scholarly journals Measuring local volume fraction, long-wavelength correlations, and fractionation in a phase-separating polydisperse fluid

2014 ◽  
Vol 141 (16) ◽  
pp. 164901 ◽  
Author(s):  
J. J. Williamson ◽  
R. M. L. Evans
Keyword(s):  
Volume Fraction ◽  
Long Wavelength ◽  
Local Volume ◽  
Local Volume Fraction

Permeability in the Mushy Zone

2010 ◽  
Vol 649 ◽  
pp. 399-408 ◽  
Author(s):  
R.G. Erdmann ◽  
D.R. Poirier ◽  
A.G. Hendrick
Keyword(s):  
Mushy Zone ◽  
Volume Fraction ◽  
Primary Dendrite ◽  
Fluid Velocity ◽  
Interdendritic Liquid ◽  
Creeping Flow ◽  
Liquid Region ◽  
Local Volume ◽  
Local Volume Fraction ◽  
Deterministic Function

When modeled at macroscopic length scales, the complex dendritic network in the solid-plus-liquid region of a solidifying alloy (the “mushy zone”) has been modeled as a continuum based on the theory of porous media. The most important property of a porous medium is its permeability, which relates the macroscopic pressure gradient to the throughput of fluid flow. Knowledge of the permeability of the mushy zone as a function of the local volume-fraction of liquid and other morphological parameters is thus essential to successfully modeling the flow of interdendritic liquid during alloy solidification. In current continuum models, the permeability of the mushy zone is given as a deterministic function of (1) the local volume fraction of liquid and (2) a characteristic length scale such as the primary dendrite arm spacing or the reciprocal of the specific surface area of the solid-liquid interface. Here we first provide a broad overview of the experimental data, mesoscale numerical flow simulations, and resulting correlations for the deterministic permeability of both equiaxed and columnar mushy zones. A extended view of permeability in mushy zones which includes the stochastic nature of permeability is discussed. This viewpoint is the result of performing extensive numerical simulations of creeping flow through random microstructures. The permeabilities obtained from these simulations are random functions with spatial autocorrelation structures, and variations in the local permeability are shown to have dramatic effects on the flow patterns observed in such microstructures. Specifically, it is found that “lightning-like” patterns emerge in the fluid velocity and that the flows in such geometries are strongly sensitive to small variations in the solid structure. We conclude with a comparison of deterministic and stochastic permeabilities which suggests the importance of incorporating stochastic descriptions of the permeability of the mushy zone in solidification modeling.

scholarly journals Local volume fraction distributions of axons, astrocytes, and myelin in deep subcortical white matter

NeuroImage ◽  
2018 ◽  
Vol 179 ◽  
pp. 275-287 ◽  
Author(s):  
Santiago Coelho ◽  
Jose M. Pozo ◽  
Marina Costantini ◽  
J. Robin Highley ◽  
Meghdoot Mozumder ◽  
...  
Keyword(s):  
White Matter ◽  
Volume Fraction ◽  
Subcortical White Matter ◽  
Local Volume ◽  
Local Volume Fraction

Local Drag Law for Suspensions from Particle-Scale Simulations

1998 ◽  
Vol 09 (08) ◽  
pp. 1361-1371 ◽  
Author(s):  
B. Wachmann ◽  
S. Schwarzer ◽  
K. Höfler
Keyword(s):  
Volume Fraction ◽  
Dynamical Behavior ◽  
Particle Diameter ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Local Volume ◽  
Local Volume Fraction ◽  
The Mean ◽  
Drag Law

Two-phase continuum descriptions of the dynamical behavior of particulate suspensions require, among others, the formulation of a "local drag law". Such a "law" specifies the mean force fl on particles as a function of averaged local properties, most notably, the mean difference velocity [Formula: see text] of particles and fluid and the local volume fraction Φl. The subscript l shall indicate the dependence of these quantities on the size l of the averaging cell. We study fl by direct numerical simulation, solving the incompressible Navier–Stokes equation on a fixed, regular grid on a scale much smaller than the particle diameter. The particle–fluid interaction is computed by a method similar to the one proposed in [Fogelson and Peskin J. Comp. Phys.79, 50 (1988)]. We find a relation similar to the law of Richardson & Zaki, [Formula: see text], which relates the local phase difference velocity to the local volume fraction of the particles.

Local volume fraction fluctuations in random media

1997 ◽  
Vol 106 (7) ◽  
pp. 2741-2751 ◽  
Author(s):  
J. Quintanilla ◽  
S. Torquato
Keyword(s):  
Random Media ◽  
Volume Fraction ◽  
Local Volume ◽  
Local Volume Fraction

A Pulse-Echo Ultrasonic Probe for Local Volume Fraction Measurements in Liquid-Liquid Dispersions

1995 ◽  
Vol 34 (9) ◽  
pp. 3154-3158 ◽  
Author(s):  
Costas Tsouris ◽  
Michael A. Norato ◽  
Lawrence L. Tavlarides
Keyword(s):  
Volume Fraction ◽  
Ultrasonic Probe ◽  
Local Volume ◽  
Local Volume Fraction ◽  
Pulse Echo
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