Elastic Granular Flows

2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Charles S Campbell
Keyword(s):  
Shear Rate ◽  
Friction Coefficient ◽  
Granular Flows ◽  
Force Chains ◽  
Long Duration ◽  
Rapid Flow ◽  
Induced Stresses ◽  
Quasistatic Regime ◽  
Inertial Regime ◽  
Effective Friction

Large scale landslide simulations provided the surprising result that the effective friction coefficient (the ratio of shear to normal forces at the base of the slide) increased with the shear rate. This might possibly explain the effect of slide volume on the runout of large landslides, but it also indicates that landslides operated in an entirely new and unexplored flow regime.Previously, granular flows had been divided into (1) the slow, quasistatic regime, in which the effective friction coefficient is taken to be a material property and thus constant, and (2) the fast, rapid-flow regime, where the particles interact collisionally, but which scales in such a way that the effective friction coefficient is independent of the shear rate. Both indicate that the effective friction coefficient is independent of the shear rate. Consequently the landslides operated in a separate intermediate regime.This talk will discuss detailed computer simulation studies into this intermediate regime and into the transitions between regimes. In this way, it is possible to draw the entire flowmap connecting the quasistatic and rapid-flow regimes. The key was to include the elastic properties of the solid material in the set of rheological parameters; in effect this put solid properties into the rheology of granular solids, properties that were unnecessary in previous theories as a result of the plasticity and kinetic theory formalisms on which quasistatic and rapid-flow theories are respectively based. Granular flows are then divided into two broad categories, the Elastic Regimes, in which the particles are locked in force chains and interact elastically over long duration contact with their neighbors and the Inertial regimes, where the particles have broken free of the force chains. The Elastic regimes can be further subdivided into the Elastic-Quasistatic regime (the old quasistatic regime) and the Elastic-Inertial regime. The Elastic-Inertial regime is the “new” regime observed in the landslide simulations, in which the inertially induced stresses are significant compared to the elastically induced stresses. The Inertial regime can also be sub-divided into an Inertial-Non-Collisional where the stresses scale inertially, but the particles interact through long duration contacts, and the Inertial-Collisional or the old rapid-flow regime.Finally, it will be shown that Stress-Controlled flows are rheologically different from Controlled-Volume flows. Physically, there is a range of dense concentrations (solid volume fractions between 0.5 and 0.6) in which it is possible to form force chains and thus to demonstrate elastically. But there are conditions under which force chains do not form at the same average concentrations. (In other words it is possible for the material to exhibit two different states at the same concentration.) By forcing the material to support an applied loads across force chains, Stress-Controlled flows generally behave elastically through this range of concentrations under the same conditions where Controlled-Volume flows behave inertially.

scholarly journals Sidewall friction in confined surface flows of granular materials

2021 ◽  
Vol 249 ◽  
pp. 03024
Author(s):  
Patrick Richard ◽  
Alexandre Valance ◽  
Renaud Delannay
Keyword(s):  
Friction Coefficient ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Granular Materials ◽  
Granular Flows ◽  
Granular Systems ◽  
Surface Flows ◽  
Continuum Theories ◽  
Shed Light ◽  
Effective Friction

We report numerical simulations of surface granular flows confined between two sidewalls. These systems exhibit both very slow and very energetic flows. Zhu et al. [1] have shown that in energetic confined systems, the Froude number at sidewalls and the sidewall effective friction coefficient are linked through a unique relation. We show that this relation is also valid for creep flows. It is independent of the angle of the flow but depends on the sidewall-grain friction coefficient. Our results shed light on boundary conditions that have to be used at sidewalls in continuum theories aiming to capture the behavior of granular systems from creeping to energetic flows.

scholarly journals Self-diffusion scalings in dense granular flows

Soft Matter ◽  
2021 ◽  
Author(s):  
Riccardo Artoni ◽  
Michele Larcher ◽  
James T. Jenkins ◽  
Patrick Richard
Keyword(s):  
Shear Rate ◽  
Solid Fraction ◽  
Granular Flows ◽  
The Self ◽  
Granular Temperature ◽  
Restitution Coefficient ◽  
Self Diffusion ◽  
Diffusivity Tensor ◽  
Dense Granular Flows

