LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Clarke, Richard John (2005)
Languages: English
Types: Unknown
Subjects:

Classified by OpenAIRE into

arxiv: Physics::Fluid Dynamics
With a proven ability to uncover fundamental biological processes, the atomic force microscope (AFM) represents one of the most valuable and versatile tools available to the biophysical sciences. We study the unsteady small-scale flows generated within the AFM by its sensing probe (a long thin cantilever), which have received relatively little attention to date, yet which are increasingly relevant in an age of microdevices. The early parts of this thesis investigate some canonical two-dimensional flows driven by oscillations of an infinite-length rigid cantilever. These prove amenable to analysis and enable us to investigate many of the important physical phenomena and compile a comprehensive collection of asymptotic expressions for the drag. The corresponding results lay out the influence of a nearby wall, geometry and oscillation frequency. The limitations of a two-dimensional approach are then explored through the development of a novel unsteady slender-body theory (USBT) for finite-length cylinders, an asymptotic treatment of which offers corrections to traditional resistive-force-theory (RFT) methods by accounting for geometric factors and flow inertia. These ideas are then extended to the study of thin rectangular plates. Two key parameters are identified which promote two-dimensionality in the flow, namely the frequency of oscillation and the proximity of a nearby boundary. We then examine flexible cylinders and plates by coupling the hydrodynamics to linearized elastic beam and plate equations, which simulate the hydrodynamically-damped high-speed deformable motion of the AFM's cantilever, when driven either externally or by Brownian motion. In the latter case, we adopt an approach which offers notable improvements over the most advanced method currently available to the AFM community.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 2 Flows generated by an infinite-length circular cylinder 37 2.1 Numerical treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2 Asymptotic treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.1 Viscous wall interactions: Δ γ−1 . . . . . . . . . . . . . . . . . 40 2.2.2 Inviscid wall interactions: Δ γ−1 . . . . . . . . . . . . . . . . . 43 2.2.3 Viscous/inertial wall interactions: Δγ = O(1) . . . . . . . . . . . 46 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3.1 Streamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3.2 Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3 Flows generated by a finite-length circular cylinder 57 3.1 Numerical treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Asymptotic treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.1 Screening of three-dimensional effects . . . . . . . . . . . . . . . 65 3.3.2 Modified resistive-force-theory . . . . . . . . . . . . . . . . . . . 68 3.3.3 Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.4 Tilt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
    • A Effects of slip 171 A.1 Two-dimensional circular cantilever . . . . . . . . . . . . . . . . . . . . . 171 A.2 Rectangular cantilever in the lubrication limit . . . . . . . . . . . . . . . 172
    • C Unsteady two-dimensional image Stokeslets 177 C.1 Leading-order flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 C.2 Quasi-steady limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 R. K. Agarwal, K. Y. Yun, and R. Balakrishnan. Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition region. Phys. Fluids, 13:3061-3085, 2001.
    • T. R. Albrecht, S. Akamine, T. E. Carver, and C. F. Quate. Microfabrication of cantilever styli for the atomic force microscope. J. Vac. Sci. Technol. A, 8:3386-3396, 1990.
    • J. Alcaraz, L. Buscemi, M. Puig-de Morales, J. Colchero, A. Baro, and D. Navajas. Correction of microrheological measurements of soft samples with atomic force microscopy for the hydrodynamic drag on the cantilever. Langmuir, 18:716-721, 2002.
    • A. Avudainayagam and J. Geetha. Oscillatory line singularities of Stokes' flows. Int. J. Engng Sci., 31:1295-1299, 1993.
    • A. Avudainayagam and J. Geetha. Unsteady singularities of Stokes' flows in two dimensions. Int. J. Engng. Sci., 33:1713-1724, 1995.
    • A. Avudainayagam and J. Geetha. A boundary-integral equation for two-dimensional oscillatory Stokes flow past an arbitrary body. J. Eng. Math., 33:251-258, 1998.
    • A. J. Bard, F. R. F. Fan, and D. T. Pierce. Chemical imaging of surfaces with the scanning electron microscope. Science, 254:68-74, 1991.
    • J. L. Barrat and L. Bocquet. Large slip effect at a nonwetting fluid-solid interface. Phys. Rev. Lett., 82:4671-4674, 1999.
