Dynamical arching in a two dimensional granular flow

A study of grains flow in a two dimensional hopper using particle tracking and photoelastic methods is presented in this article. An intermittent network of contact forces consisting of force chains and arches is observed. This network is responsible for fluctuations in the average vertical velocity. The magnitude of these fluctuations depends on the hopper’s geometry, and it quickly reduces for large aperture size and small inclination angles. The average velocity field is described using a combination of harmonic angular functions and a power law of radial position. The mass flow rate is determined through the average velocity field and a Beverloo type scaling is obtained. We found that the effect of the inclination angle on the mass flow rate is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha/ \,(\sin\alpha)^{3/2}}$$\end{document} . It is also found that the critical aperture size, approaching jamming, depends linearly on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sin\alpha}$$\end{document} . At small D/d, the time average of the network of contact forces shows a boundary with characteristics resembling the free fall arch. We show that an arch can be built following the principal compression orientation of the stress tensor which captures the characteristics of the arches observed experimentally.