SPINNING RODS: Experiments

1
SPINNING RODS Experiments Theory

Adam Brooks1, Roberto Camassa1, 2, Jing Hao4,5,
Terry Jo Leiterman1,3, Richard M. McLaughlin1,3,
Richard Superfine4,5, Jonathan Toledo1, Leandra
Vicci
ABSTRACT Singularity theory was used to study
mixing and transport properties of the fluid
motion induced by a spheroid sweeping out a
double cone in free space in the low Reynolds
number regime. Further, slender body theory was
used to develop an asymptotic solution for a
slender cylinder attached to a no slip plane and
sweeping out an upright cone. A table-top
experiment is used to validate these models.
These models have been used to benchmark
micro-fluidic experiments that can be used to
further our understanding of transport and mixing
in ciliated tissues. Joint work with Rich
McLaughlin, Roberto Camassa, Terry Jo Leiterman,
Richard Superfine, Jing Hao, Leandra Vicci, Adam
Brooks. UNC RTG Fluids Group Team.
The Model
The Table Top Experiment
Micro Fluidic Experiment
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Electron microscope image of nanowire
Rod Diameter 0.1 cm Rod Length 1 cm Rotation
Rate 4 RPM

• No-slip on spheroid
• Farfield linear flow

Karo Syrup Viscosity 1000 cm2/s
3D magnetic Force Microscope

Slender Body Theory
Top and side view of air bubbles near a spinning
rod

• Asymptotic 3D time varying solution for spheroid
  sweeping a double cone (angle k)

Rod Diameter 200 nm Rod Length 20 ?m Rotation
Rate 5 Hz
Water Viscosity 0.01 cm2/s
Top
Side
Table Top Calibration
Video tracked bead trajectory with theory overlaid


Multiple exposure image of rod from top view
Simplified ray paths
Particle trajectories computed with RK4
Biological Application
Comparison of Model with Macro Scale Experiment
Hydrodynamic Stresses STRETCH DNA
Blakeslet model superimposed on video tracked
bubble trajectory
Different conformations of a DNA molecule near a
spinning nano-rod
Consecutive frames of a single DNA molecule near
a spinning nano-rod
Thanks NSF, NIH, UNC

Support 1 NSF RTG DMS-0502266
2 NSF DMS-0308687 3 DMS 0104329
DMS 0509423 4 NIH
P41-EB002025 5 NIH
1R01EB000761-01
More Information terryjo_at_amath.unc.edu