Dynamical Study of Granular Flow through a Two-Dimensional Hopper
Lina Yang1,2, Yu-Qi Chen1,2**
1Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 2School of Physical Sciences, University of Chinese Academy of Science, Beijing 100049
Abstract：The mass flow rate of a granular flow through an aperture under gravity is a long-standing challenge issue in physical science. We show that for steady flow field close to laminar flow, the dynamical equations together with the continue equation and Mohr-circle description of the stress are closed, and hence solvable. In a case of streamline guided by the two-dimensional hopper, we obtain a consistent condition and use it to determine the stress and the velocity distribution. Our result indicates that 3/2 power scaling behavior is recovered with a coefficient $C(\mu,\alpha)$ being a function of frictional coefficient and the hopper angle. It is found that the predicted coefficient $C(\mu,\alpha)$ is compatible with previous studies.
2019, Vol. 36 
