scholarly journals Critical Yield Numbers of Rigid Particles Settling in Bingham Fluids and Cheeger Sets

2017 ◽  
Vol 77 (2) ◽  
pp. 638-663 ◽  
Author(s):  
Ian A. Frigaard ◽  
José A. Iglesias ◽  
Gwenael Mercier ◽  
Christiane Pöschl ◽  
Otmar Scherzer
Keyword(s):  
Bingham Fluids ◽  
Rigid Particles ◽  
Critical Yield ◽  
Cheeger Sets

Yield limit analysis of particle motion in a yield-stress fluid

2017 ◽  
Vol 819 ◽  
pp. 311-351 ◽  
Author(s):  
Emad Chaparian ◽  
Ian A. Frigaard
Keyword(s):  
Yield Stress ◽  
Numerical Study ◽  
Creeping Flow ◽  
Viscoplastic Fluid ◽  
Yield Limit ◽  
Yield Stress Fluid ◽  
Rigid Particles ◽  
Aspect Ratios ◽  
Wide Range ◽  
Critical Yield

A theoretical and numerical study of yield-stress fluid creeping flow about a particle is presented. Yield-stress fluids can hold rigid particles statically buoyant if the yield stress is large enough. In addressing sedimentation of rigid particles in viscoplastic fluids, we should know this critical ‘yield number’ beyond which there is no motion. As we get close to this limit, the role of viscosity becomes negligible in comparison to the plastic contribution in the leading order, since we are approaching the zero-shear-rate limit. Admissible stress fields in this limit can be found by using the characteristics of the governing equations of perfect plasticity (i.e. the sliplines). This approach yields a lower bound of the critical plastic drag force or equivalently the critical yield number. Admissible velocity fields also can be postulated to calculate the upper bound. This analysis methodology is examined for three families of particle shapes (ellipse, rectangle and diamond) over a wide range of aspect ratios. Numerical experiments of either resistance or mobility problems in a viscoplastic fluid validate the predictions of slipline theory and reveal interesting aspects of the flow in the yield limit (e.g. viscoplastic boundary layers). We also investigate in detail the cases of high and low aspect ratio of the particles.

scholarly journals Brownian dynamics of fully confined suspensions of rigid particles without Green’s functions

2019 ◽  
Vol 150 (16) ◽  
pp. 164116 ◽  
Author(s):  
Brennan Sprinkle ◽  
Aleksandar Donev ◽  
Amneet Pal Singh Bhalla ◽  
Neelesh Patankar
Keyword(s):  
Brownian Dynamics ◽  
Green's Functions ◽  
Green’S Functions ◽  
Rigid Particles ◽  
Confined Suspensions

scholarly journals New insights on homogenization for hexagonal-shaped composites as Cosserat continua

Meccanica ◽  
2021 ◽  
Author(s):  
Marco Colatosti ◽  
Nicholas Fantuzzi ◽  
Patrizia Trovalusci ◽  
Renato Masiani
Keyword(s):  
Continuum Theory ◽  
Representative Elementary Volume ◽  
Elementary Volume ◽  
Displacement Fields ◽  
Micropolar Continuum ◽  
Rigid Particles ◽  
Hexagonal Shape ◽  
Classical Models ◽  
Elastic Interfaces ◽  
Cosserat Continua

AbstractIn this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials.

The Inductive Coil Technique for High-Pressure Measurements: An Analysis of Nonhomogeneous Material Environment as a Source of Irreproducibility and Error

1967 ◽  
Vol 89 (3) ◽  
pp. 554-560 ◽  
Author(s):  
A. A. Giardini
Keyword(s):  
High Pressure ◽  
Internal Pressure ◽  
Elastic Constants ◽  
Graphical Form ◽  
Pressure Measurements ◽  
Pressure Data ◽  
Nonhomogeneous Material ◽  
Resistivity Measurements ◽  
Material Environment ◽  
Critical Yield

Significant sources of error independent of the apparatus are analyzed on the basis of experimental experience and elastic theory. All are mechanical in nature and subject to corrective action. The most serious is found to be self-generating internal pressure differences which result from differential elastic and dimensional values in multicomponent assemblies. High-pressure data on elastic constants, relative critical yield stresses, radial displacements, and ratios of external to internal pressure for various compositional arrangements of pyrophyllite, MgO, NaCl, and AgCl are given in graphical form. Observance of suggested corrective measures can render the inductive coil technique capable of operational accuracies of 2 percent or better in compressibility and resistivity measurements.

The falling of spheres through Bingham fluids

1992 ◽  
Vol 65 (1) ◽  
pp. 69-75 ◽  
Author(s):  
Brian J. Briscoe ◽  
Mathias Glaese ◽  
Paul F. Luckham ◽  
Shaoran Ren
Keyword(s):  
Bingham Fluids

Finite stopping time problems and rheometry of Bingham fluids

2002 ◽  
Vol 102 (1) ◽  
pp. 97-107 ◽  
Author(s):  
R.R. Huilgol ◽  
B. Mena ◽  
J.M. Piau
Keyword(s):  
Stopping Time ◽  
Bingham Fluids ◽  
Stopping Time Problems

scholarly journals Effects of particulates and lipids on the hydraulic conductivity of Matrigel

2008 ◽  
Vol 105 (2) ◽  
pp. 621-628 ◽  
Author(s):  
William J. McCarty ◽  
Melissa F. Chimento ◽  
Christine A. Curcio ◽  
Mark Johnson
Keyword(s):  
Extracellular Matrix ◽  
Hydraulic Conductivity ◽  
Weight Fraction ◽  
Low Density Lipoproteins ◽  
Blood Vessel Wall ◽  
Connective Tissues ◽  
Rigid Particles ◽  
Ldl Particles ◽  
Transmission Electron ◽  
Theoretical Predictions

The hydraulic conductivity of a connective tissue is determined both by the fine ultrastructure of the extracellular matrix and the effects of larger particles in the interstitial space. In this study, we explored this relationship by examining the effects of 30- or 90-nm-diameter latex nanospheres or low-density lipoproteins (LDL) on the hydraulic conductivity of Matrigel, a basement membrane matrix. The hydraulic conductivity of Matrigel with latex nanospheres or LDL particles added at 4.8% weight fraction was measured and compared with the hydraulic conductivity of Matrigel alone. The LDL-derived lipids in the gel were visualized by transmission electron microscopy and were seen to have aggregated into particles up to 500 nm in size. The addition of these materials to the medium markedly decreased its hydraulic conductivity, with the LDL-derived lipids having a much larger effect than did the latex nanospheres. Debye-Brinkman theory was used to predict the effect of addition of particles to the hydraulic conductivity of the medium. The theoretical predictions matched well with the results from adding latex nanospheres to the medium. However, LDL decreased hydraulic conductivity much more than was predicted by the theory. The validation of the theoretical model for rigid particles embedded in extracellular matrix suggests that it could be used to make predictions about the influence of particulates (e.g., collagen, elastin, cells) on the hydraulic conductivity of the fine filamentous matrix (the proteoglycans) in connective tissues. In addition, the larger-than-predicted effects of lipidlike particles on hydraulic conductivity may magnify the pathology associated with lipid accumulation, such as in Bruch's membrane of the retina during macular degeneration and the blood vessel wall in atherosclerosis.

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