The self-diffusivity tensor in homogeneously sheared dense granular flows is anisotropic. We show how its components depend on solid fraction, restitution coefficient, shear rate, and granular temperature.

scholarly journals Boundary Friction of ZDDP Tribofilms

2020 ◽  
Vol 69 (1) ◽  
Author(s):  
Jie Zhang ◽  
Mao Ueda ◽  
Sophie Campen ◽  
Hugh Spikes
Keyword(s):  
Friction Coefficient ◽  
Group Structure ◽  
Boundary Friction ◽  
Considerable Proportion ◽  
Base Oil ◽  
Characteristic Boundary ◽  
Long Duration ◽  
Structure Boundary ◽  
Alkoxy Groups ◽  
20 Nm

AbstractThe frictional properties of ZDDP tribofilms at low entrainment speeds in boundary lubrication conditions have been studied in both rolling/sliding and pure sliding contacts. It has been found that the boundary friction coefficients of these tribofilms depend on the alkyl structure of the ZDDPs. For primary ZDDPs, those with linear alkyl chains give lower friction those with branched alkyl chain ZDDPs, and a cyclohexylmethyl-based ZDDP gives markedly higher friction than non-cyclic ones. Depending on alkyl structure, boundary friction coefficient in rolling-sliding conditions can range from 0.09 to 0.14. These differences persist over long duration tests lasting up to 120 h. For secondary ZDDPs, boundary friction appears to depend less strongly on alkyl structure and in rolling-sliding conditions stabilises at ca 0.115 for the three ZDDPs studied. Experiments in which the ZDDP-containing lubricant is changed after tribofilm formation by a different ZDDP solution or a base oil indicate that the characteristic friction of the initial ZDDP tribofilm is lost almost as soon as rubbing commences in the new lubricant. The boundary friction rapidly stabilises at the characteristic boundary friction of the replacement ZDDP, or in the case of base oil, a value of ca 0.115 which is believed to represent the shear strength of the bare polyphosphate surface. The single exception is when a solution containing a cyclohexylethyl-based ZDDP is replaced by base oil, where the boundary friction coefficient remains at the high value characteristic of this ZDDP despite the fact that rubbing in base oil removes about 20 nm of the tribofilm. XPS analysis of the residual tribofilm reveals that this originates from presence of a considerable proportion of C-O bonds at the exposed tribofilm surface, indicating that not all of the alkoxy groups are lost from the polyphosphate during tribofilm formation. Very slow speed rubbing tests at low temperature show that the ZDDP solutions give boundary friction values that vary with alkyl group structure in a similar fashion to rolling-sliding MTM tests. These variations in friction occur immediately on rubbing, before any measurable tribofilm can develop. This study suggest that ZDDPs control boundary friction by adsorbing on rubbing steel or tribofilm surfaces in a fashion similar to organic friction modifiers. However it is believed that, for primary ZDDPs, residual alkoxy groups still chemically bonded to the phosphorus atoms of newly-formed polyphosphate/phosphate tribofilm may also contribute to boundary friction. This understanding will contribute to the design of low friction, fuel efficient crankcase engine oils. Graphical Abstract

HYDRODYNAMIC CHARACTERISTICS OF ELECTRORHEOLOGICAL FLUID IN A PARALLEL DUCT FLOW

2001 ◽  
Vol 15 (06n07) ◽  
pp. 980-987
Author(s):  
K. SHIMADA ◽  
S. KAMIYAMA
Keyword(s):  
Shear Rate ◽  
Friction Coefficient ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Apparent Viscosity ◽  
Wall Friction ◽  
Hydrodynamic Characteristics ◽  
Duct Flow ◽  
Newtonian Viscosity

An experimental investigation is conducted to clarify the hydrodynamic characteristics of ERF with elastic particles of smectite in a two-dimensional parallel duct of various widths. Experimental data on pressure difference to a volumetric flow rate in a supplying D.C. electric field are measured. These data are arranged to obtain the apparent viscosit by using the integral method of rheology. From the data of apparent viscosity, the wall friction coefficient is obtained. The increment of the apparent viscosity caused by the applying electric field is a function of shear rate as well as the electric field strength and the width of the duct. However, the wall friction coefficient is not a function of elecric field strength and the width of the parallel duct, but only of shear rate. The yield stress is a function of the width of the parallel duct as well as of electric field strength. The ratio of Non-Newtonian viscosity in the apparent viscosity is varied by the intensity of the shear rate.

Lateral Friction Behavior of a Thin, Tensioned Tape Wrapped Over a Grooved Roller: Experiments and Theory

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Hankang Yang ◽  
Johan B. C. Engelen ◽  
Walter Häberle ◽  
Mark A. Lantz ◽  
Sinan Müftü
Keyword(s):  
Friction Coefficient ◽  
Axial Direction ◽  
Friction Behavior ◽  
Stick Slip ◽  
Friction Forces ◽  
Lateral Dynamics ◽  
Lateral Tape Motion ◽  
Complex Interactions ◽  
Recording Tape ◽  
Effective Friction

Effects of friction forces on the lateral dynamics of a magnetic recording tape, wrapped around a grooved roller are investigated experimentally and theoretically. Tape is modeled as a viscoelastic, tensioned beam subjected to belt-wrap pressure and friction forces. Including the effects of stick and slip and velocity dependence of the friction force render the tape's equation of motion nonlinear. In the experiments, tape was wrapped under tension around a grooved roller in a customized tape path. The tape running speed along the axial direction was set to zero, thus only the lateral effects were studied. The grooved roller was attached to an actuator, which moved the roller across the tape. Tests were performed in slow and fast actuation modes. The slow mode was used to identify an effective static, or breakaway, friction coefficient. In the fast mode, the roller was actuated with a 50 Hz sinusoid. The same effective friction coefficient was deduced from the fast actuation mode tests. This test mode also revealed a periodic stick–slip phenomenon. The stick-to-slip and slip-to-stick transitions occurred when the tape vibration speed matched the roller actuation speed. Both experiments and theory show that upon slip, tape vibrates primarily at its natural frequency, and vibrations are attenuated relatively fast due to frictional and internal damping. This work also shows that an effective friction coefficient can be described that captures the complex interactions in lateral tape motion (LTM) over a grooved roller.

Granular shear flows at the elastic limit

2002 ◽  
Vol 465 ◽  
pp. 261-291 ◽  
Author(s):  
CHARLES S. CAMPBELL
Keyword(s):  
Stress Reduction ◽  
Particle Surface ◽  
Surface Friction ◽  
Internal Force ◽  
Force Chains ◽  
Rheological Parameter ◽  
Nonlinear Behaviour ◽  
Static Regime ◽  
Computer Simulation Studies ◽  
Inertial Regime

This paper describes computer simulation studies of granular materials under dense conditions where particles are in persistent contact with their neighbours and the elasticity of the material becomes an important rheological parameter. There are two regimes at this limit, one for which the stresses scale with both elastic and inertial properties (called the elastic–inertial regime), and a non-inertial quasi-static regime in which the stresses scale purely elastically (elastic–quasi-static). In these elastic regimes, the forces are generated by internal force chains. Reducing the concentration slightly causes a transition from an elastic to a purely inertial behaviour. This transition occurs so abruptly that a 2% concentration reduction can be accompanied by nearly three orders of magnitude of stress reduction. This indicates that granular flows near this limit are prone to instabilities such as those commonly observed in shear cells. Unexpectedly, there is no path between inertial (rapid) flow and quasi-static flow by varying the shear rate at a fixed concentration; only by reducing the concentration can one cause a transition from quasi-static to inertial flow. The solid concentrations at which this transition occurs as well as the magnitude of the stresses in the elastic regimes are strong functions of the particle surface friction, because the surface friction strongly affects the strength of the force chains. A parametric analysis of the elastic regime generated flowmaps showing the various regimes that might be realized in practice. Many common materials such as sand require such large shear rates to reach the elastic–inertial regime that it is unattainable for all practical purposes; such materials will demonstrate either an elastic–quasi-static behaviour or a pure inertial behaviour depending on the concentration – with many orders of magnitude of stress change between them. Finally, the effects of nonlinear contacts are investigated and an appropriate scaling is proposed that accounts for the nonlinear behaviour in the elastic–quasi-static regime.

