Stokes' second flow problem in a high-frequency limit: Application to nanomechanical resonators

Journal of Fluid Mechanics

Volumn 586, Issue , 2007, Pages 249-258

  Yakhot, Victor ^a   Colosqui, Carlos ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; COMPUTATIONAL GEOMETRY; NANOMECHANICS; NEWTONIAN FLOW; PRESSURE; VISCOELASTICITY;

FREQUENCY VARIATION; HIGH-FREQUENCY LIMIT; NANOMECHANICAL RESONATORS; PRESSURE VARIATION;

NANOFLUIDICS;

BOLTZMANN EQUATION; COMPUTATIONAL GEOMETRY; NANOFLUIDICS; NANOMECHANICS; NEWTONIAN FLOW; PRESSURE; VISCOELASTICITY;

NEWTONIAN FLUID; SECONDARY FLOW; STOKES FORMULA; VISCOELASTIC FLUID;

EID: 37749025747     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007007148     Document Type: Article

References (18)

1. BENZI, R., SUCCI, S. & VERGASSOLA, M. 1992 The lattice Boltzmann equation: Theory and applications. Phys. Rep. 222, 145.
2. BHATNAGAR, P. L., GROSS, E. & KROOK, M. 1954 A model for collisions in gases I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511-525.
3. BINNING, C., QUATE, C. F. & GERBER, C. 1986 Atomic force microscope. Phys. Rev. Lett. 56, 930-933.
4. BIRD, R. B., STEWART, W. E. & LIGHTFOOT, E. R. E. 2002 Transport Phenomena, 2nd Edn. Wiley and Sons.
5. BRODKEY, R. S. 1967 The Phenomena of Fluid Motions. Dover.
6. CHEN, H., KANDASAMY, S., ORSZAG, S. A., SHOCK, R., SUCCI S. & YAKHOT, V. 2003 Extended Boltzmann kinetic equation for turbulent flows. Science 301, 633-636.
7. CHEN, H., ORSZAG, S. A., STAROSELSKY, I. & Succi, S. 2004 Expanded analogy between Boltzmann kinetic theory of fluids and turbulence. J. Fluid Mech. 519, 301-313.
8. CHEN, S. Y. & DOOLEN, G. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329-xxx.
9. CLELAND, A. N. & ROUKES, M. L. 1998 A nanometer-scale mechanical electrometer. Nature 392, 160-162.
10. COLOSQUI, C. & YAKHOT, V. 2007 Lattice Boltzmann simulations of second Stokes flow problem. J. Mod. Phys. (in press).
11. EKINCI, K. L., HUANG, X. M. & ROUKES, M. L. 2004 Ultrasensitive mass detection. Appl. Phys. Lett. 84, 4469.
12. KARABACAK, D. M., YAKHOT, V. & EKINCI, K. L. 2007 High frequency nanofluidics: Experimental study with nano-mechanical resonators. Phys. Rev. Lett. (in press) (ArXiv, cond-mat/0703230).
13. LANDAU, L. D. & LIFSHITZ, E. M. 1959 Fluid Mechanics. Pergamon.
14. LANDAU, L. D. & LIFSHITZ, E. M. 1981 Physical Kinetics. Butterworth-Heinemann.
15. ROSENAU, P. 1993 Random walker and the telegrapher's equation: A paradigm of generalized hydrodynamics. Phys. Rev. E 48, R655-657.
16. SERVICE, R. B. 2006 Tipping scales - just barely. Science 312, 683.
17. STOKES, G. G. 1851 On the effect of the internal friction in fluids on the motion of pendulums. Camb. Phil. Trans. IX, 8.
18. VERBRIDGE, S. S., BELLAN, L. M., PARPIA, J. M. & CRAIGHEAD, H. G. 2006 Optically driven resonance of nanoscale flexural oscillators in fluids. Nano Lett. 6, 2109-2114.