Complex dynamics of three interacting spheres in a rotating drum

Abstract

Numerous studies have demonstrated the potential for particles in fluids to exhibit complicated dynamical behavior. In this work, we study a horizontal rotating drum filled with pure glycerol and three large, heavy spheres. The rotation of the drum causes the spheres to cascade and tumble and thus interact with each other. We find several different behaviors of the spheres depending on the drum rotation rate. Simpler states include the spheres remaining well separated, or states where two or all three of the spheres come together and cascade together. We also see two more complex states, where two or three of the spheres move erratically. The main signature of this erratic motion is that pairs of spheres intermittently approach each other ͑sometimes colliding͒ and then separate; the time between collisions is variable even for a fixed rotation rate. We characterize these disordered states and find a complex phase space with a rich set of behaviors. This experiment serves as a simple model system to demonstrate complex behavior in simple fluid dynamical systems.

An experimental study of the motion of a light sphere in a rotating viscous fluid

“…The motion at the fixed points adjacent to the wall are studied in detail by Ashmore et al (2005) who show that cavitation is an essential component of the force balance and Yang et al (2006), who study the effects of roughness in the interactions with the wall. The dynamical motion including chaos was subsequently studied in detail by Davidheiser et al (2010). When many particles are added to a rotating cylinder of viscous fluid, axial segregation and pattern formation can occur (see Seiden & Thomas 2011, and references therein).…”