scholarly journals Asymmetric breaking size-segregation waves in dense granular free-surface flows

2016 ◽  
Vol 794 ◽  
pp. 460-505 ◽  
Author(s):  
P. Gajjar ◽  
K. van der Vaart ◽  
A. R. Thornton ◽  
C. G. Johnson ◽  
C. Ancey ◽  
...  
Keyword(s):  
Particle Motion ◽  
Wave Structure ◽  
Free Surface Flows ◽  
Pyroclastic Flows ◽  
Breaking Wave ◽  
Size Segregation ◽  
Small Particles ◽  
Flux Function ◽  
Large Particles ◽  
Over The Top

Debris and pyroclastic flows often have bouldery flow fronts, which act as a natural dam resisting further advance. Counter intuitively, these resistive fronts can lead to enhanced run-out, because they can be shouldered aside to form static levees that self-channelise the flow. At the heart of this behaviour is the inherent process of size segregation, with different sized particles readily separating into distinct vertical layers through a combination of kinetic sieving and squeeze expulsion. The result is an upward coarsening of the size distribution with the largest grains collecting at the top of the flow, where the flow velocity is greatest, allowing them to be preferentially transported to the front. Here, the large grains may be overrun, resegregated towards the surface and recirculated before being shouldered aside into lateral levees. A key element of this recirculation mechanism is the formation of a breaking size-segregation wave, which allows large particles that have been overrun to rise up into the faster moving parts of the flow as small particles are sheared over the top. Observations from experiments and discrete particle simulations in a moving-bed flume indicate that, whilst most large particles recirculate quickly at the front, a few recirculate very slowly through regions of many small particles at the rear. This behaviour is modelled in this paper using asymmetric segregation flux functions. Exact non-diffuse solutions are derived for the steady wave structure using the method of characteristics with a cubic segregation flux. Three different structures emerge, dependent on the degree of asymmetry and the non-convexity of the segregation flux function. In particular, a novel ‘lens-tail’ solution is found for segregation fluxes that have a large amount of non-convexity, with an additional expansion fan and compression wave forming a ‘tail’ upstream of the ‘lens’ region. Analysis of exact solutions for the particle motion shows that the large particle motion through the ‘lens-tail’ is fundamentally different to the classical ‘lens’ solutions. A few large particles starting near the bottom of the breaking wave pass through the ‘tail’, where they travel in a region of many small particles with a very small vertical velocity, and take significantly longer to recirculate.

scholarly journals Asymmetric flux models for particle-size segregation in granular avalanches

2014 ◽  
Vol 757 ◽  
pp. 297-329 ◽  
Author(s):  
P. Gajjar ◽  
J. M. N. T. Gray
Keyword(s):  
Particle Size ◽  
Small Particle ◽  
Volume Fraction ◽  
Free Surface Flows ◽  
Two Dimensions ◽  
Combined Processes ◽  
Maximum Point ◽  
Size Segregation ◽  
Flux Function ◽  
Large Particles

AbstractParticle-size segregation commonly occurs in both wet and dry granular free-surface flows through the combined processes of kinetic sieving and squeeze expulsion. As the granular material is sheared downslope, the particle matrix dilates slightly and small grains tend to percolate down through the gaps, because they are more likely than the large grains to fit into the available space. Larger particles are then levered upwards in order to maintain an almost uniform solids volume fraction through the depth. Recent experimental observations suggest that a single small particle can percolate downwards through a matrix of large particles faster than a large particle can be levered upwards through a matrix of fines. In this paper, this effect is modelled by using a flux function that is asymmetric about its maximum point, differing from the symmetric quadratic form used in recent models of particle-size segregation. For illustration, a cubic flux function is examined in this paper, which can be either a convex or a non-convex function of the small-particle concentration. The method of characteristics is used to derive exact steady-state solutions for non-diffuse segregation in two dimensions, with an inflow concentration that is (i) homogeneous and (ii) normally graded, with small particles above the large. As well as generating shocks and expansion fans, the new asymmetric flux function generates semi-shocks, which have characteristics intersecting with the shock just from one side. In the absence of diffusive remixing, these can significantly enhance the distance over which complete segregation occurs.

scholarly journals Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches

2008 ◽  
Vol 19 (1) ◽  
pp. 61-86 ◽  
Author(s):  
M. SHEARER ◽  
J. M. N. T. GRAY ◽  
A. R. THORNTON
Keyword(s):  
Particle Size ◽  
Free Surface ◽  
Shear Flow ◽  
Free Surface Flows ◽  
Size Segregation ◽  
Small Particles ◽  
Surface Flows ◽  
Scalar Conservation Law ◽  
Large Particles ◽  
Scalar Conservation

