Casimir Rack and Pinion Ramin Golestanian Department of Physics and Astronomy University of Sheffiel

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Casimir Rack and PinionRamin GolestanianDepartm
ent of Physics and AstronomyUniversity of
Sheffield

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Significance of Casimir Force

• Tiny at Micron-scale
• It took 50 years to be verified!
• Dominant at Nano-scale
• Strongest distance dependence
• unwanted effects stiction
• harnessed for good use novel NEMS

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Geometry Challenge

• Practical Aspect
• Realistic machine parts
• Fundamental Aspect
• Pair-wise summation?

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Geometry Challenge

• Expansion in Dielectric Contrast

Not so easy
R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)
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Geometry Challenge

• Convergence properties

• CM

R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)
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Normal Casimir Force

• Is it practical in making nano-mechanical
  devices?
• Not really

• Repulsive Casimir Force does it exist?

Alchemy of nano-mechanics
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Lateral Casimir Force

• Theoretical Prediction
• Josephson-like force between corrugated
  surfaces

R. Golestanian M. Kardar, Phys. Rev. Lett. 78,
3421 (1997) T. Emig, A. Hanke, R. Golestanian
M. Kardar, Phys. Rev. A 67, 022114 (2003)
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Lateral Casimir Force

• Experimental Verification

F. Chen, U. Mohideen, G. L. Klimchitskaya, V.
M. Mostepanenko, Phys. Rev. Lett. 88, 101801
(2002)
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Rack and Pinion

• Powered by Quantum Vacuum
• Force transduction with no contact could
  potentially solve wear problem in nano-mechanical
  systems

A. Ashourvan, M.F. Miri, R. Golestanian, Phys.
Rev. Lett. 98, 140801 (2007)
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Equation of Motion
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Equation of Motion

• Relevant parameters

• Uniformly moving rack

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No Dissipation

• The equation is integrable nonlinear pendulum

• Skipping Velocity

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No Dissipation

• Pinion Velocity vs Rack Velocity and initial
  Offset

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No Dissipation

• The effect of external load on the skipping
  transition

similar to solid friction
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Weak Dissipation

• The skipping transition boundary

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Weak Dissipation

• Pinion Velocity vs Rack Velocity and Load

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Strong Dissipation

• Pinion Velocity vs Rack Velocity and Load

• Stall Force

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Vibrating Rack and Pinion

• Is it possible to rectify a symmetric oscillatory
  motion?

A. Ashourvan, M.F. Miri, R. Golestanian, Phys.
Rev. E 75, 040103 (R)(2007)

• See also T. Emig, Phys. Rev. Lett. 98, 160801
  (2007)

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Vibrating Rack and Pinion

• Equation of motion

• Solution

• Pinion Velocity

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Vibrating Rack and Pinion

• Basin of attraction for forward motion

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Vibrating Rack and Pinion

• Parameter values for forward motion

• Stall Force

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Feasibility

• Realistic values for the lateral Casimir force
  amplitude

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Feasibility

• Realistic values for skipping velocity

Not so small after all
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Conclusion

• Casimir forces are dominant at nano-scale ?
• Knowledge of Casimir forces can be used to avoid
  unwanted effects in NEMS
• They can be used to design nano-mechanical
  devices mechanical engineering with quantum
  vacuum fluctuation forces!
• Non-contact lateral force transduction can solve
  the wear problem
• Despite expectation, the Casimir grip can be
  strong

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CollaboratorsA. Ashourvan (IASBS, Zanjan)M.F.
Miri (IASBS, Zanjan)Acknowledgement
THANK YOU