Radial segregation patterns in rotating granular mixtures: waviness selection.

Area of Science:

• Physics
• Granular materials science
• Fluid dynamics

Background:

• Granular materials exhibit complex behaviors when subjected to rotation.
• Radial segregation, where particles of different sizes separate radially, is a common phenomenon in rotating drums.
• Understanding the factors influencing pattern formation is crucial for predicting and controlling granular flows.

Purpose of the Study:

• To model and experimentally investigate the radial segregation patterns in a thin rotating drum containing beads of two sizes.
• To predict the relationship between pattern waviness and drum fill level.
• To determine the selection mechanism for the waviness of steady segregation patterns.

Main Methods:

• Development of a mathematical model to describe radial segregation patterns.
• Theoretical prediction of a cutoff waviness (w(c)) based on drum fill level.
• Experimental validation using a thin rotating drum with two distinct bead sizes.
• Analysis of pattern waviness (w) and its comparison with the predicted cutoff.

Main Results:

• Experimental results align with theoretical predictions, showing that observed pattern waviness (w) is always less than or equal to the cutoff waviness (w(c)).
• A strong dependence of the cutoff waviness on the drum's fill level was experimentally confirmed.
• Steady segregation patterns were found to exclusively exhibit waviness equal to the cutoff waviness (w = w(c)).

Conclusions:

• The waviness of radial segregation patterns in a rotating drum is effectively low-pass filtered, with a cutoff determined by the fill level.
• The observed waviness of steady patterns is selected by this low-pass filtering mechanism.
• This study provides a quantitative understanding of pattern selection in granular segregation.