    • A. B. Basset. A Treatise on Hydrodynamics, vol. 2. Cambridge: Deighton Bell, 1888.
    • G. K. Batchelor. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech., 44:419-440, 1970.
    • J. Baudry, E. Charlaix, A. Tonck, and D. Mazuyer. Experimental evidence for a large slip effect at a nonwetting fluid-solid interface. Langmuir, 17:5232-5236, 2001.
    • G. Binnig, C. F. Quate, and C. Gerber. Atomic force microscope. Phys. Rev. Lett., 56: 930-933, 1986.
    • G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel. Tunneling through a controllable vacuum gap. Appl. Phys. Lett., 40:178-180, 1982.
    • J. R. Blake. A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc., 70:303-310, 1971.
    • J. R. Blake. A model for the micro-structure in ciliated organisms. J. Fluid Mech., 55: 1-23, 1972.
    • J. R. Blake. Singularities of viscous flow. Part II: Applications to slender body theory. J. Eng. Math., 8:113-124, 1974.
    • J. R. Blake. On the generation of viscous toroidal eddies in a cylinder. J. Fluid Mech., 95:209-222, 1979.
    • J. R. Blake. Mechanics of muco-ciliary transport. IMA J. Appl. Math., 32:69-87, 1984.
    • J. R. Blake and A. T. Chwang. Fundamental singularities of viscous flow. Part I: The image systems in the vicinity of a stationary no-slip boundary. J. Eng. Math., 8:23- 29, 1974.
    • L Bocquet and J. L. Barrat. Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids. Phys. Rev. E, 49:3079-3092, 1994.
    • E. Bonaccurso, S. Butt, and V. S. J. Craig. Surface roughness and hydrodynamic boundary slip of a Newtonian fluid in a completely wetting system. Phys. Rev. Lett., 90: 144501, 2003.
    • E. Bonaccurso, M. Kappl, and H. S. Butt. Hydrodynamic force measurements: Boundary slip of water on hydrophilic surfaces and electrokinetic effects. Phys. Rev. Lett., 88: 076103, 2002.
    • C. Brennen and H. Winet. Fluid mechanics of propulsion by cilia and flagella. Ann. Rev. Fluid Mech., 9:339-398, 1977.
    • H. Brenner. The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Eng. Sci, 16:242-251, 1961.
    • H. Brenner. Effect of finite boundaries on the Stokes resistance of an arbitrary particle. J. Fluid Mech., 12:35-48, 1962.
    • H. Brenner. The Stokes resistance of an arbitrary particle: IV. arbitrary fields of flow. Chem. Eng. Sci., 19:703, 1964.
    • M. M. Britton and P. T. Callaghan. Two-phase shear band structures at uniform stress. Phys. Rev. Lett., 78:4930-4933, 1997.
    • M. Broday. Motion of nanobeads proximate to plasma membranes during single particle tracking. B. Math. Biol., 64:531-563, 2002.
    • C.J. Brokaw. Non-sinusoidal bending waves of sperm flagella. J. Exp. Biol., 43:155-169, 1965.
    • N. A. Burnham, D. D. Dominguez, R. L. Mowery, and R. J. Colton. Probing the surface forces of monolayer films with an atomic-force microscope. Phys. Rev. Lett., 64:1931- 1934, 1990.
    • C. Bustamante, J. Vesenka, C. L. Tang, W. Rees, M. Guthod, and R. Keller. Circular DNA imaged in air by scanning force microscopy. Biochemistry, 31:22-26, 1992.
    • H.-J. Butt and M. Jaschke. Calculation of thermal noise in atomic force microscopy. Nanotechnology, 6:1995, 1995.
    • H.-J. Butt, P. Siedle, K. Seifert, K. Fendler, T. Seeger, E. Bamberg, A. L. Weisenhorn, K. Goldie, and A. Engel. Scan speed limit in atomic force microscopy. J. Microsc., 169:75-84, 1993.
    • P. W. Carpenter. The hydrodynamic stability of flow of Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech., 170:199-232, 1986.
    • P. W. Carpenter and A. D. Garrad. The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien-Schlichting instabilities. J. Fluid Mech., 155: 465-510, 1985.
    • E. Chadwick. A slender-body theory in Oseen flow. Proc. Roy. Soc. London A, 458: 2007-2016, 2002.
    • D. Chandler. Introduction to modern statistical physics. Oxford University Press, 1987.
    • G. Y. Chen, R. J. Warmack, T. Thundat, and D. P. Allison. Resonance response of scanning force microscopy cantilevers. Rev. Sci. Instrum., 65:2532-2537, 1994.
    • J. H. J. Cho, B. M. Law, and F. Rieutord. Dipole-dependent slip of Newtonian fluids at smooth solid hydrophobic surfaces. Phys. Rev. Lett., 92:166102, 2004.
    • C. H. Choi, K. Johan, A. Westin, and K. S. Breuer. Apparent slip flows in hydrophilic and hydrophobic microchannels. Phys. Fluids, 15:2897-2902, 2003.
    • J. W. M. Chon, , P. Mulvaney, and J. E. Sader. Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids. J. Appl. Phys., 87:3978-3988, 2000.
    • J. Chu and M-U. Kim. Two-dimensional oscillatory Stokes flows between two parallel planes. Fluid Dyn. Res., 29:7-24, 2001.
    • J. Chu and M-U. Kim. Two-dimensional oscillatory Stokes flow in the region with a semi-infinite plate parallel to an infinite plane wall. Fluid Dyn. Res., 31:229-251, 2002.
    • J. Chu and M-U. Kim. Oscillatory Stokes flow due to motions of a circular disk parallel to an infinite plane wall. Fluid Dyn. Res., 34:77-97, 2004.
    • A. T. Chwang and T. Yao-Tsu Wu. Hydromechanics of low-Reynolds number flow. Part 1. Rotation of axisymmetric prolate bodies. J. Fluid Mech., 63:607-622, 1974.
    • A.T. Chwang and T.Y. Wu. A note on the helical movement of micro-organisms. Proc. Roy. Soc. B, 178:327-346, 1971.
    • R. J. Clarke, S. M. Cox, P. M. Williams, and O. E. Jensen. The drag on a microcantilever oscillating near a wall. J. Fluid Mech. (to appear), 2005a.
    • R. J. Clarke, O. E. Jensen, J. Billingham, and P. M. Williams. Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis. Proc. Roy. Soc. London A (submitted), 2005b.
    • J.P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma. A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy. Rev. Sci. Instrum., 64:403-405, 1993.
    • C. Cottin-Bizonne, C. Barentin, E. Charlaix, L. Boequet, and J. L. Barrat. Dynamics of simple liquids at heterogeneous surfaces: Molecular dynamics simulations and hydrodynamic description. Eur. Phys. J. E., 15:427-438, 2004.
    • C. Cottin-Bizonne, J. L. Barrat, L Bocquet, and E. Charlaix. Low-friction flows of liquid at nanopatterned interfaces. Nature Mat., 2:237-240, 2003.
    • C. Cottin-Bizonne, B. Cross, A. Steinberger, and E. Charlaix. Boundary slip on smooth hydrophobic surfaces: intrinsic effects and possible artifacts. Phys. Rev. Lett., 94: 056102, 2005.
    • R. G. Cox. The motion of long slender bodies in a viscous fluid. Part I: General theory. J. Fluid Mech., 44:791-810, 1970.
    • R. G. Cox. The motion of long slender bodies in a viscous fluid. Part 2: Shear flow. J. Fluid Mech., 45:625-657, 1971.
    • V. Craig and C. Neto. In situ calibration of colloid probe cantilevers in force microscopy: hydrodynamic drag on a sphere approaching a wall. Langmuir, 17:6018-6022, 2001.
    • V. S. J. Craig, C. Neto, and D. R. M. Williams. Shear-dependent boundary slip in aqueous Newtonian liquid. Phys. Rev. Lett., 87:054504, 2001.
    • D. M. Czajkowsky, M. J. Allen, V. Elings, and Z. F. Shao. Direct visualization of surfacecharge in aqueous-solution. Ultramicroscopy, 74:1-5, 1998.
    • A. M. J. Davis. A hydrodynamic model of the oscillating screen viscometer. Phys. Fluids A, 5:2095-2103, 1993a.
    • A. M. J. Davis. Some asymmetric Stokes flows that are structurally similar. Phys. Fluids A, 5:2086-2094, 1993b.
