Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-23T22:45:21.369Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy dissipation in microfluidic beam resonators

Published online by Cambridge University Press:  22 March 2010

JOHN E. SADER ,
THOMAS P. BURG  and
SCOTT R. MANALIS
JOHN E. SADER*
Affiliation:
Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia
THOMAS P. BURG
Affiliation:
Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Max Planck Institute for Biophysical Chemistry, 37077 Goettingen, Germany
SCOTT R. MANALIS
Affiliation:
Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: jsader@unimelb.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

The fluid–structure interaction of resonating microcantilevers immersed in fluid has been widely studied and is a cornerstone in nanomechanical sensor development. In many applications, fluid damping imposes severe limitations by strongly degrading the signal-to-noise ratio of measurements. Recently, Burg et al. (Nature, vol. 446, 2007, pp. 1066–1069) proposed an alternative type of microcantilever device whereby a microfluidic channel was embedded inside the cantilever with vacuum outside. Remarkably, it was observed that energy dissipation in these systems was almost identical when air or liquid was passed through the channel and was 4 orders of magnitude lower than that in conventional microcantilever systems. Here, we study the fluid dynamics of these devices and present a rigorous theoretical model corroborated by experimental measurements to explain these observations. In so doing, we elucidate the dominant physical mechanisms giving rise to the unique features of these devices. Significantly, it is found that energy dissipation is not a monotonic function of fluid viscosity, but exhibits oscillatory behaviour, as fluid viscosity is increased/decreased. In the regime of low viscosity, inertia dominates the fluid motion inside the cantilever, resulting in thin viscous boundary layers – this leads to an increase in energy dissipation with increasing viscosity. In the high-viscosity regime, the boundary layers on all surfaces merge, leading to a decrease in dissipation with increasing viscosity. Effects of fluid compressibility also become significant in this latter regime and lead to rich flow behaviour. A direct consequence of these findings is that miniaturization does not necessarily result in degradation in the quality factor, which may indeed be enhanced. This highly desirable feature is unprecedented in current nanomechanical devices and permits direct miniaturization to enhance sensitivity to environmental changes, such as mass variations, in liquid.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 215 - 250
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Basak, S., Raman, A. & Garimella, S. V. 2006 Hydrodynamic loading of microcantilevers vibrating in viscous fluids. J. Appl. Phys. 99, 114906.CrossRefGoogle Scholar
Batchelor, G. K. 1974 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Berger, R., Gerber, C., Lang, H. P. & Gimzewski, J. K. 1997 Micromechanics: a toolbox for femtoscale science: ‘Towards a laboratory on a tip’. Microelectron. Engng 35, 373–379.CrossRefGoogle Scholar
Binnig, C., Quate, C. F. & Gerber, C. 1986 Atomic force microscope. Phys. Rev. Lett. 56, 930–933.CrossRefGoogle ScholarPubMed
Burg, T. P., Godin, M., Knudsen, S. M., Shen, W., Carlson, G., Foster, J. S., Babcock, K. & Manalis, S. R. 2007 Weighing of biomolecules, single cells and single nanoparticles in fluid. Nature 446, 1066–1069.CrossRefGoogle ScholarPubMed
Burg, T. P. & Manalis, S. R. 2003 Suspended microchannel resonators for biomolecular detection. Appl. Phys. Lett. 83, 2698–2700.CrossRefGoogle Scholar
Burg, T. P., Sader, J. E. & Manalis, S. R. 2009 Non-monotonic energy dissipation in microfluidic resonators. Phys. Rev. Lett. 102, 228103.CrossRefGoogle Scholar
Butt, H.-J., Siedle, P., Seifert, K., Fendler, K., Seeger, T., Bamberg, E., Weisenhorn, A., Goldie, K. & Engel, A. 1993 Scan speed limit in atomic force microscopy. J. Microsc. 169, 75–84.CrossRefGoogle Scholar
Chon, J. W. M., Mulvaney, P. & Sader, J. E. 2000 Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids. J. Appl. Phys. 87, 3978–3988.CrossRefGoogle Scholar
Chu, W.-H. 1963 Vibration of fully submerged cantilever plates in water. Tech. Rep. No. 2, DTMB, Contract NObs-86396(X), Southwest Research Institute, San Antonio, Texas.Google Scholar
Clarke, R. J., Cox, S. M., Williams, P. M. & Jensen, O. E. 2005 The drag on a microcantilever oscillating near a wall. J. Fluid Mech. 545, 397–426.CrossRefGoogle Scholar
Crighton, D. G. 1983 Resonant oscillations in fluid-loaded struts. J. Sound Vib. 87, 429–437.CrossRefGoogle Scholar
Enoksson, P., Stemme, G. & Stemme, E. 1996 Silicon tube structures for a fluid-density sensor. Sens. Actuators A 54, 558–562.CrossRefGoogle Scholar
Fu, Y. & Price, W. G. 1987 Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. J. Sound Vib. 118, 495–513.CrossRefGoogle Scholar
Fukuma, T., Kobayashi, K., Matsushige, K. & Yamada, H. 2005 True atomic resolution in liquid by frequency-modulation atomic force microscopy. Appl. Phys. Lett. 87, 034101.CrossRefGoogle Scholar
Green, C. P. & Sader, J. E. 2005 Small amplitude oscillations of a thin beam immersed in a viscous fluid near a solid surface. Phys. Fluids 17, 073102.CrossRefGoogle Scholar
Landweber, L. 1967 Vibration of a flexible cylinder in a fluid. J. Ship Res. 11, 143–150.Google Scholar
Lavrik, N. V., Sepaniak, M. J. & Datskos, P. G. 2004 Cantilever transducers as a platform for chemical and biological sensors. Rev. Sci. Instrum. 75, 2229–2253.CrossRefGoogle Scholar
Lindholm, U. S., Kana, D. D., Chu, W.-H. & Abramson, H. N. 1965 Elastic vibration characteristics of cantilever plates in water. J. Ship Res. 9, 11–22.CrossRefGoogle Scholar
Naik, T., Longmire, E. K. & Mantell, S. C. 2003 Dynamic response of a cantilever in liquid near a solid wall. Sens. Actuators A 102, 240–254.CrossRefGoogle Scholar
Paul, M. R. & Cross, M. C. 2004 Stochastic dynamics of nanoscale mechanical oscillators immersed in a viscous fluid. Phys. Rev. Lett. 92, 235501.CrossRefGoogle Scholar
Sader, J. E. 1998 Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys. 84, 64–76.CrossRefGoogle Scholar
Sparks, D., Smith, R., Straayer, M., Cripe, J., Schneider, R., Chimbayo, A., Anasari, S. & Najafi, N. 2003 Measurement of density and chemical concentration using microfluidic chip. Lab Chip. 3, 19–21.CrossRefGoogle ScholarPubMed
Timoshenko, S. & Young, D. H. 1968 Elements of Strength of Materials. D. Van Nostrand.Google Scholar
Westberg, D., Paul, O., Anderson, G. & Baltes, H. 1997 A CMOS-compatible fluid density sensor. J. Micromech. Microengng 7, 253–255.CrossRefGoogle Scholar
Yasumura, K. Y., Stowe, T. D., Chow, E. M., Pfafman, T., Kenny, T. W., Stipe, B. C. & Rugar, D. 2000 Quality factors in micron- and submicron-thick cantilevers J. Microelectromech. Syst. 9, 117–125.CrossRefGoogle Scholar