Simple model for reverse buoyancy in a vibrated granular system

TL;DR

This paper investigates reverse buoyancy in vibrated granular systems, demonstrating a simple mechanical model that accurately predicts the vertical motion of objects based on their density.

Contribution

It introduces a straightforward one-dimensional model explaining reverse buoyancy, aligning well with experimental observations in vibrated granular beds.

Findings

The model accurately predicts rising and sinking velocities.

Experimental data confirms the simple behavior of velocity versus density.

Reverse buoyancy can be explained by a balance of buoyancy and frictional forces.

Abstract

Large objects, immersed in a homogeneous granular system, migrate when subjected to vibrations. Under certain conditions large heavy objects rise and similar light ones sink to the bottom. This is called reverse buoyancy. We report an experimental study of this singular behavior, for a large sphere immersed in a deep granular bed. A simple mechanism is proposed to describe the motion of a sphere, inside a vertically vibrated granular system. When reverse buoyancy is observed, the measured vertical velocity of the immersed object, as a function of its density, shows a simple behavior. With a one-dimensional mechanical model that takes into account a buoyancy force and the frictional drag, we obtain the rising velocity for heavy objects and the sinking rate for light ones. The model yields a very good qualitative and quantitative agreement with the experiment.