Hayley H. Shen

The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations

Application of the kinetic theory of gases to granular flows has greatly increased our understanding of ‘rapid’ granular flows. One of the underlying assumptions is that particles interact only through binary collisions. For a given set of material and flow parameters, as the concentration increases, the transition from a binary collision mode to other modes of interaction occurs. Kinetic theory can no longer be applied. A numerical model is utilized to simulate the mechanical behaviour of a small assembly of uniform, inelastic, frictional, deformable disks in a simple shear flow. There are two objectives: to obtain the ‘empirical’ constitutive law and to gain insight into the mechanisms that operate in the transitional and quasi-static regimes. In a simple shear flow, spatially and temporally averaged dimensionless stresses

Shear Stress Induces Preimplantation Embryo Death That Is Delayed by the Zona Pellucida and Associated with Stress-Activated Protein Kinase-Mediated Apoptosis

\tau^*_{ij} = \tau_{ij}/(\rho_{\rm s}D^2\dot{\gamma}^2)

On applying granular flow theory to a deforming broken ice field

are functions of the concentration C , the dimensionless shear rate

A Monte Carlo solution for rapidly shearing granular flows based on the kinetic theory of dense gases

B =\dot{\gamma}/(K_n/m)^{\frac{1}{2}}

Internal parameters and regime map for soft polydispersed granular materials

, and material parameters ζ n , K s / K n and μ. Here

Simulation of pancake-ice dynamics in a wave field

\dot{\gamma}

Modeling the solid phase stress in a fluid-solid mixture

is the shear rate, K n is the normal stiffness of an assumed viscoelastic contact force model, K s / K n is the ratio of tangential to normal stiffness, ζ n is the normal damping coefficient, μ is the friction coefficient, and ρ s , D and m are the particle density, diameter and mass, respectively. The range of B from 0.001 to 0.0707 was investigated for C ranging from 0.5 to 0.9, with material constants fixed as ζ n = 0.0709 (corresponding to the restitution coefficient e = 0.8 in binary impacts), K s / K n = 0.8 and μ = 0.5. It is found that for lower concentrations ( C ij are nearly independent of B , while for higher concentrations ( C > 0.75) τ* ij monotonically decreases as B increases. Moreover, their relationship in this regime is well approximated by power law: τ* ij ∝ B −n ( C ) . The powers n ij range from nearly zero for C = 0.775 (corresponding to the familiar square power dependency of dimensional stresses on the shear rate in the rapid flow regime), to nearly two for C = 0.9 (corresponding to shear-rate independence in quasi-static regime). The intermediate concentration range corresponds to transition. Distinct mechanisms that govern transitional and quasi-static regimes are observed and discussed.

Constitutive equations for a simple shear flow of a disk shaped granular mixture

Abstract In this study, we discovered that embryos sense shear stress and sought to characterize the kinetics and the enzymatic mechanisms underlying induction of embryonic lethality by shear stress. Using a rotating wall vessel programmed to produce 1.2 dynes/cm2 shear stress, it was found that shear stress caused lethality within 12 h for E3.5 blastocysts. Embryos developed an approximate 100% increase in mitogen-activated protein kinase 8/9 (formerly known as stress-activated protein kinase/junC kinase 1/2) phosphorylation by 6 h of shear stress that further increased to approximately 350% by 12 h. Terminal deoxynucleotidyltransferase dUTP nick end labeling/apoptosis was at baseline levels at 6 h and increased to approximately 500% of baseline at 12 h, when irreversible commitment to death occurred. A mitogen-activated protein kinase 8/9 phosphorylation inhibitor, D-JNKI1, was able to inhibit over 50% of the apoptosis, suggesting a causal role for mitogen-activated protein kinase 8/9 phosphorylation in the shear stress-induced lethality. The E2.5 (compacted eight-cell/early morula stage) embryo was more sensitive to shear stress than the E3.5 (early blastocyst stage) embryo. Additionally, zona pellucida removal significantly accelerated shear stress-induced lethality while having no lethal effect on embryos in the static control. In conclusion, preimplantation embryos sense shear stress, chronic shear stress is lethal, and the zona pellucida lessens the lethal and sublethal effects of shear stress. Embryos in vivo would not experience as high a sustained velocity or shear stress as induced experimentally here. Lower shear stresses might induce sufficient mitogen-activated protein kinase 8/9 phosphorylation that would slow growth or cause premature differentiation if the zona pellucida were not intact.

Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea

SummaryThe prediction of arctic ocean ice dynamics relies on a correct modelling of the stresses acting on the ice field, including the Coriolis effect, wind and current stresses and the ice interaction. Observations made in the past decade show significant ice interaction and flow patterns which can be consistently modeled with a plastic rheology. The main local physical process considered in these rheologies is the pressure ridging phenomenon. However recent arctic field work carried out in the marginal ice zone (less than 100 km from the edge of the ice field) shows the ice very near the edge to consist of a large number of discrete floes. While a plastic rheology may well have application under compact conditions in this region, under dispersed conditions the rheology may be different. In order to address this issue, in this work the ice floe collisions induced by ice deformation are analyzed. The internal kinematics as represented by the ice floe fluctuations is derived. Comparisons between the results and field data show excellent correlation. However, the theoretically predicted floe fluctuations are about one order of magnitude lower than the field measurements. Possibilities for this discrepancy are proposed and discussed.

A conceptual model for pancake-ice formation in a wave field

A Monte Carlo simulation is developed for the study of rapidly deforming, steady, simple shear flows of inelastic disks or spheres. The simulation is based on the theoretical framework of the kinetic theory of dense gases. In the simulation, space is discarded in an explicit sense and replaced by an isotropic, homogeneous, and uncorrelated space based on the assumption of a state of simple shear, a uniform concentration field, and molecular chaos. The simulation generates a distribution of particle velocities which corresponds to the parameters of the flow. The velocity distribution is a numerical solution to the Boltzmann equation under these conditions. The Monte Carlo simulation defines the limits to the accuracy of analytical granular flow theories based on the kinetic theory and the assumption of molecular chaos.