VISCOSITY METHOD FOR THE DETERMINATION OF THE THICKNESS OF SOLVATION LAYERS NEAR PARTICLES DISPERSED IN A LIQUID

2005 ◽  
Vol 12 (03) ◽  
pp. 457-462 ◽  
Author(s):  
SHAOXIAN SONG ◽  
YIMIN ZHANG ◽  
TOMLINSON FORT
Keyword(s):  
Size Distribution ◽  
Spherical Particle ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Viscosity Method ◽  
Theoretical Derivation ◽  
Solid Spheres

In this paper, we present a method for determining the thickness of solvation layers near spherical particles dispersed in a liquid through measurements of the viscosity of the dispersion as a function of the volume fraction of the dry particles in the dispersion and the size distribution of the particles. It is termed viscosity method. The theoretical derivation for the method is based on Einstein's theory of viscosity of dispersions, while two assumptions are made: 1. Solvation layers contribute to increasing the viscosity of the dispersion in c times as the same volume of rigid solid spheres. 2. The thickness of solvation layers is the same near every chemically similar spherical particle in a given dispersion.

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.

Brownian diffusion of particles with hydrodynamic interaction

1976 ◽  
Vol 74 (1) ◽  
pp. 1-29 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Brownian Motion ◽  
Particle Flux ◽  
Chemical Potential ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Brownian Diffusion ◽  
Thermodynamic Force ◽  
Uniform Size ◽  
Reynolds Number Flow

The classical theory of Brownian motion applies to suspensions which are so dilute that each particle is effectively alone in infinite fluid. We consider here the modifications to the theory that are needed when rigid spherical particles are close enough to interact hydrodynamically. It is first shown that Brownian motion is a diffusion process of the conventional kind provided that the particle configuration does not change significantly during a viscous relaxation time. The original argument due to Einstein, which invokes an equilibrium situation, is generalized to show that the particle flux in probability space due to Brownian motion is the same as that which would be produced by the application of a certain ‘thermodynamic’ force to each particle. We then use this prescription to deduce the Brownian diffusivities in two different types of situation. The first concerns a dilute homogeneous suspension which is being deformed, and the relative translational diffusivity of two rigid spherical particles with a given separation is calculated from the properties of the low-Reynolds-number flow due to two spheres moving under equal and opposite forces. The second concerns a suspension in which there is a gradient of concentration of particles. The thermodynamic force on each particle in this case is shown to be equal to the gradient of the chemical potential of the particles, which brings considerations of the multi-particle excluded volume into the problem. Determination of the particle flux due to the action of this force is equivalent to determination of the sedimentation velocity of particles falling through fluid under gravity, for which a theoretical result correct to the first order in volume fraction of the particles is available. The diffusivity of the particles is found to increase slowly as the concentration rises from zero. These results are generalized to the case of a (dilute) inhomogeneous suspension of several different species of spherical particle, and expressions are obtained for the diagonal and off-diagonal elements of the diffusivity matrix. Numerical values of all the relevant hydrodynamic functions are given for the case of spheres of uniform size.

scholarly journals A Lattice Model for Elastic Particulate Composites

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1584 ◽  
Author(s):  
Darius Zabulionis ◽  
Vytautas Rimša
Keyword(s):  
Mechanical Response ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Particulate Composite ◽  
High Volume ◽  
Spherical Particles ◽  
Particulate Composites ◽  
The Finite Element Method ◽  
Network Method

In the present article, a version of the lattice or spring network method is proposed to model the mechanical response of elastic particulate composites with a high volume fraction of spherical particles and with a much weaker matrix compared to the stiffness of the particles. The main subject of the article is the determination of the axial stiffnesses of the springs of the cell. A comparison of the mechanical response of a three-dimensional particulate composite cube obtained using the finite element method and the proposed methodology showed that the efficiency of the proposed methodology increases with an increasing volume fraction of the particles.

Analysis of polydisperse bubbles in the aluminium–hydrogen system using a size-dependent contrast

2006 ◽  
Vol 39 (5) ◽  
pp. 676-682 ◽  
Author(s):  
M. Paskevicius ◽  
C. E. Buckley
Keyword(s):  
Size Distribution ◽  
Small Angle ◽  
High Pressures ◽  
Volume Fraction ◽  
Average Volume ◽  
Size Dependent ◽  
Angle Scattering ◽  
Fraction Size

The characterization of hydrogen defects in an aluminium–hydrogen system was performed previously [Buckleyet al.(2001).J. Appl. Cryst.34, 119–129] using small-angle scattering, inelastic neutron scattering and electron microscopy techniques. This analysis resulted in the determination of the relative change in lattice parameter as a result of hydrogen introduction into the Al matrix. However, this method relied on the average volume of the bubbles of hydrogen and also the pressure in a bubble of average volume. The characterization of the Al–H system has been improved by considering the size polydispersity of the hydrogen bubbles. The determination of a volume-fraction size distribution of the bubbles from small-angle scattering data has allowed a polydispersity analysis to be undertaken. A size-dependent contrast has been utilized in the modification of the volume-fraction size distribution into a more accurate form that accounts for varying concentrations of hydrogen within bubbles of different sizes. The determination of the size-dependent contrast is based upon an equation of state for molecular hydrogen which incorporates the compressibility of hydrogen under high pressures. The formation of alane (AlH3) is also investigated, as it can be formed by the chemisorption of hydrogen in aluminium under high pressures. The polydispersity analysis has allowed a more accurate description of the Al–H system and can be applied to similar scattering systems where the scattering length density is not constant over the whole scattering size regime.

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