We have studied the phenomenon of squeeze film damping in a liquid with a microfabricated vibrating plate oscillating in its fundamental mode with out-of-plane motion. It is paramount that this phenomenon be understood so that proper choices can be made in terms of sensor design and packaging. The influences of plate-wall distance , effective plate radius , and fluid viscosity and density on squeeze film damping have been studied. We experimentally observe that the drag force is inertia dominated and scales as even when the plate is far away from the wall, a surprising but understandable result for a microfluidic device where the ratio of to the viscous penetration depth is large. We observe as well that the drag force scales as , which is inconsistent with squeeze film damping in the lubrication limit. These two cubic power laws arise due to the role of inertia in the high frequency limit.
Issue Section:
Fundamental Issues and Canonical Flows
Keywords:
damping,
drag,
liquid films,
lubrication,
microfluidics,
microsensors,
plates (structures),
vibrations,
viscosity
1.
Cleveland
, J. P.
, Manne
, S.
, Bocek
, D.
, and Hansma
, P. K.
, 1993, “A Nondestructive Method for Determining the Spring Constant of Plates for Scanning Force Microscopy
,” Rev. Sci. Instrum.
0034-6748, 64
, pp. 403
–405
.2.
Chen
, G. Y.
, Warmack
, R. J.
, Thundat
, T.
, Allison
, D. P.
, and Huang
, A.
, 1994, “Resonance Response of Scanning Force Microscopy Plates
,” Rev. Sci. Instrum.
0034-6748, 65
, pp. 2532
–2537
.3.
Walters
, D. A.
, Cleveland
, J. P.
, Thomson
, N. H.
, Hansma
, P. K.
, Wendman
, M. A.
, Gurley
, G.
, and Elings
, V.
, 1996, “Short Plates for Atomic Force Microscopy
,” Rev. Sci. Instrum.
0034-6748, 67
, pp. 3583
–3590
.4.
Kawakatsu
, H.
, and Saya
, D.
, 2002, “Millions of Plates for Atomic Force Microscopy
,” Rev. Sci. Instrum.
0034-6748, 73
, pp. 1188
–1192
.5.
Bhiladvala
, R. B.
, and Wang
, Z. J.
, 2004, “Effect of Fluids on the Q Factor and Resonant Frequency of Oscillating Micrometer and Nanometer Scale Beams
,” Phys. Rev. E
1063-651X, 69
, p. 036307
.6.
Bergaud
, C.
, and Nicu
, L.
, 2000, “Viscosity Measurements Based on Experimental Investigations of Composite Plate Beam Eigenfrequencies in Viscous Media
,” Rev. Sci. Instrum.
0034-6748, 71
, pp. 2487
–2591
.7.
Oden
, P. I.
, Chen
, G. Y.
, Steele
, R. A.
, Warmack
, R. J.
, and Thundat
, T.
, 1996, “Viscous Drag Measurements Utilizing Microfabricated Plates
,” Appl. Phys. Lett.
0003-6951, 68
, pp. 3814
–3816
.8.
Naik
, T.
, Longmire
, E. K.
, and Mantell
, S. C.
, 2003, “Dynamic Response of a Plate in Liquid Near a Solid Wall
,” Sens. Actuators, A
0924-4247, 102
, pp. 240
–254
.9.
Patois
, R.
, and Vairac
, P.
, 1999, “Measurement of Fluid Properties With a Near-Field Acoustic Sensor
,” Appl. Phys. Lett.
0003-6951, 75
, pp. 295
–297
.10.
Harrison
, C.
, Tavernier
, E.
, Vancauwenberghe
, O.
, Donzier
, E.
, Hsu
, K.
, Goodwin
, A. R. H.
, Marty
, F.
, and Mercier
, B.
, 2007, “On the Response of a Resonating Plate in a Liquid Near a Solid Wall
,” Sens. Actuators, A
0924-4247, 134
, pp. 414
–426
.11.
Clarke
, R. J.
, Cox
, S. M.
, Williams
, P. M.
, and Jensen
, O. E.
, 2005, “The Drag on a Micro-Cantilever Oscillating Near a Wall
,” J. Fluid Mech.
0022-1120, 545
, pp. 397
–426
.12.
Harrison
, C.
, Ryu
, S.
, Goodwin
, A. R. H.
, Hsu
, K.
, Donzier
, E.
, Marty
, F.
, and Mercier
, B.
, 2006, “A MEMS Sensor for the Measurement of Density-Viscosity for Oilfield Applications
,” Proc. SPIE
0277-786X, 6111
, pp. 61110D
.13.