    • N. J. De Mestre. Low-Reynolds-number fall of slender cylinders near boundaries. J. Fluid Mech., 58:641-656, 1973.
    • N. J. De Mestre and W. B. Russel. Low-Reynolds-number translation of a slender cylinder near a plane wall. J. Eng. Math., 9:81-91, 1975.
    • W. R. Dean and P. E. Montagnon. On the steady motion of viscous liquid in a corner. Proc. Camb. Phil. Soc., pages 389-394, 1949.
    • J. Ding and Y. Wenjiig. A fast integral approach for drag force calculations due to oscillatory slip Stokes flow. Int. J. Numer. Meth. Eng., 60:1535-1567, 2004.
    • J. M. Dorrepaal, M. E. O'Neill, and K. B. Ranger. Two-dimensional Stokes flow with cylinders and line singularities. Mathematika, 31:65-75, 1984.
    • U. Durig, F. Pohl, and F. Rohrer. Near field optical scanning microscopy. J. Appl. Phys., 59:3318-3327, 1986.
    • L. Durlofsky and J. F. Brady. Analysis of the Brinkman equations as a model for flow in porous media. Phys. Fluids, 30:3329-3341, 1987.
    • F. Elmer and M. Dreier. Eigenfrequencies of a rectanguler atomic force microscope cantilever in a medium. J. Appl. Phys., 81:7709-7714, 1997.
    • E. Evans. Probing the relation between force-lifetime-and chemistry in single molecular bonds. Annu. Rev. Biophys. Biomol. Struct., 30:105-128, 2001.
    • M. Faraday. On a peculiar class of acoustical figures, and on certain forms assumed by groups of particles on vibrating elastic surfaces. Trans. Roy. Soc. (London), 121: 229-340, 1831.
    • O. H. Faxen. Die Bewung einer starren Kugel L¨angs der Achse eines mit z¨aher Flu¨ssigkeit gefu¨llten Rohres. Arkiv. Mat. Astr. Fys., 17:27, 1923.
    • O. H. Faxen. Der Widerstand gegen die Bewegung einer starren Kugel in einer z¨ahen Flu¨ssigkeit, die zwischen zwei parallelen, ebenen W¨anden eingeschlossen ist. Ark. Mat. Astr. Fys., 18:29, 1924.
    • J. Feng, P. Ganatos, and S. Weinbaum. The general motion of a circular disk in a Brinkman medium. Phys. Fluids, 10:2137-2146, 1998a.
    • J. Feng, P. Ganatos, and S. Weinbaum. Motion of a sphere near planar confining boundaries in a Brinkman medium. J. Fluid Mech., 375:265-296, 1998b.
    • J. Feng and D. D. Joseph. The unsteady motion of solid bodies in creeping flows. J. Fluid Mech., 303, 1995.
    • F. Feuillebois and A. Lasek. On the rotational historic term in non-stationary Stokes flow. Q. Jl. Mech. Appl. Math., 31:435-443, 1977.
    • M. D. Finn and S. M. Cox. Stokes flow in a mixer with changing geometry. J. Eng. Math., 41:75-99, 2001.
    • E.-L. Florin, V. T. Moy, and H. E. Gaub. Adhesion forces between individual ligandreceptor pairs. Science, 264:415-417, 1994.
    • J. Foss, C. Tropea, and A. Yarin. Handbook of experimental fluid dynamics. Springer, New-York, 2005.
    • C. D. Frisbie, L. F. Rozsnyai, A. Noy, M. S. Wrighton, and C. M. Lieber. Functional-group imaging by chemical force microscopy. Science, 265:2071-2074, 1994.
    • P. D. Frymier, R. M. Ford, and H. C. Berg. 3-dimensional tracking of motile bacteria near a solid planar surface. P. Natl. Acad. Sci. USA, 92:6195-6199, 1995.
    • M Gad-El-Hak. Flow physics in MEMS. Mec. Ind., 2:313-341, 2001.
    • M.A. Gallis and J.R. Torczynski. An improved reynolds-equation model for gas damping of microbeam motion. J. Microelectromech. Sys., 13:653-659, 2004.
    • E. Gavze. The accelerated motion of rigid bodies in non-steady Stokes flow. Int. J. Multiphase Flow, 16:153-166, 1990.
    • J. Geer. Stokes flow past a slender body of revolution. J. Fluid Mech., 78:577-600, 1976.
