1. Casimir Rack and Pinion Ramin Golestanian Department of Physics and Astronomy University of Sheffield

2. 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

3. Geometry Challenge Practical Aspect Fundamental Aspect
Realistic ``machine parts’’
Fundamental Aspect
Pair-wise summation?

4. Geometry Challenge Expansion in Dielectric Contrast Not so easy …
R. Golestanian, Phys. Rev. Lett. 95, (2005)

5. Geometry Challenge Convergence properties CM:
R. Golestanian, Phys. Rev. Lett. 95, (2005)

6. Normal Casimir Force
Is it practical in making nano-mechanical devices?
Not really …
Repulsive Casimir Force: does it exist?
Alchemy of nano-mechanics …

7. 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, (2003)

8. Lateral Casimir Force Experimental Verification
F. Chen, U. Mohideen, G. L. Klimchitskaya, &
V. M. Mostepanenko, Phys. Rev. Lett. 88, (2002)

9. 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, (2007)

10. Equation of Motion R q
x=Rq y W H y x l

11. Equation of Motion
Relevant parameters:
Uniformly moving rack:

12. No Dissipation The equation is integrable: nonlinear pendulum
Skipping Velocity:

13. No Dissipation
Pinion Velocity vs Rack Velocity and initial Offset

14. No Dissipation The effect of external load on the skipping transition
similar to solid friction

15. Weak Dissipation
The skipping transition boundary

16. Weak Dissipation
Pinion Velocity vs Rack Velocity and Load

17. Strong Dissipation Pinion Velocity vs Rack Velocity and Load
Stall Force

18. Vibrating Rack and Pinion
Is it possible to rectify a symmetric oscillatory motion?
A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. E 75, (R)(2007)
See also: T. Emig, Phys. Rev. Lett. 98, (2007)

19. Vibrating Rack and Pinion
Equation of motion:
Solution:
Pinion Velocity:

20. Vibrating Rack and Pinion
Basin of attraction for forward motion

21. Vibrating Rack and Pinion
Parameter values for forward motion
Stall Force:

22. Feasibility
Realistic values for the lateral Casimir force amplitude

23. Feasibility Realistic values for skipping velocity
Not so small after all …

24. 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

25. Collaborators: A. Ashourvan (IASBS, Zanjan) M. F
Collaborators: A. Ashourvan (IASBS, Zanjan) M.F. Miri (IASBS, Zanjan) Acknowledgement:
THANK YOU