Microscopic Description of the Granular Fluidity Field in Nonlocal Flow Modeling

Zhang, Qiong; Kamrin, Ken

doi:10.1103/physrevlett.118.058001

Cited by 114 publications

(175 citation statements)

References 60 publications

(100 reference statements)

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“…This NGF model is rooted in the introduction of a scalar state field named granular fluidity and denoted as g(x), which exists throughout the granular media. This "g" field is a kinematically observable state variable (Zhang & Kamrin, 2017) that is defined by a reaction-diffusion form equation, similar to that of Landau-type equation:…”

Section: Inertial Rheologymentioning

confidence: 99%

“…The gaseous regime was the first to be accurately described (Bagnold, 1954(Bagnold, , 1956 while the quasi-static and intermediate regimes have been increasingly better described in the past decade (GDR-MiDi, 2004;F. da Cruz et al, 2005;Zhang & Kamrin, 2017). While in volcanology the Inertial number is not (generally) used to scale experiments, it is an essential parameter to ensure scaling of the mean particle rearrangement timescale over the flow deformation timescale and it was shown to control granular flow rheology (Andreotti et al, 2013;Forterre & Pouliquen, 2008).…”

Section: Bidisperse Distributions and Implications For The Modeling Omentioning

confidence: 99%

“…This NGF model is rooted in the introduction of a scalar state field named granular fluidity and denoted as g ( x ), which exists throughout the granular media. This “ g ” field is a kinematically observable state variable (Zhang & Kamrin, ) that is defined by a reaction‐diffusion form equation, similar to that of Landau‐type equation:

t_{0} \overset{g}{true} = A^{2} d^{2} \nabla^{2} g - ∆ μ ((), \frac{μ_{s} - μ}{μ_{2} - μ}) g - b \sqrt{\frac{ρ_{s} d^{2}}{p} μ} g^{2}

wherein t 0 is a constant time scale and μ 2 = μ static + ∆μ . ∆μ and b are material constants.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

2019

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Granular flows are found across multiple geophysical environments and include pyroclastic density currents, debris flows, and avalanches, among others. The key to describing transport of these hazardous flows is the rheology of these complex multiphase mixtures. Here we use the multiphase model MFIX in 2‐D for concentrated currents to examine the implications of rheological assumptions and validate this approach through comparison to experiments of both frictional and fluidized flows made of glass beads (Sauter mean grain‐size of 75 μm). Because the rheology of highly polydisperse, highly angular, polydensity granular mixtures is poorly known, we focus on simplified monodisperse or bidisperse mixtures described by the frictional flow theory of Schaeffer (1987, https://doi.org/10.1016/0022-0396(87)90038-6) and Srivastava‐Sundaresan, often referred to as the Princeton model (Srivastava & Sundaresan, 2003, https://doi.org/10.1016/S0032-5910(02)00132-8). We show that simulations including the latter model replicate well the flow shape, kinematics, and pore fluid pressure that match well‐constrained dam‐break experiments of initially fluidized or pressure‐balanced granular flows. Simulations reveal that pore fluid pressure is intrinsically modulated by dilation and compaction of the flow and hence can be generated in concentrated pyroclastic density currents. We use these simulations to interpret basal pore pressure signals from local flow properties (mixture density, solid velocity, and pore fluid pressure). Rheological changes retard these simulated flows considerably near the predicted runout, but most continuum models cannot inherently predict a zero velocity. We suggest an inertial number parameter that can be used to approximate deposition, and this approach could be a valuable tool used to validate simulations against natural pyroclastic current examples.

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Section: Inertial Rheologymentioning

confidence: 99%

Section: Bidisperse Distributions and Implications For The Modeling Omentioning

confidence: 99%

t_{0} \overset{g}{true} = A^{2} d^{2} \nabla^{2} g - ∆ μ ((), \frac{μ_{s} - μ}{μ_{2} - μ}) g - b \sqrt{\frac{ρ_{s} d^{2}}{p} μ} g^{2}

wherein t 0 is a constant time scale and μ 2 = μ static + ∆μ . ∆μ and b are material constants.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

2019

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“…[], Gaume et al . [], and Zhang and Kamrin [] suggest a correction for nonlocal behavior based on the notion of a field variable termed the “granular fluidity,” which itself is defined in terms of a granular temperature.…”

Section: The Dynamics Of Hydrogranular Mediamentioning

confidence: 99%

On the kinematics and dynamics of crystal‐rich systems

2017

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Partially molten rocks, often called a mush, are examples of a hydrogranular mixture where the dynamics are controlled by both fluid and crystal‐crystal interactions. An obstacle to progress in understanding high‐temperature hydrogranular systems has been the lack of adequate levels of description of microphysical processes. Here we rationalize the hydrogranular kinematic and dynamic states by applying the concept of particle (crystal) force chains. We exemplify this with discrete‐element computational fluid dynamic simulations of the intrusion of a basaltic melt into an olivine‐basalt mush, where crystal‐scale force chains, crystal transport, and melt mixing are resolved. To describe the microscale kinematics of the system, we introduce the coordination number and the fabric tensors of particle contacts and forces. We quantify the changing contact and force fabric anisotropy, coaxiality, and the connectedness of the mush, under dynamic conditions. To describe the dynamics, particle and fluid characteristic response times are derived. These are used to define local and bulk Stokes numbers, and viscous and inertia numbers, which quantify the multiphase coupling under crystal‐rich conditions. We employ the Sommerfeld number, which describes the importance of crystal‐melt lubrication, with a viscous number to illustrate the dynamic regimes of crystal‐rich magmas. We show that the notion of mechanical “lock up” is not uniquely identified with a particular crystal volume fraction and that distinct mechanical behaviors can emerge simultaneously within a crystal‐rich system. We also posit that this framework describes magmatic fabrics and processes which “unlock” a crystal mush prior to eruption or mixing.

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“…Third, there is generally no clear separation of length-scales, i.e., the microscopic (particle) and macroscopic scales (that of hydrodynamic fields, like the density or the velocity) are not clearly separated like in molecular fluids [60,63]. All in all, a proper constitutive law to describe granular matter is still work in progress [64,65].…”

Section: Granular Mattermentioning

confidence: 99%

The impact of raindrops on sand

Jong¹

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Microscopic Description of the Granular Fluidity Field in Nonlocal Flow Modeling

Cited by 114 publications

References 60 publications

Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

On the kinematics and dynamics of crystal‐rich systems

The impact of raindrops on sand

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