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

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Presentation transcript:

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

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

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

Geometry Challenge Expansion in Dielectric Contrast Not so easy … R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)

Geometry Challenge Convergence properties CM: R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)

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 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)

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

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 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)

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

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

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