Symmetry Relations in Viscoplastic Drag Laws

The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of non-linear viscoplastic fluids. This follows from Edelen's non-linear generalization of the Onsager relation for the special case of \emph{strongly dissipative} rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction-velocity response given by a dissipation potential. This leads to a non-linear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to non-linear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces

On the stability of the μ(I)\mu(I)-rheology for granular flow

This article deals with the Hadamard instability of the so-called $\mu(I)$ model of dense rapidly-sheared granular flow, as reported recently by Barker et al. (2015,this journal, ${\bf 779}$, 794-818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wave-vector stretching by the base flow. We provide a closed form solution for the linear stability problem and show that wave-vector stretching leads to asymptotic stabilization of the non-convective instability found by Barker et al. We also explore the stabilizing effects of higher velocity gradients achieved by an enhanced-continuum model based on a dissipative analog of the van der Waals-Cahn-Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyper-stress, as the analog of a special Korteweg stress, with surface viscosity representing the counterpart of elastic surface tension. Based on the enhanced continuum model, we also present a model of steady shear bands and their non-linear stability against parallel shearing. Finally, we propose a theoretical connection between the non-convective instability of Barker et al. and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the numerical simulation of continuum field equations involving the $\mu(I)$ rheology and variants thereof.Comment: 30 pages, 13 figure

Migrational Instabilities in Particle Suspensions

This work deals with an instability arising from the shear-induced migration of particles in dense suspensions coupled with a dependence of viscosity on particle concentration. The analysis summarized here treats the inertialess (Re = O) linear stability of homogeneous simple shear flows for a Stokesian suspension model of the type proposed by Leighton and Acrivos (1987). Depending on the importance of shear-induced migration relative to concentration-driven diffusion, this model admits short-wave instability arising from wave-vector stretching by the base flow and evolving into particle-depleted shear bands. Moreover, this instability in the time-dependent problem corresponds to loss of ellipticity in the associated static problem (Re = O, Pe = O). While the isotropic version of the Leighton-Acrivos model is found to be stable with their experimentally determined parameters for simple shear, it is known that the stable model does not give a good quantitative description of particle clustering in the core of pipe flow (Nott and Brady 1994). This leads to the conjecture that an appropriate variant on the above model could explain such clustering as a two-phase bifurcation in the base flow

Mickey’s Trailer and Environmental Thought: Disney Cartoons and Countryside

The influence of popular cartoons on environmental cognition is explored in this essay through readings of Mickey’s Trailer, a 1938 cartoon directed by Ben Sharpsteen for Walt Disney. Other materials considered include Ford Motor Company’s 1937-38 film coproduced by Wilder Pictures, Glacier International Park, which promotes motor-tourism and automobile ownership, and Ben Sharpsteen’s other work for Walt Disney. The article also examines the ideas of physical and “illusional” zoning in the city, especially the way that they were applied in the mid-twentieth century. Physical zoning involved separating incompatible land uses, whereas illusional zoning entailed seeing what you wanted to see. What does Mickey’s Trailer say about how people can live, and can it inform where people choose to live? The essay muses that appreciations of nature and the environment are influenced by popular culture

Still Waiting for Madame President: Hillary Clinton and the Oval Office

This essay investigates gender in politics through the prism of Hillary Clinton’s 2008 campaign for the Democratic nomination. It looks at the reactions to that campaign in the media, both in 2008 and as a probable second Clinton campaign emerges for 2016. Topics explored include whether the reactions to Clinton’s campaigns are generic or specific to Clinton herself, and whether gender remains a limiting force in American political life

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

Tensile stress contribution of flow-oriented slender particles in non-newtonian fluids

A formula is derived for the intrinsic stress contribution from closely-spaced, rod-like rigid particles suspended in a non-Newtonian liquid subject to a simple extensional flow.The present results indicate that, compared to the Newtonian-fluid result given previously by Batchelor [1], a much smaller particle-stress effect may occur in non-Newtonian fluid, owing to shear thinning and possible tensile stiffening in the fluid itself. While unsubstantiated by any critical experimental test, this prediction appears to agree qualitatively with some recent experimental observations of Charrier and Rieger [29] on glass fibers in polymer melts.Further work is suggested for the relevant slender-body theory, particularly the far-field body influence in non-linear fluids.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21846/1/0000249.pd

An elastohydrodynamic theory for the rheology of concentrated suspensions of deformable particles

The equations which govern thin films of a Newtonian liquid confined between deformable solid surfaces are applied to the regions of near contact in a concentrated suspension of deformable particles.For the case of slightly deformable elastic particles, one obtains the socalled "elastohydrodynamic" equations of lubrication theory.The appropriate asymptotic solution of these equations yields estimates for the viscosity, of a form proposed earlier by Frankel and Acrivos [1] for rigid particles, as well as a relaxation time for a suspension of near spheres. The present method, which goes beyond the dissipation calculation of Frankel and Acrivos to a derivation of the full stress tensor, yields the same form of dependence of viscosity on particle concentration. However, there is an as yet unexplained difference between the methods in the value of a numerical coefficient determined by the assumed packing of the spheres.While further work is needed on the kinetic theory for fluid suspensions, the methods employed here for the derivation of the stress tensor should have direct utility for certain solid dispersions, where it is possible to specify a priori the particle-packing in the system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22965/1/0000532.pd

Tribute to Krzysztof Wilmanski

Some 20 years ago, Krzysztof Wilmanski began his research into the theory of porous and granular media, fields that are addressed in this special issue of Acta Mechanica. In contrast to earlier models for such media, Wilmanski introduced the porosity as a material field, and he derived a particular balance equation for this quantity based on thermodynamic arguments. A principal application of the resulting continuum model has been the investigation of linear wave propagation. This was the topic of one minisymposium at the 8th European Solid Mechanics Conference in the Graz University of Technology, Austria, 9–13 July 2012

A note on a statistical-mechanical treatment of activation-limited surface diffusion

A brief review is given of a class of simple statistical-mechanical models for surface diffusion, applicable to the limiting case where diffusional “hopping” is controlled by the thermal activation rate of the adsorbed particle. A theoretical result of Reyes, for the pre-exponential or “frequency” factor, is discussed and compared briefly to experiment. Приводится краткий обзор класса простых статистическо-механических моделей поверхностной диффузии, примени-мых в предельных случаях, когда диффузионные “прыжки” контролируются скоростью термической активации адсорбированных частиц. Теоретические результаты Рейса отно-сительно предэкспоненциального множителя или “частот-ного” фактора обсуждаются и сравниваются с экспериментальными значениями.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43572/1/11144_2005_Article_BF02075122.pd