Casimir Rack and Pinion

Ramin GolestanianDepartment of Physics and Astronomy

University of Sheffield

Significance of Casimir Force

• Tiny at Micron-scaleIt took 50 years to be verified!

• Dominant at Nano-scaleStrongest distance dependence

unwanted effects: stiction

harnessed for good use: novel NEMS

Geometry Challenge

• Practical AspectRealistic ``machine parts’’

• Fundamental AspectPair-wise summation?

Geometry Challenge

• Expansion in Dielectric Contrast

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

Not so easy …

Geometry Challenge

• Convergence properties

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

CM:

Normal Casimir Force

• Is it practical in making nano-mechanical devices?

Not really …

• Repulsive Casimir Force: does it exist?

Alchemy of nano-mechanics …

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)

Lateral Casimir Force

• Experimental Verification

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

Rack and Pinion

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

Powered by Quantum Vacuum

Force transduction with no contact could potentially solve wear problem in nano-mechanical systems

Equation of Motion

R

x=R

y

W

H

y

x

Equation of Motion

Relevant parameters:

Uniformly moving rack:

No Dissipation

The equation is integrable: nonlinear pendulum

Skipping Velocity:

No Dissipation

Pinion Velocity vs Rack Velocity and initial Offset

No Dissipation

The effect of external load on the skipping transition

similar to solid friction

Weak Dissipation

The skipping transition boundary

Weak Dissipation

Pinion Velocity vs Rack Velocity and Load

Strong Dissipation

Pinion Velocity vs Rack Velocity and Load

Stall Force

Vibrating Rack and Pinion

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

Is it possible to rectify a symmetric oscillatory motion?

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

Vibrating Rack and Pinion

Equation of motion:

Pinion Velocity:

Solution:

Vibrating Rack and Pinion

Basin of attraction for forward motion

Vibrating Rack and Pinion

Parameter values for forward motion

Stall Force:

Feasibility

Realistic values for the lateral Casimir force amplitude

Feasibility

Realistic values for skipping velocity

Not so small after all …

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

THANK YOU

Collaborators:

A. Ashourvan (IASBS, Zanjan)M.F. Miri (IASBS, Zanjan)

Acknowledgement: