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Related Experiment Video

Updated: Jun 12, 2026

One-Step Approach to Fabricating Polydimethylsiloxane Microfluidic Channels of Different Geometric Sections by Sequential Wet Etching Processes

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Streamline jumping: a mixing mechanism.

Ivan C Christov¹, Julio M Ottino, Richard M Lueptow

¹Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 21, 2010

Summary

Granular flows in rotating drums exhibit complex dynamics. A new mixing mechanism, streamline jumping, emerges as the flow layer thins, leading to potentially chaotic behavior.

Area of Science:

Physics
Applied Mathematics
Fluid Dynamics

Background:

Tumbled granular flows in rotating drums are common in industrial processes.
Understanding granular flow dynamics is crucial for process optimization.
Previous models often simplify the complex behavior of granular materials.

Purpose of the Study:

To investigate the singular limit of granular flows in rotating drums.
To identify novel mixing mechanisms in granular flows.
To characterize the emergent dynamical system and its properties.

Main Methods:

Analysis of quasi-two-dimensional rotating drum experiments.
Mathematical modeling of granular flow dynamics.
Identification of piecewise isometries as the limiting dynamical system.

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Main Results:

The limiting dynamics belong to a class of piecewise isometries.
A new mixing mechanism, termed streamline jumping, was identified.
Streamline jumping is linked to the horizontal motion of the free surface.

Conclusions:

Granular flow dynamics in the singular limit are complex and potentially chaotic.
Streamline jumping provides a mechanism for mixing without traditional streamline crossing.
The study offers new insights into the fundamental physics of granular flows.