Dense, dry granular avalanches are very efficient at sorting the larger particles towards the free surface of the flow, and finer grains towards the base, through the combined processes of kinetic sieving and squeeze expulsion. This generates an inversely graded particle-size distribution, which is fundamental to a variety of pattern formation mechanisms, as well as subtle size-mobility feedback effects, leading to the formation of coarse-grained lateral levees that create channels in geophysical flows, enhancing their run-out. In this paper we investigate some of the properties of a recent model [Gray, J. M. N. T. & Thornton, A. R. (2005) A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. 461, 1447–1473]; [Thornton, A. R., Gray, J. M. N. T. & Hogg, A. J. (2006) A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid. Mech. 550, 1–25] for the segregation of particles of two sizes but the same density in a shear flow typical of shallow avalanches. The model is a scalar conservation law in space and time, for the volume fraction of smaller particles, with non-constant coefficients depending on depth within the avalanche. It is proved that for steady flow from an inlet, complete segregation occurs beyond a certain finite distance down the slope, no matter what the mixture at the inlet. In time-dependent flow, dynamic shock waves can develop; they are interfaces separating different mixes of particles. Shock waves are shown to be stable if and only if there is a greater concentration of large particles above the interface than below. Constructions with shocks and rarefaction waves are demonstrated on a pair of physically relevant initial boundary value problems, in which a region of all small particles is penetrated from the inlet by either a uniform mixture of particles or by a layer of small particles over a layer of large particles. In both cases, and under a linear shear flow, solutions are constructed for all time and shown to have similar structure for all choices of parameters.

scholarly journals A theory for particle size segregation in shallow granular free-surface flows

2005 ◽  
Vol 461 (2057) ◽  
pp. 1447-1473 ◽  
Author(s):  
J.M.N.T Gray ◽  
A.R Thornton
Keyword(s):  
Free Surface ◽  
Plug Flow ◽  
Mixture Theory ◽  
Free Surface Flows ◽  
Size Segregation ◽  
Void Space ◽  
Small Particles ◽  
Surface Flows ◽  
Large Particles ◽  
Steady State Solutions

Abstract Granular materials composed of a mixture of grain sizes are notoriously prone to segregation during shaking or transport. In this paper, a binary mixture theory is used to formulate a model for kinetic sieving of large and small particles in thin, rapidly flowing avalanches, which occur in many industrial and geophysical free-surface flows. The model is based on a simple percolation idea, in which the small particles preferentially fall into underlying void space and lever large particles upwards. Exact steady-state solutions have been constructed for general steady uniform velocity fields, as well as time-dependent solutions for plug-flow, that exploit the decoupling of material columns in the avalanche. All the solutions indicate the development of concentration shocks, which are frequently observed in experiments. A shock-capturing numerical algorithm is formulated to solve general problems and is used to investigate segregation in flows with weak shear.

scholarly journals Segregation-induced fingering instabilities in granular free-surface flows

2012 ◽  
Vol 709 ◽  
pp. 543-580 ◽  
Author(s):  
M. J. Woodhouse ◽  
A. R. Thornton ◽  
C. G. Johnson ◽  
B. P. Kokelaar ◽  
J. M. N. T. Gray
Keyword(s):  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Small Scale ◽  
Size Segregation ◽  
Numerical Resolution ◽  
Bulk Motion ◽  
Large Particles ◽  
Ill Posed

AbstractParticle-size segregation can have a significant feedback on the bulk motion of granular avalanches when the larger grains experience greater resistance to motion than the fine grains. When such segregation-mobility feedback effects occur the flow may form digitate lobate fingers or spontaneously self-channelize to form lateral levees that enhance run-out distance. This is particularly important in geophysical mass flows, such as pyroclastic currents, snow avalanches and debris flows, where run-out distance is of crucial importance in hazards assessment. A model for finger formation in a bidisperse granular avalanche is developed by coupling a depth-averaged description of the preferential transport of large particles towards the front with an established avalanche model. The coupling is achieved through a concentration-dependent friction coefficient, which results in a system of non-strictly hyperbolic equations. We compute numerical solutions to the flow of a bidisperse mixture of small mobile particles and larger more resistive grains down an inclined chute. The numerical results demonstrate that our model is able to describe the formation of a front rich in large particles, the instability of this front and the subsequent evolution of elongated fingers bounded by large-rich lateral levees, as observed in small-scale laboratory experiments. However, our numerical results are grid dependent, with the number of fingers increasing as the numerical resolution is increased. We investigate this pathology by examining the linear stability of a steady uniform flow, which shows that arbitrarily small wavelength perturbations grow exponentially quickly. Furthermore, we find that on a curve in parameter space the growth rate is unbounded above as the wavelength of perturbations is decreased and so the system of equations on this curve is ill-posed. This indicates that the model captures the physical mechanisms that drive the instability, but additional dissipation mechanisms, such as those considered in the realm of flow rheology, are required to set the length scale of the fingers that develop.

