Tracking Particles in Tumbling Containers

Abstract

In answer to the question why is fluid dynamics more developed as a science than granular dynamics, one may cite that the Navier-Stokes equations of fluid motion are more developed and more extensively tested. A collection of grains—moving or static—inherently involves the intermediate or mesoscopic scales of motion: the strong separation of scales from the molecular to the macroscopic flow (Batchelor, 1967) that permits the continuum equations to well embody the physics of flowing fluids does not exist with granular materials, even for the smallest sized grains. Though this is undoubtedly true and represents a substantial theoretical challenge, perhaps in answering our question, we should not discount the ability of the aesthetic qualities of the flows themselves to motivate investigations. Fluid flows are beautiful. Typically opaque grains, on the other hand, mask what motivational beauty might lie in granular flow patterns. In this paper I describe some recent experiments visualising the granular transport in tumbling containers. In §2 I describe quasi-2-dimensional experiments in a rotating disk where the patterns can be observed by eye. These are experiments with the desirable qualities that the mixing behaviour can be explicitly viewed, quantified, and substantially modelled. In §3 I describe experiments in the 3-dimensional extension of the disk—a rotating tube. The 3-d flow is visualised with a non-invasive magnetic resonance imaging (MRI) technique which gives direct information on the radial and axial flow patterns. Non-invasive imaging (Nakagawa et al., 1993; Broadbelt et al., 1993; Nikitidis et al., 1994; Jaeger et al., 1996) seems on the verge of providing a wealth of new experimental information on 3-d granular flows.

Here are sands, ignoble things, ... -Francis Beaumont (1586–1616)