Clarke
, R. J.
, Jensen
, O. E.
, Billingham
, J.
, and Williams
, P. M.
, 2006, “Three-Dimensional Flow Due to a Microplate Oscillating Near a Wall: An Unsteady Body Analysis
,” Proc. R. Soc. London, Ser. A
0950-1207, 462
, pp. 913
–933
.14.
Chu
, J. H.
, and Kim
, M. -U.
, 2004, “Oscillatory Stokes Flow Due to Motions of a Circular Disk Parallel to an Infinite Plane Wall
,” Fluid Dyn. Res.
0169-5983, 34
, pp. 77
–97
.15.
Karniadakis
, G.
, Beskok
, A.
, and Aluru
, N.
, 2005, Microflows and Nanoflows, Fundamentals and Simulation
, Springer
, New York
, Chap. 6.16.
Pelesko
, J. A.
, and Bernstein
, D. H.
, 2002, Modeling NEMS and MEMS
, CRC
, Boca Raton, FL
, pp. 307
–314
.17.
Timoshenko
, S.
, and Young
, D. H.
, 1968, Elements of Strength of Materials
, Van Nostrand
, Princeton
.18.
Landau
, L. D.
, and Lifshitz
, E. M.
, 1959, Fluid Mechanics
, Pergamon
, New York
.19.
Williams
, J. A.
, 2005, Engineering Tribology
, Cambridge University Press
, Cambridge
.20.
Bao
, M. -H.
, 2000, Handbook of Sensors and Actuators: Micro Mechanical Transducers: Pressure Sensors, Accelerometers, and Gyroscopes
, Elsevier
, New York
.21.
Starr
, J. B.
, 1990, “Squeeze-Film Damping in Solid-State Accelerometers
,” IEEE Sol. Stat. Sens.
, 44
, pp. 44
–47
.22.
Szeri
, A. Z.
, 1998, Fluid Film Lubrication
, Cambridge University Press
, New York
.23.
Roters
, A.
, and Johannsmann
, D.
, 1996, “Distance-Dependent Noise Measurements in Scanning Force Microscopy
,” J. Phys.: Condens. Matter
0953-8984, 8
, pp. 7561
.24.
Chen
, G. Y.
, Warmack
, R. J.
, Oden
, P. I.
, and Thundat
, T.
, 1996, “Transient Response of Tapping Scanning Force Microscopy in Liquids
,” J. Vac. Sci. Technol. B
1071-1023, 14
, pp. 1313
–1317
.25.
Gelbert
, M.
, Biesalski
, M.
, Ruhe
, J.
, and Johannsmann
, D.
, 2000, “Collapse of Polyelectrolyte Brushes Probed by Noise Analysis of a Scanning Force Microscope Plate
,” Langmuir
0743-7463, 16
, pp. 5774
–5784
.26.
Ma
, H.
, Jimenez
, J.
, and Rajagopalan
, R.
, 2000, “Brownian Fluctuation Spectroscopy Using Atomic Force Microscopes
,” Langmuir
0743-7463, 16
, pp. 2254
–2261
.27.
Brenner
, H.
, 1961, “The Slow Motion of a Sphere Through a Viscous Fluid Towards a Plane Surface
,” Chem. Eng. Sci.
0009-2509, 16
, pp. 242
–251
.28.
Nnebe
, I.
, and Schneider
, J. W.
, 2004, “Characterization of Distance-Dependent Damping in Tapping-Mode Atomic Force Microscopy Force Measurements in Liquid
,” Langmuir
0743-7463, 20
, pp. 3195
–3201
.29.
Alcaraz
, J.
, Buscemi
, L.
, Puig-de-Morales
, M.
, Colchero
, J.
, Baro
, A.
, and Navajas
, D.
, 2002, “Correction of Microrheological Measurements of Sofá Simples With Atomic Force Microscopy for the Hydrodynamic Drag on the Plate
,” Langmuir
0743-7463, 18
, pp. 716
–721
.30.
Marion
, J. B.
, and Thornton
, S. T.
, 1988, Classical Dynamics
, Harcourt Brace Jovanovich
, San Diego, CA
.31.
Zhang
, W.
, and Stone
, H.
, 1998, “Oscillatory Motions of Circular Disks and Nearly Spherical Particles in Viscous Flows
,” J. Fluid Mech.
0022-1120, 367
, pp. 329
–358
.32.
Pozrikidis
, C.
, 1989, “A Singularity Method for Unsteady Linearized Flow
,” Phys. Fluids A
0899-8213, 1
, pp. 1508
–1520
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