A non-local rheology for dense granular flows

2009 ◽  
Vol 367 (1909) ◽  
pp. 5091-5107 ◽  
Author(s):  
Olivier Pouliquen ◽  
Yoel Forterre
Keyword(s):  
Granular Flows ◽  
Constitutive Law ◽  
Local Theory ◽  
Plane Shear ◽  
Static Regime ◽  
Entire Flow ◽  
Non Local ◽  
Inclined Planes ◽  
Inertial Regime ◽  
Dense Granular Flows

A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.

Granular Flows in the Elastic Limit

2000 ◽  
Vol 627 ◽  
Author(s):  
Charles S. Campbell
Keyword(s):  
Shear Rate ◽  
Friction Coefficient ◽  
Phase Change ◽  
Stress Ratio ◽  
Elastic Response ◽  
Recent Computer ◽  
Interparticle Contacts ◽  
Interparticle Friction ◽  
Computer Simulation Studies ◽  
Elastic Particle

ABSTRACTThis paper describes recent computer simulation studies into the rheological behavior of granular materials in the regime that lies between the quasistatic and rapid-flow regime. This investigation was prompted by studies of landslides, hopper flows and the “phase change” (i.e. the change between solidlike and fluid-like behavior) all of which indicated that the shear-to-normal stress ratio (the effective friction coefficient for the material) increased with shear rate. The results presented herein do demonstrate that the stress ratio varies with a dimensionless parameter created by scaling the shear rate with the stiffness of the interparticle contacts. In dense regimes, the stresses themselves scale with the stiffness indicating that they are generated by the elastic response of particle networks. Such speculation is supported by studies that show that the normal stresses are strongly dependent on the interparticle friction coefficient which affects the ability of internal elastic particle structures to support load and by the time variation of stress, which shows a spiky behavior as the structures form and break. However, analyses also indicate that these observations cannot explain the hopper, landslide and phase-change as these systems operate in regimes different from those in which the effect was observed. Finally, the effects of non-linear contacts are investigated and an appropriate scaling that takes the non-linearity into account is proposed.

Transport phenomena in an agitated vessel with an eccentrically located impeller

2011 ◽  
Vol 65 (2) ◽  
Author(s):  
Magdalena Cudak ◽  
Joanna Karcz ◽  
Anna Kiełbus-Rąpała
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Friction Coefficient ◽  
Transport Phenomena ◽  
Turbulent Regime ◽  
Cylindrical Wall ◽  
Flow Measurements ◽  
Rushton Turbine ◽  
Agitated Vessel ◽  
Inner Diameter

AbstractThe paper presents results of an experimental analysis of the transport phenomena at the vicinity of the wall of an unbaffled agitated vessel with an eccentrically located impeller. Distributions of the transport coefficients were experimentally studied using an electrochemical method within the turbulent regime of the Newtonian liquid flow. Measurements were carried out in an agitated vessel with the inner diameter T = 0.3 m. Liquid height in the vessel was equal to the inner diameter, H = T. The agitated vessel was equipped with a Rushton or a Smith turbine or an A 315 impeller. Eccentricity of the impeller shaft was varied from 0 to 0.53. Local values of the dimensionless shear rate, shear stress, dynamic velocity and friction coefficient were integrated numerically for the whole surface area of the cylindrical wall of the vessel. Averaged values of these quantities were correlated with the impeller eccentricity and modified Reynolds number. The proposed Eqs. (5)–(8), with the coefficients given in Table 2, have no equivalent in open literature concerning this subject. Distributions of the shear rate, γ/n, and friction coefficient, f, at the vicinity of the cylindrical wall of the unbaffled vessel equipped with eccentric Rushton or Smith turbine or A 315 impeller are very uneven and they depend significantly on the impeller eccentricity, e/R. Maximum local values of these variables are located on the wall section closest to the impeller blades. From among the tested impellers, the greatest effects of the impeller eccentricity, e/R, and the liquid turbulence (described by the modified Reynolds number Re P,M) on the averaged dimensionless shear rate (γ/n)m and friction coefficient, f m, are found for the radial-flow Rushton turbine located eccentrically in an unbaffled agitated vessel.

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