Calculation of the virtual mass of spherical particles in a dispersed medium

1985 ◽  
Vol 25 (5) ◽  
pp. 735-744
Author(s):  
A. E. Kroshilin ◽  
V. E. Kroshilin
Keyword(s):  
Spherical Particles ◽  
Virtual Mass ◽  
Dispersed Medium

Ensemble-Average Equations of a Particulate Mixture

1997 ◽  
Vol 119 (2) ◽  
pp. 428-434 ◽  
Author(s):  
L. M. Liljegren
Keyword(s):  
Fluid Transport ◽  
Transport Equations ◽  
Ensemble Average ◽  
Spherical Particles ◽  
Particle Phase ◽  
Virtual Mass ◽  
The Third ◽  
Continuity Equations ◽  
Two Phases ◽  
Drag Term

A method of evaluating the transfer terms appearing in the ensemble-average fluid transport equation is developed and applied to obtain the transport equations describing flow of a dilute particulate mixture containing solid spherical particles. The equations apply in the limit where interactions between phases are both quasi-steady and viscous, which is defined as flows that meet the three criterion Ref(a/ℒ)2 ≪ 1, vfτ/a2 ≫ 1, and Rep ≪ 1. In this limit, the terms describing transfer of momentum between the two phases of the mixture are evaluated to O(1) in the particle radius and O(γp) in the particle phase density. The continuity equations and consistency principle are exact. When the first two conditions are not met, the transport equations require the terms that describe virtual mass forces; when the third is not met, the transport equations require terms that describe Oseen corrections to the drag term.

Virtual mass and drag in two-phase flow

1991 ◽  
Vol 225 ◽  
pp. 177-196 ◽  
Author(s):  
B. U. Felderhof
Keyword(s):  
Equilibrium Distribution ◽  
Hard Spheres ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Spherical Particles ◽  
Inviscid Fluid ◽  
Virtual Mass ◽  
Ensemble Averaging ◽  
Two Phase ◽  
Numerical Predictions

We study virtual mass and drag effects in a fluid suspension consisting of spherical particles immersed in an incompressible, nearly inviscid fluid. We derive average equations of motion for the fluid phase and the particle phase by the method of ensemble averaging. We show that the virtual mass and drag coefficients may be expressed exactly in terms of the dielectric constant of a corresponding dielectric suspension with the same distribution of particles. We make numerical predictions for the case of an equilibrium distribution of hard spheres.

STEM Study of Surface Plasmon Excitation in Small Spherical Particles

1990 ◽  
Vol 48 (2) ◽  
pp. 42-43
Author(s):  
Daniel UGARTE
Keyword(s):  
Energy Loss ◽  
Spherical Particles ◽  
Small Particles ◽  
Bulk Materials ◽  
Low Loss ◽  
Plasmon Excitation ◽  
Surface Modes ◽  
Surface Plasmon Excitation ◽  
Analytical Electron ◽  
Analytical Electron Microscope

Small particles exhibit chemical and physical behaviors substantially different from bulk materials. This is due to the fact that boundary conditions can induce specific constraints on the observed properties. As an example, energy loss experiments carried out in an analytical electron microscope, constitute a powerful technique to investigate the excitation of collective surface modes (plasmons), which are modified in a limited size medium. In this work a STEM VG HB501 has been used to study the low energy loss spectrum (1-40 eV) of silicon spherical particles [1], and the spatial localization of the different modes has been analyzed through digitally acquired energy filtered images. This material and its oxides have been extensively studied and are very well characterized, because of their applications in microelectronics. These particles are thus ideal objects to test the validity of theories developed up to now.Typical EELS spectra in the low loss region are shown in fig. 2 and energy filtered images for the main spectral features in fig. 3.

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