle aspect ratio varies from one to six. Compared to frictionless spherical particles, smaller stresses are obtained for the glued-spheres and cylindrical particle systems in dilute and moderately dense flows due to the loss of translational energy, which is partially converted to rotational energy, for the non-spherical particles. For dilute granular flows of non-spherical particles, stresses are primarily affected by the particle aspect ratio rather than the surface geometry. As the particle aspect ratio increases, the effective particle projected area in the plane perpendicular to the flow direction increases, so that the probability of the occurrence of the particle collisions increases, leading to a reduction in particle velocity fluctuation and therefore a decrease in the stresses. Hence, a simple modification is made to the kinetic theory for granular flows to describe the stress tensors for dilute flows of non-spherical particles by incorporating a normalized effective particle projected area to account for the effect of particle collision probability. For dense granular flows, the stresses depend on both the particle aspect ratio and the surface geometry. Sharp stress increases at high solid volume fractions are observed for the glued-spheres particles with large aspect ratios due to the bumpy surfaces, which impede the flow. However, smaller stresses are obtained for the true cylindrical particles with large aspect ratios at high solid volume fractions. This trend is attributed to the combined effects of the smooth particle surfaces and the particle alignments such that the major/long axes of particles are aligned in the flow direction. In addition, the apparent friction coefficient, defined as the ratio of shear to normal stresses, is found to decrease as the particle aspect ratio increases and/or the particle surface becomes smoother at high solid volume fractions.

scholarly journals Effect of Nanostructure on Thermal Conductivity of Nanofluids

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Saba Lotfizadeh ◽  
Themis Matsoukas
Keyword(s):  
Thermal Conductivity ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Numerical Study ◽  
Hollow Spheres ◽  
Structural Features ◽  
Solid Particles ◽  
Spherical Particles ◽  
Colloidal Gel ◽  
The One

The presence of colloidal particles is known to increase the thermal conductivity of base fluids. The shape and structure of the solid particles are important in determining the magnitude of enhancement. Spherical particles—the only shape for which analytic theories exist—produce the smallest enhancement. Nonspherical shapes, including clusters formed by colloidal aggregation, provide substantially higher enhancements. We conduct a numerical study of the thermal conductivity of nonspherical structures dispersed in a liquid at fixed volume fraction in order to identify structural features that promote the conduction of heat. We find that elongated structures provide high enhancements, especially if they are long enough to create a solid network (colloidal gel). Cross-linking further enhances thermal transport by directing heat in multiple directions. The most efficient structure is the one formed by hollow spheres consisting of a solid shell and a core filled by the fluid. In both dispersed and aggregated forms, hollow spheres provide enhancements that approach the theoretical limit set by Maxwell’s theory.

A Verified Non-Linear Regression Model for Elastic Stiffness Estimates of Finite Composite Domains Considering Combined Effects of Volume Fractions, Shapes, Orientations, Locations, and Number of Multiple Inclusions

2018 ◽  
Author(s):  
Ilige S. Hage ◽  
Charbel Y. Seif ◽  
Ré-Mi Hage ◽  
Ramsey F. Hamade
Keyword(s):  
Linear Regression ◽  
Aspect Ratio ◽  
Regression Model ◽  
Linear Regression Model ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Elastic Stiffness ◽  
Test Cases ◽  
Combined Effects ◽  
Volume Fractions

A non-linear regression model using SAS/STAT (JMP® software; Proc regression module) is developed for estimating the elastic stiffness of finite composite domains considering the combined effects of volume fractions, shapes, orientations, inclusion locations, and number of multiple inclusions. These estimates are compared to numerical solutions that utilized another developed homogenization methodology by the authors (dubbed the generalized stiffness formulation, GSF) to numerically determine the elastic stiffness tensor of a composite domain having multiple inclusions with various combinations of geometric attributes. For each inclusion, these considered variables represent the inclusions’ combined attributes of volume fraction, aspect ratio, orientation, number of inclusions, and their locations. The GSF methodology’s solutions were compared against literature-reported solutions of simple cases according to such well-known techniques as Mori-Tanaka and generalized self-consistent type methods. In these test cases, the effect of only one variable was considered at a time: volume fraction, aspect ratio, or orientation (omitting the number and locations of inclusions). For experimental corroboration of the numerical solutions, testing (uniaxial compression) was performed on test cases of 3D printed test cubes. The regression equation returns estimates of the composite’s ratio of normalized longitudinal modulus (E11) to that of the matrix modulus (Em) or E11/Em when considering any combination of all of the aforementioned inclusions’ variables. All parameters were statistically analyzed with the parameters retained are only those deemed statistically significant (p-values less than 0.05). Values returned by the regression stiffness formulation solutions were compared against values returned by the GSF formulation numerical and against the experimentally found stiffness values. Results show good agreement between the regression model estimates as compared with both numerical and experimental results.

scholarly journals The hydrodynamics of confined dispersions

2011 ◽  
Vol 687 ◽  
pp. 254-299 ◽  
Author(s):  
James W. Swan ◽  
John F. Brady
Keyword(s):  
High Frequency ◽  
Volume Fraction ◽  
Viscous Incompressible Fluid ◽  
Colloidal Dispersion ◽  
Spherical Particles ◽  
Stokesian Dynamics ◽  
Point Forces ◽  
Suspension Dynamics ◽  
Log Linear ◽  
Short Time

AbstractA method is proposed for computing the low-Reynolds-number hydrodynamic forces on particles comprising a suspension confined by two parallel, no-slip walls. This is constructed via the two-dimensional analogue of Hasimoto’s solution (J. Fluid Mech., vol. 5, 1959, pp. 317–328) for a periodic array of point forces in a viscous, incompressible fluid, and, like Hasimoto, the summation of interactions is accelerated by substitution and superposition of ‘Ewald-like’ forcing. This method is akin to the accelerated Stokesian dynamics technique (J. Fluid Mech., vol. 448, 2001, pp. 115–146) and models the suspension dynamics with log–linear computational scaling. The effectiveness of this approach is demonstrated with a calculation of the high-frequency dynamic viscosity of a colloidal dispersion as function of volume fraction and channel width. Similarly, the short-time self-diffusivity for and the sedimentation rate of spherical particles in a confined suspension are determined. The results demonstrate the influence of confining geometry on the transport of small particles, which is becoming increasingly important for micro- and biofluidics.

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