    • A. J. Gil, J. Colchero, M. Luna, J. Gomez-Herrero, and A. M. Baro. Adsorption of water on solid surfaces studied by scanning force microscopy. Langmuir, 16:5086-5092, 2000.
    • M. Grandbois, W. Dettmann, M. Benoit, and H. E. Gaub. Affinity imaging of red blood cells using an atomic force microscope. J. Histochem. Cytochem., 48:719-724, 2000.
    • S. Granick, X. Y. Zhu, and H. Lee. Slippery questions about complex fluids flowing past solids. Nature Mat., 2:221-227, 2003.
    • J Gray and G.J. Hancock. The propulsion of sea-urchin spermatozoa. Proc. Roy. Soc., 32:96-121, 1955.
    • C. P. Green and J. E. Sader. Torsional frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys., 92: 6262-6274, 2002.
    • C. P. Green and J. E. Sader. Small amplitude oscillations of a thin beam immersed in a viscous fluid near a solid surface. Phys. Fluids, 17:073102, 2005.
    • N. H. Green, S. Allen, M. C. Davies, C. J. Roberts, S. J. B. Tendler, and P. M. Williams. Force sensing and mapping by atomic force microscopy. Trends in Analytical Chemistry, 21:64-72, 2002.
    • W. W. Hackborn. Asymmetric Stokes' flow between parallel planes due to a rotlet. J. Fluid Mech., 218:531-546, 1980.
    • P. Hall and D. T. Papegeorgiou. The onset of chaos in a class of Navier-Stokes solutions. J. Fluid Mech., 393:59-87, 1999.
    • P. Hallet, G. Offer, and M. J. Miles. Atomic force microscopy of the myosin molecule. Biophys. J., 68:1604-1606, 1995.
    • G. J. Hancock. The self propulsion of microscopic organisms through liquids. Proc. Roy. Soc., A214:96-121, 1953.
    • P. K. Hansma, J. P. Cleveland, M. Radmacher, D. A. Walters, P. E. Hillner, M. Benzanilla, M. Fritz, D. Vie, H. G. Hansma, C. B. Prater, J. Massie, L. Fukunaga, J. Gurley, and V. Elings. Tapping mode atomic-force microscopy in liquids. Appl. Phys. Lett., 64: 1738-1740, 1994.
    • P. K. Hansma, B. Drake, O. Marti, S. A. Gould, and C. B. Prater. The scanning ionconductance microscope. Science, 243:641-643, 1989.
    • H. Hasimoto and O. Sano. Stokeslets and eddies in creeping flow. Ann. Rev. Fluid Mech., 12:335-363, 1980.
    • E. H. Hauge and Martin-Lo¨f. Fluctuating-hydrodynamics and Brownian motion. J. Stat. Phys., 7:259-281, 1973.
    • C. L. Henry, C. Neto, D. R. Evans, S. Biggs, and V. S. J. Craig. The effect of surfactant adsorption on liquid boundary slippage. Physica A, 339:60-65, 2004.
    • J. B. Heymann, D. J. Mu¨ller, K. Mitsuoka, and A. Engel. Electron and atomic force microscopy of membrane proteins. Curr. Opin. Struct. Biol., 7:543-549, 1997.
    • J. J. L. Higdon. The generation of feeding currents by flagellar motions. J. Fluid Mech., 94:305-330, 1979a.
    • J. J. L. Higdon. A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech., 90: 685-711, 1979b.
    • J. J. L. Higdon. The hydrodynamics of flagellar propulsion: helical waves. J. Fluid Mech., 94:331-351, 1979c.
    • E. J. Hinch. Application of the Langevin equation to fluid suspensions. J. Fluid Mech., 72:499-511, 1975.
    • R. Hocquart. Regime instante d'un liquide dens lequel un ellipsoide de revolution tourne outour de don axe. C. R. Acad. Sci. Paris, 283A:1119-1122, 1976.
    • R. Hocquart and E. J. Hinch. The long-time tail of the angular velocity autocorrelation function for a rigid-Bronwian particle of arbitrary centrally symmetric shape. J. Fluid Mech., 137:217-220, 1983.
    • C. Huh and L. E. Scriven. Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Int. Sci., 35:85-101, 1971.
