A frictional Cosserat model for the slow shearing of granular materials

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

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THE INFLUENCE OF SLIP AND JUMP BOUNDARY CONDITIONS ON THE CYLINDRICAL COUETTE FLOW

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202502001738 ◽

2002 ◽

Vol 12 (03) ◽

pp. 445-459 ◽

Cited By ~ 5

Author(s):

LILIANA M. GRAMANI CUMIN ◽

GILBERTO M. KREMER ◽

FELIX SHARIPOV

Keyword(s):

Angular Velocity ◽

Boundary Conditions ◽

Couette Flow ◽

Rarefied Gas ◽

Thermodynamic Force ◽

Heat Conducting ◽

Field Equations ◽

Viscous Stress Tensor ◽

Heat Flux Vector ◽

Cylindrical Couette Flow

The solution of the field equations of the cylindrical Couette flow problem for a rarefied gas is found when the state of equilibrium between the cylinders is perturbed by the following small thermodynamic forces: (i) a pressure difference; (ii) an angular velocity difference; and (iii) a temperature difference. The flow is analyzed within the framework of continuum mechanics by using the field equations that follow from the balance equations of mass, momentum and energy of a viscous and heat conducting gas. These equations are solved analytically by considering slip and jump boundary conditions. The fields of density, velocity, temperature, heat flux vector and viscous stress tensor are calculated as functions of the Knudsen number and of the angular velocity of the rotating cylinders for each thermodynamic force. The asymptotic behaviors of these fields are compared with those obtained from a kinetic model of the Boltzmann equation. The influence of the slip and jump boundary conditions on the solutions is also discussed.

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Experimental Surface Profile of Dense Granular Media in Cylindrical Couette Flow

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.110-116.776 ◽

2011 ◽

Vol 110-116 ◽

pp. 776-782

Author(s):

Arkadeep Kumar

Keyword(s):

Granular Materials ◽

Couette Flow ◽

Granular Media ◽

Graphical Representation ◽

Radial Distance ◽

Surface Profile ◽

Average Diameter ◽

Material Surface ◽

Translation Stage ◽

Cylindrical Couette Flow

Granular materials have widespread use in the industry. The flow of granular media requires careful studies through experiments to understand the rheology of these complex materials. The present work determines the surface profile of dense granular media subjected to cylindrical Couette flow. A translation stage is used to obtain measurement of depth varying with radial distance. A depth gauge attached to the translation stage is used to measure the surface profile. Glass beads (average diameter 0.8-1 mm) and mustard seeds (average diameter 1.2-1.4 mm) are used as model granular materials. Two different Couette gaps are used (4cm and 3cm). Cylinders with smooth surfaces, as well as coated with emery paper are used. The surface profile varies with material, surface roughness of the cylinders, and the gap between the two cylinders. The comparison of the various cases has been done by graphical representation. The probable reasons for the development of such a surface profile are given.

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Analysis of shear bands in slow granular flows using a frictional Cosserat model

MRS Proceedings ◽

10.1557/proc-627-bb4.3 ◽

2000 ◽

Vol 627 ◽

Author(s):

Prabhu R. Nott ◽

K. Kesava Rao ◽

L. Srinivasa Mohan

Keyword(s):

Scaling Laws ◽

Shear Bands ◽

Shear Layers ◽

Theoretical Description ◽

Field Variable ◽

Cosserat Continuum ◽

Momentum Balance ◽

Rigid Plastic ◽

Independent Field ◽

Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

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Mathematical modeling of Couette flow in anomalous thermoviscous liquid

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2011.1.013 ◽

2011 ◽

Vol 8 (1) ◽

pp. 143-152

Author(s):

S.F. Khizbullina

Keyword(s):

Mathematical Modeling ◽

Angular Velocity ◽

Numerical Experiment ◽

Temperature Dependence ◽

Steady Flow ◽

Couette Flow ◽

Outer Cylinder ◽

Flow Regimes ◽

Constant Angular Velocity ◽

Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

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The structure of a highly decelerated axisymmetric turbulent boundary layer

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.845 ◽

2021 ◽

Vol 929 ◽

Author(s):

N. Agastya Balantrapu ◽

Christopher Hickling ◽

W. Nathan Alexander ◽

William Devenport

Keyword(s):

Boundary Layer ◽

Pressure Gradient ◽

Shear Layer ◽

Layer Thickness ◽

Boundary Layer Thickness ◽

Large Scale ◽

Convection Velocity ◽

Mean Flow ◽

Mean Velocity ◽

The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

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Frictional properties between geocells filled with granular material

10.7764/rdlc.20.2.332 ◽

2021 ◽

Vol 20 (2) ◽

pp. 332-345

Author(s):

Gökhan Altay ◽

◽

Cafer Kayadelen ◽

Taha Taskiran ◽

Baki Bagriacik ◽

...

Keyword(s):

Granular Material ◽

Normal Stress ◽

Granular Materials ◽

Direct Shear ◽

Shear Tests ◽

Direct Shear Tests ◽

Frictional Properties ◽

Geotechnical Structures ◽

Series Of Experiments ◽

Restricted Volume

The parameters concerning the interaction between geocell and granular materials is required for the design of many geotechnical structures. With this in mind, a series of experiments using simple direct shear tests are conducted in order to understand the frictional properties between geocells filled with granular materials. The 54 test samples are prepared by filling the geocell with granular materials having three different gradations. These samples are tested at three different relative densities under three different normal stress levels. As a result, it was observed that interface resistance between the geocells filled with granular material is found to be generally greater than in the samples without geocells. Additionally, these samples with geocells are found to be stiffer; this is due to the fact that the samples with geocell gained more cohesion because geocells confined the grains within a restricted volume.

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