14 research outputs found
A finite element implementation of the nonlocal granular rheology
Inhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models has been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finite element-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom – the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (1) linear shear with gravity, (2) annular shear flow without gravity, and (3) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh independent.National Science Foundation (U.S.) (Grant NSF-CBET-1253228
Continuum modeling of size-segregation and flow in dense, bidisperse granular media: Accounting for segregation driven by both pressure gradients and shear-strain-rate gradients
Dense mixtures of particles of varying size tend to segregate based on size
during flow. Granular size-segregation plays an important role in many
industrial and geophysical processes, but the development of coupled, continuum
models capable of predicting the evolution of segregation dynamics and flow
fields in dense granular media across different geometries has remained a
longstanding challenge. One reason is because size-segregation stems from two
driving forces: (1) pressure gradients and (2) shear-strain-rate gradients.
Another reason is due to the challenge of integrating segregation models with
rheological constitutive equations for dense granular flow. In this paper, we
build upon our prior work, which combined a model for
shear-strain-rate-gradient-driven segregation with a nonlocal continuum model
for dense granular flow rheology, and append a model for
pressure-gradient-driven segregation. We perform discrete element method (DEM)
simulations of dense flow of bidisperse granular systems in two flow
geometries, in which both segregation driving forces are present: namely,
inclined plane flow and planar shear flow with gravity. Steady-state DEM data
from inclined plane flow is used to determine the dimensionless material
parameters in the pressure-gradient-driven segregation model for both spheres
and disks. Then, predictions of the coupled, continuum model accounting for
both driving forces are tested against DEM simulation results across different
cases of both inclined plane flow and planar shear flow with gravity, while
varying parameters such as the size of the flow geometry, the driving
conditions of flow, and the initial conditions. Overall, we find that it is
crucial to account for both driving forces to capture segregation dynamics in
dense, bidisperse granular media across both flow geometries with a single set
of parameters.Comment: 25 pages with 9 figure
Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media
Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maximum radii of laser-nucleated bubbles decreased more rapidly than acoustically nucleated bubbles as the gel stiffness increased. For water and low stiffness gels, the collapse times were well predicted by a Rayleigh cavity, but bubbles collapsed faster than predicted in the higher stiffness gels. The growth and collapse phases occurred symmetrically (in time) about the maximum radius in water but not in gels, where the duration of the growth phase decreased more than the collapse phase as gel stiffness increased. Numerical simulations of the bubble dynamics in viscoelastic media showed varying degrees of success in accurately predicting the observations
Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media
Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maximum radii of laser-nucleated bubbles decreased more rapidly than acoustically nucleated bubbles as the gel stiffness increased. For water and low stiffness gels, the collapse times were well predicted by a Rayleigh cavity, but bubbles collapsed faster than predicted in the higher stiffness gels. The growth and collapse phases occurred symmetrically (in time) about the maximum radius in water but not in gels, where the duration of the growth phase decreased more than the collapse phase as gel stiffness increased. Numerical simulations of the bubble dynamics in viscoelastic media showed varying degrees of success in accurately predicting the observations
Nonlocal continuum modeling of dense granular flow in a split-bottom cell with a vane-shaped intruder
Nonlocal modeling of granular flows down inclines
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.National Science Foundation (U.S.) (NSF-CBET-1253228
Small-amplitude acoustics in bulk granular media
We propose and validate a three-dimensional continuum modeling approach that predicts small-amplitude acoustic behavior of dense-packed granular media. The model is obtained through a joint experimental and finite-element study focused on the benchmark example of a vibrated container of grains. Using a three-parameter linear viscoelastic constitutive relation, our continuum model is shown to quantitatively predict the effective mass spectra in this geometry, even as geometric parameters for the environment are varied. Further, the model's predictions for the surface displacement field are validated mode-by-mode against experiment. A primary observation is the importance of the boundary condition between grains and the quasirigid walls.Schlumberger-Doll Research Cente