    • S. W. Hui, R. Viswanathan, J. A. Zasadzinski, and J. N. Israelachvili. The structure and stability of phospholipid bilayers by atomic force microscopy. Biophys. J., 68: 171-178, 1995.
    • J.L. Hutter and J. Bechhoefer. Calibration of atomic-force microscope tips. Rev. Sci. Instrum., 64:1868-1873, 1993.
    • N. Ishida, T. Inoue, M. Miyahara, and K. Higashitani. Nanobubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy. Langmuir, 16: 6377-6380, 2000.
    • J. N. Israelachvili. Measurement of the viscosity of liquids in very thin films. J. Colloid Interf. Sci., 110:263-271, 1986a.
    • J. N. Israelachvili. Measurement of the viscosity of liquids in very thin films. J. Colloid Int. Sci., 110:263-271, 1986b.
    • H. Janovjak, J. Struckmeier, and D. J. Mu¨ller. Hydrodynamic effects in fast AFM singlemolecule force measurements. Eur. Biophys. J. Biophys. Lett., pages 1-12, 2004.
    • G. B. Jeffery. Plane stress and plane strain in bipolar cooordinates. Phil. Trans. Roy. Soc, 221:265-293, 1921.
    • D. J. Jeffrey and Y. Onishi. The slow motion of a cylinder next to a plane wall. Q. J. Mech. Appl. Math., 34:129-137, 1981.
    • R. E. Johnson. An improved slender body theory for Stokes flow. J. Fluid Mech., 99: 411-431, 1980.
    • P. Joseph and P. Tabeling. Direct measurement of the apparent slip length. Phys. Rev. E, 71:035303, 2005.
    • R. P. Kanwal. Rotatory and longitudinal oscillations of axi-symmetric bodies in a viscous fluid. Q. Jl. Mech. Appl. Math., 8:146, 1955a.
    • R. P. Kanwal. Vibrations of elliptic cylinders and a flat plate in a viscous fluids. Z. Angew. Math. Mech., 35:17-22, 1955b.
    • R. P. Kanwal. Drag on an axially symmetric body vibrating slowly along its axis in a viscous fluid. J. Fluid Mech., 19:631, 1964.
    • R. P. Kanwal. Note on slow rotation or rotary oscillation of axisymmetric bodies in hydrodynamics and magnetohydrodynamics. J. Fluid Mech., 41:721-726, 1970.
    • M-U. Kim, K. W. Kim, Y.-H. Cho, and B. M. Kwak. Hydrodynamic force on a plate near the plane wall. Part I: plate in sliding motion. Fluid Dyn. Res., 29:137-170, 2001a.
    • M-U. Kim, K. W. Kim, Y.-H. Cho, and B. M. Kwak. Hydrodynamic force on a plate near the plane wall. Part II: plate in squeezing motion. Fluid Dyn. Res., 29:171-198, 2001b.
    • S. Kim and W. B. Russel. The hydrodynamic interations between two spheres in a Brinkman medium. J. Fluid Mech., 154:253-268, 1985.
    • S. Kirstein, M. Mertesdorf, and M. Schonhoff. The influence of a viscous fluid on the vibration dynamics of scanning near-field optical microscopy fiber probes and atomic force microscopy cantilevers. J. Appl. Phys., 1998.
    • J. Koplik, J. R. Banavar, and J. F. Willemsen. Molecular dynamics of fluid flow at solidsurfaces. Phys. Fluids, 1:781-794, 1989.
    • N. Liron and S. Mochon. Stokes flow for a Stokeslet between parallel flat plates. J. Eng. Math., 10:287-303, 1976.
    • M. Loewenberg. The unsteady Stokes resistance of arbitrarily oriented, finite-length cylinders. Phys. Fluids, 5:3004-3006, 1993.
    • M. Loewenberg. Asymmetric, oscillatory motion of a finite-length cylinder: The macroscopic effect of particle edges. Phys. Fluids, 6:1095-1107, 1994a.
    • M. Loewenberg. Axisymmetric unsteady Stokes flow past an oscillating finite-length cylinder. J. Fluid Mech., 265:265-288, 1994b.
    • Y. Magariyama, M. Ichibu, K. Nakata, K. Baba, T. Ohtani, S. Kudo, and T. Goto. Difference in bacterial motion between forward and backward swimming caused by the wall effect. Biophys. J., 88:3648-3658, 2005.