An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 2. Bidisperse systems

1998 ◽  
Vol 363 ◽  
pp. 57-77 ◽  
Author(s):  
M. K. LYON ◽  
L. G. LEAL
Keyword(s):  
Large Particle ◽  
Particle Concentration ◽  
Volume Fraction ◽  
Balance Model ◽  
Concentration Profiles ◽  
Size Segregation ◽  
Small Particles ◽  
Concentrated Suspensions ◽  
Particle Volume ◽  
Large Particles

In this paper we report experimental velocity and concentration profiles for suspensions possessing a bidisperse distribution of particle size undergoing pressure-driven flow through a parallel-wall channel. In addition to the overall concentration distributions determined by implementing the modified laser Doppler velocimetry method described in Part 1 (Lyon & Leal 1998), concentration profiles for the particles of each size were measured by sampling the position of marked tracer particles across 60% of the channel gap. Non-uniform overall particle concentration distributions and blunted velocity profiles were found at bulk particle volume fractions of 0.30 and 0.40, which were equal to the monodisperse data of Part 1, within experimental uncertainty. The large-particle concentration profiles were non-uniform down to a large-particle bulk volume fraction of 0.075, while non-uniform distributions of the small particles were only found when the volume fraction of small particles in the bulk was greater than or equal to 0.20. Experiments in which at least half the suspended particulate volume was occupied by large particles revealed enrichment of the large particles in the centreline region of the channel. This size segregation was found to increase as the total number of suspended particles decreased. Finally, the data from experiments in which a uniform small-particle concentration profile was measured were compared with suspension balance model (McTigue & Jenkins 1992; Nott & Brady 1994) predictions for parameter values that corresponded only to the large particles. While close agreement with the large-particle concentration profiles was found, this comparison also reflected the fact that the small particles bring the suspension viscosity to a regime that is more sensitive to the particle concentration, rather than simply providing an increment in background viscosity to the suspending liquid.

scholarly journals Segregation-induced finger formation in granular free-surface flows

2016 ◽  
Vol 809 ◽  
pp. 168-212 ◽  
Author(s):  
J. L. Baker ◽  
C. G. Johnson ◽  
J. M. N. T. Gray
Keyword(s):  
Granular Flows ◽  
Free Surface Flows ◽  
Pyroclastic Flows ◽  
Coarse Grained ◽  
Momentum Balance ◽  
Large Particles ◽  
Averaged Model ◽  
Well Posed ◽  
Dense Granular Flows ◽  
New System

Geophysical granular flows, such as landslides, pyroclastic flows and snow avalanches, consist of particles with varying surface roughnesses or shapes that have a tendency to segregate during flow due to size differences. Such segregation leads to the formation of regions with different frictional properties, which in turn can feed back on the bulk flow. This paper introduces a well-posed depth-averaged model for these segregation-mobility feedback effects. The full segregation equation for dense granular flows is integrated through the avalanche thickness by assuming inversely graded layers with large particles above fines, and a Bagnold shear profile. The resulting large particle transport equation is then coupled to depth-averaged equations for conservation of mass and momentum, with the feedback arising through a basal friction law that is composition dependent, implying greater friction where there are more large particles. The new system of equations includes viscous terms in the momentum balance, which are derived from the $\unicode[STIX]{x1D707}(I)$-rheology for dense granular flows and represent a singular perturbation to previous models. Linear stability calculations of the steady uniform base state demonstrate the significance of these higher-order terms, which ensure that, unlike the inviscid equations, the growth rates remain bounded everywhere. The new system is therefore mathematically well posed. Two-dimensional simulations of bidisperse material propagating down an inclined plane show the development of an unstable large-rich flow front, which subsequently breaks into a series of finger-like structures, each bounded by coarse-grained lateral levees. The key properties of the fingers are independent of the grid resolution and are controlled by the physical viscosity. This process of segregation-induced finger formation is observed in laboratory experiments, and numerical computations are in qualitative agreement.

