Spinning Rods: Experiment and Theory.

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Spinning Rods Experiment and Theory.

• THE RMX TEAM Rich McLaughlin, Roberto Camassa,
  Leandra Vicci, Rich Superfine, Liz Bouzarth,
  Longhua Zhao, Terry Jo Leiterman, Hao
  Jing,Jonathan Toledo, David Marron, Adam Brooks,
  Ben LaRoque, Brian Bouzarth

What is the response of a fluid when driven by
cylindrically symmetric rod spinning an upright
cone

How is this motion changed or unchanged when
symmetries are broken


Elucidates fundamental origins of basic flow
structures in stokes regime. Applications to
biology.
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Micro-scale RMX Experiment
Comparison of Micro-scale trajectory and
Blakeslet model
The Model
The Micro-Scale Experiment

• challenges
• Thermal fluctuations/ Brownian motion
• No side view

Nano-wire
Side view of Model Trajectories
3D FM
Tracking of micro-scale trajectory
Top view of Model Trajectories
Epicycle Amp. Vs. Radius
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The Macro-Scale Experiment Basics
Setup
Plexiglas tank
cameras
rod (cigar?)
magnet
Making the cone
field lines
magnet
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Side View
Top View
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The Macro-Scale Experiment Calibration
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The Macro-Scale Experiment Comparison with
Theory
Comparison with Blakeslet model
Epicycle Amp. Vs. Radius
Epicycle Amp. cm
Radius cone radii
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The Macro-Scale Experiment Asymmetric Rod
broken cylindrical symm.
What differences should we expect?

broken symmetry lifted degeneracy

Experimental Results
Comparison with Theory
side view
Experimental Trajectory
Simulation
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The Macro-Scale Experiment Asymmetric Rod
Plans for future work
EM picture of nano-rod
Microscale Trajectory
BTW, why study bent rods?
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SUMMARY

• Studied fluid motion induced by a cylindrically
  symmetric rod sweeping out an upright cone
• Agrees quantitatively with model
• Time scale associated with orbit and epicycle

• What happens when cylindrical symmetry broken?
• Agrees qualitatively with singularity theory
  simulations
• 3rd time scale observed corresponding to large
  scale torioidal motion

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Acknowledgements

• Rich McLaughlin, Roberto Camassa, Leandra Vicci,
  Rich Superfine
• Liz Bouzarth, Longhua Zhao, Terry Jo Leiterman,
  Hao Jing
• David Marron, Adam Brooks, Ben LaRoque, Brian
  Bouzarth
• Ben Evans, Adam Shields
• Michael Minion, Ricardo Cortez
• Research supported by NSF RTG DMS-0502266