Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow |
| |
Authors: | Lindsay B H May Michael Shearer Karen E Daniels |
| |
Institution: | 1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA 2. Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
|
| |
Abstract: | Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution
of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the
shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven
shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from
experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying
the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer
of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily
long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function
which separates the shear band from the rest of the material. Each solution of the initial value problem is nonstandard, involving
curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise
linear case. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|