Structure of Microphase-Separated Silica/Siloxane Molecular Composites

1989 ◽  
Vol 171 ◽  
Author(s):  
Dale W. Schaefer ◽  
James E. Mark ◽  
David Mccarthy ◽  
Li Jian ◽  
C. -C. Sun ◽  
...  
Keyword(s):  
Phase Separation ◽  
Kinetic Studies ◽  
Organic Content ◽  
Small Particles ◽  
X Ray ◽  
Filled Elastomers ◽  
Polymeric Networks ◽  
Large Particles ◽  
Molecular Composites

ABSTRACTThe structure of several classes of silica/siloxane molecular composites is investigated using small-angle x-ray and neutron scattering. These filled elastomers can be prepared through different synthethic protocols leading to a range of fillers including particulates with both rough and smooth surfaces, particulates with dispersed interfaces, and polymeric networks. We also find examples of bicontinuous filler phases that we attribute to phase separation via spinodal decomposition. In-situ kinetic studies of particulate fillers show that the precipitate does not develop by conventional nucleation-and-growth. We see no evidence of growth by ripening whereby large particles grow by consumption of small particles. Rather, there appears to be a limiting size set by the elastomer network itself. Phase separation develops by continuous nucleation of particles and subsequent growth to the limiting size. We also briefly report studies of polymer-toughened glasses. In this case, we find no obvious correlation between organic content and structure.

Analysis of the Particles’ Movement Over the Flat and Profiled Rotating Discs surface in the Velocity Layer of the Viscous Gas

2021 ◽  
Vol 6 (2) ◽  
pp. 17-23
Author(s):  
Valeriy I. Pinakov ◽  
Konstantin V. Kulik ◽  
Boris E. Grinberg
Keyword(s):  
Qualitative Difference ◽  
Surface Region ◽  
Vertex Angle ◽  
Oscillation Regime ◽  
Small Particles ◽  
Magnus Force ◽  
Near Surface ◽  
Rotating Discs ◽  
Large Particles ◽  
Velocity Layer

Experiments on the rotating in the air cones with vertex angle β = 120º and flat disc shown that on frequencies Ω ≥ 2.5 hertz exists a qualitative difference in movement for the particles with diameters d ≈ 1 mm and d ≈ 0.1 mm. The particles with d ≈ 0.1 mm move in the near-surface region, the particles with d ≈ 1 mm jump up to 3 cm. Comparison of the spherical and aspheric (ellipsoid with axles d, d and 4 /3 d) particles' kinematics moving shown the inevitability of the large particles jump occurrence. Large particles come to self-oscillation regime by reason of periodically appearance of the Magnus force. Small particles are localized in the velocity layer

scholarly journals Effects of dynamic fragmentation on the impact force exerted on rigid barrier: centrifuge modelling

2019 ◽  
Vol 56 (9) ◽  
pp. 1215-1224 ◽  
Author(s):  
C.W.W. Ng ◽  
C.E. Choi ◽  
D.K.H. Cheung ◽  
Y. Cui
Keyword(s):  
Volume Fraction ◽  
Impact Force ◽  
Inertial Particles ◽  
Size Segregation ◽  
Centrifuge Modelling ◽  
Rigid Barrier ◽  
Flow Energy ◽  
Dynamic Fragmentation ◽  
Large Particles ◽  
The Impact

Bi-dispersity is a prerequisite for grain-size segregation, which transports the largest particles to the flow front. These large and inertial particles can fragment upon impacting a barrier. The amount of fragmentation during impact strongly influences the force exerted on a rigid barrier. Centrifuge modelling was adopted to replicate the stresses for studying the effects of bi-dispersity in a granular assembly and dynamic fragmentation on the impact force exerted on a model rigid barrier. To study the effects of bi-dispersity, the ratio between the diameters of small and large particles (δs/δl), characterizing the particle-size distribution (PSD), was varied as 0.08, 0.26, and 0.56. The volume fraction of the large particles was kept constant. A δs/δl tending towards unity characterizes inertial flow that exerts sharp impulses, and a diminishing δs/δl characterizes the progressive attenuation of these sharp impulses by the small particles. Flows dominated by grain-contact stresses (δs/δl < 0.26), as characterized by the Savage number, are effective at attenuating dispersive stresses of the large particles, which are responsible for reducing dynamic fragmentation. By contrast, flows dominated by grain-inertial stresses (δs/δl > 0.26) exhibit up to 66% more impulses and 4.3 times more fragmentation. Dynamic fragmentation of bi-disperse flows impacting a rigid barrier can dissipate about 30% of the total flow energy.

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