scholarly journals A simple justification of effective models for conducting or fluid media with dilute spherical inclusions

2021 ◽  
pp. 1-23
Author(s):  
David Gérard-Varet
Keyword(s):  
Stokes Equation ◽  
Effective Viscosity ◽  
Volume Fraction ◽  
Spherical Inclusions ◽  
Effective Media ◽  
Fluid Media ◽  
Low Volume ◽  
Random Distributions ◽  
Effective Models ◽  
The Stokes Equation

We present a gentle approach to the justification of effective media approximations, for PDE’s set outside the union of n ≫ 1 spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as n → + ∞ by simple arguments.

Observation of dislocations in dynamically loaded Cu-SiO2

1986 ◽  
Vol 44 ◽  
pp. 424-425
Author(s):  
D. S. Pritchard
Keyword(s):  
Electron Microscope ◽  
Strain Rate ◽  
Single Crystal ◽  
Transmission Electron Microscope ◽  
Volume Fraction ◽  
Screw Dislocations ◽  
Spherical Inclusions ◽  
Transmission Electron ◽  
Crystal Dispersion ◽  
Strain Rate Loading

The effect of varying the strain rate loading conditions in compression on a copper single crystal dispersion-hardened with SiO2 particles has been examined. These particles appear as small spherical inclusions in the copper lattice and have a volume fraction of 0.6%. The structure of representative crystals was examined prior to any testing on a transmission electron microscope (TEM) to determine the nature of the dislocations initially present in the tested crystals. Only a few scattered edge and screw dislocations were viewed in those specimens.

LOW CONCENTRATION LIMIT FOR A FLUID FLOW THROUGH A FILTER

1998 ◽  
Vol 08 (04) ◽  
pp. 623-643 ◽  
Author(s):  
SANJA MARUŠIĆ
Keyword(s):  
Asymptotic Behavior ◽  
Fluid Flow ◽  
Volume Fraction ◽  
Periodic Array ◽  
Concentration Limit ◽  
Global Flow ◽  
Low Concentration ◽  
Flow Through ◽  
Low Volume ◽  
Filtration Law

A fluid flow through an ∊-periodic array of obstacles distributed on a hypersurface (filter) is considered. The study of the asymptotic behavior as ∊→0 for two critical sizes of obstacles ∊ and ∊2 gives two different laws describing a global flow. In this paper we study the case of an intermediate obstacle size ∊β, 1 < β < 2 and we prove the continuity of the filtration law in the low-volume fraction limit.

Nanoparticles-Laden Gas Film in Aerostatic Thrust Bearing

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Zhiru Yang ◽  
Dongfeng Diao ◽  
Xue Fan ◽  
Hongyan Fan
Keyword(s):  
Effective Viscosity ◽  
Flow Model ◽  
Thrust Bearing ◽  
Volume Fraction ◽  
Load Capacity ◽  
Sio2 Nanoparticles ◽  
Enhancement Effect ◽  
The Novel ◽  
Two Phase ◽  
Air Film

Nanoparticles-laden gas film (NLGF) was formed by adding SiO2 nanoparticles with volume fraction in the range of 0.014–0.330% and size of 30 nm into the air gas film in a thrust bearing. An effective viscosity of the gas-solid two phase lubrication media was introduced. The pressure distribution in NLGF and the load capacity of the thrust bearing were calculated by using the gas-solid two phase flow model with the effective viscosity under the film thicknesses range of 15–60 μm condition. The results showed that the NLGF can increase the load capacity when the film thickness is larger than 30 μm. The mechanism of the enhancement effect of load capacity was attributed to the increase of the effective viscosity of the NLGF from the pure air film, and the novel lubrication media of the NLGF can be expected for the bearing industry application.

Suspensions with a tunable effective viscosity: a numerical study

2012 ◽  
Vol 693 ◽  
pp. 345-366 ◽  
Author(s):  
L. Jibuti ◽  
S. Rafaï ◽  
P. Peyla
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Spherical Particles ◽  
Dimensionless Number ◽  
Particle Rotation ◽  
Concentrated Suspensions ◽  
Sheared Suspensions ◽  
Neutrally Buoyant ◽  
Universal Behaviour

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

scholarly journals 3D MORPHOLOGICAL ANALYSIS OF COMPOSITE MATERIALS WITH AGGREGATES OF SPHERICAL INCLUSIONS

2011 ◽  
Vol 22 (1) ◽  
pp. 153 ◽  
Author(s):  
Arnaud Delarue ◽  
Dominique Jeulin
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Empirical Distribution ◽  
Geodesic Distance ◽  
Shortest Paths ◽  
Morphological Properties ◽  
3D Images ◽  
Spherical Inclusions ◽  
New Information ◽  
The Matrix

Composite materials containing aggregates of spherical inclusions are studied from 3D images obtained by X-ray microtomography. Using two point statistics in different directions, and the empirical distribution of orientations of pairs of inclusions, interesting details concerning the anisotropy of the distribution of inclusions are obtained and are related to the method of construction for these materials. Some 3D morphological properties, available on the 3D images, give new information on the shape and the distribution of aggregates: tortuosity of shortest paths in the matrix, local volume fraction, geodesic distance function, local histograms of numbers of objects.

scholarly journals Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

2018 ◽  
Vol 90 (6) ◽  
pp. 1085-1098 ◽  
Author(s):  
Isha Malhotra ◽  
Sujin B. Babu
Keyword(s):  
Self Assembly ◽  
Patch Size ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Interaction Strength ◽  
Colloidal System ◽  
Angle Distribution ◽  
Volume Fractions ◽  
Low Volume ◽  
A Chain

Abstract In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

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