    • L. T. Mazzola, C. W. Frank, S. P. A. Fodor, C. Mosher, R. Lartius, and E. Henderson. Discrimination of DNA hydridization using chemical force microscopy. Biophys. J., 76:2922-2933, 1999.
    • C. Neto, V. S. J. Craig, and D. R. M. Williams. Evidence of shear-dependent boundary slip in Newtonian liquids. Eur. Phys. J., 12:S71-S74, 2003.
    • R. Pit, H. Hervert, and L. Leger. Direct experimental evidence of slip in hexadecane: solid interfaces. Phys. Rev. Lett., 85:980-983, 2000.
    • C. Pozrikidis. A singularity method for unsteady linearized flow. Phys. Fluids, 9:1508- 1520, 1989a.
    • C. Pozrikidis. A study of linearized oscillatory flow past particles by the boundaryintegral method. J. Fluid Mech., 202:17-41, 1989b.
    • N. Riley. Steady streaming. Ann. Rev. Fluid Mech., 33:43-65, 2001.
    • A. Roters and D. Johannsmann. Distance-dependent noise measurements in scanning force microscopy. J. Phys. Condens. Matter, 8:7561-7577, 1996.
    • S. Roy, R. Raju, H. F. Chuang, B. A. Cruden, and M. Meyyappan. Modeling gas flow through microchannels and nanopores. J. Appl. Phy., 93:4870-4879, 2003.
    • W. B. Russel, E. J. Hinch, L. G. Leal, and G. Tieffenbruck. Rods falling near a vertical wall. J. Fluid Mech., 83:273-287, 1977.
    • J. E. Sader. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys., 84:64-76, 1998.
    • J. E. Sader. Calibration of rectangular atomic force microscope cantilevers. Rev. Sci. Instrum., 70:3967-3969, 1999.
    • J. E. Sader. Susceptibility of atomic force microscope cantilevers to lateral forces. Rev. Sci. Instrum., 74:2438-2443, 2003.
    • H. Schlichting. Berechnung ebener periodischer Grenzschichtstromungen. Phys. Z, 33: 327-335, 1932.
    • W. R. Schowalter. The behaviour of complex fluids at solid boundaries. J. NonNewtonian Fluid Mech., 29:25-36, 1988.
    • J. T. Stuart, R. C. DiPrima, P. M. Eagles, and A. Davey. On the instability of the flow in a squeeze lubrication film. Proc. Roy. Soc. Lond. A, 430:347-375, 1990.
    • E. O. Tuck. Calculation of unsteady flow due to small motions of cylinders in a viscous fluid. J. Eng. Math., 3:29-44, 1969.
    • M. Van Dyke. Album of fluid motion. Parabolic Press, 1982.
    • M. P. L. Werts, E. W. van der Vegte, and G. Hadziioannou. Surface chemical reactions probed with scanning force microscopy. Langmuir, 13:4939-4942, 1997.
    • C. H. Wiggins, D. Riveline, and R. E. Goldstein. Trapping and wiggling: elastohydrodynamics of driven microfilaments. Biophys. J., 74:1043-1060, 1998.
    • W. E. Williams. Boundary effects in Stokes flow. J. Fluid Mech., 24:285, 1966a.
    • W. E. Williams. A note on slow vibrations in a viscous fluid. J. Fluid Mech., 25:589-590, 1966b.
    • R. G. Winkler, J. P. Spatz, S. Sheiko, M. Moller, P. Reineker, and O. Marti. Imaging material properties by resonant tapping-force microscopy: a model investigation. Phys. Rev. B., 54:8908-8912, 1996.
    • C. W. Wolgemuth, T. R. Powers, and R. E. Goldstein. Twirling and whirling: viscous dynamics of rotating elastic filaments. Phys. Rev. Lett., 84:1623-1626, 2000.
    • D. L. Worcester, R. G. Miller, and P. J. Bryant. Atomic force microscopy of purple membranes. J. Micros., 152:817-821, 1988.
    • G. K Youngren and A. Acrivos. Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech., 69, 1975.
    • Y. Zhu and S. Granick. Rate-dependent slip of newtonian liquid at smooth surfaces. Phys. Rev. Lett., 87:096105, 2001.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article