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Research Papers: Contact Mechanics

A Model of Capillary-Driven Flow Between Contacting Rough Surfaces

[+] Author and Article Information
Amir Rostami

G. W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: amir.rostami@gatech.edu

Jeffrey L. Streator

G. W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: jeffrey.streator@me.gatech.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received December 31, 2015; final manuscript received June 15, 2016; published online October 10, 2016. Assoc. Editor: Sinan Muftu.

J. Tribol 139(3), 031401 (Oct 10, 2016) (12 pages) Paper No: TRIB-15-1465; doi: 10.1115/1.4034211 History: Received December 31, 2015; Revised June 15, 2016

A liquid film can flow between two solid surfaces in close proximity due to capillary effects. Such flow occurs in natural processes such as the wetting of soils, drainage through rocks, water rise in plants and trees, as well as in engineering applications such as liquid flow in nanofluidic systems and the development of liquid bridges within small-scale devices. In this work, a numerical model is formulated to describe the radial capillary-driven flow between two contacting, elastic, annular rough surfaces. A mixed lubrication equation with capillary-pressure boundary conditions is solved for the pressure within the liquid film and both macro- and micro-contact models are employed to account for solid–solid contact pressures and interfacial deformation. Measurements of interfacial spreading rate are performed for liquids of varying viscosity flowing between an optical flat and a metallic counter surface. Good agreement is found between modeling and experiment. A semi-analytical relation is developed for the capillary flow between the two contacting surfaces.

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References

Tyree, M. T. , 2003, “ Plant Hydraulics: The Ascent of Water,” Nature, 423(6943), p. 923. [CrossRef] [PubMed]
Fredlund, D. G. , and Rahardjo, H. , 1993, Soil Mechanics for Unsaturated Soils, Wiley, New York.
Maboudian, R. , and Howe, R. T. , 1997, “ Critical Review: Adhesion in Surface Micromechanical Structures,” J. Vac. Sci. Technol. B, 15(1), pp. 1–20. [CrossRef]
Maboudian, R. , 1998, “ Surface Processes in MEMS Technology,” Surf. Sci. Rep., 30(6), pp. 207–269. [CrossRef]
Komvopoulos, K. , 2003, “ Adhesion and Friction Forces in Microelectromechanical Systems: Mechanisms, Measurement, Surface Modification Techniques, and Adhesion Theory,” J. Adhes. Sci. Technol., 17(4), pp. 477–517. [CrossRef]
van Spengen, W. M. , 2003, “ MEMS Reliability From a Failure Mechanisms Perspective,” Microelectron. Reliab., 43(7), pp. 1049–1060. [CrossRef]
Raccurt, O. , Tardif, F. , d'Avitaya, F. A. , and Vareine, T. , 2004, “ Influence of Liquid Surface Tension on Stiction of SOI MEMS,” J. Micromech. Microeng., 14(7), pp. 1083–1090. [CrossRef]
Koppaka, S. B. , and Phinney, L. M. , 2005, “ Release Processing Effects on Laser Repair of Stiction-Failed Microcantilevers,” J. Microelectromech. Syst., 14(2), pp. 410–418. [CrossRef]
Wu, D. , Fang, N. , Sun, C. , and Zhang, X. , 2006, “ Stiction Problems in Releasing of 3D Microstructures and Its Solution,” Sens. Actuators A, 128(1), pp. 109–115. [CrossRef]
Maboudian, R. , and Carraro, C. , 2004, “ Surface Chemistry and Tribology of MEMS,” Annu. Rev. Phys. Chem., 55(1), pp. 35–54. [CrossRef] [PubMed]
Zhu, L. , Xu, J. , Zhang, Z. , Hess, D. W. , and Wong, C. , 2005, “ Lotus Effect Surface for Prevention of Microelectromechanical System (MEMS) Stiction,” Electronic Components and Technology Conference, pp. 1798–1801.
Zhu, L. , Xu, J. , Zhang, Z. , Hess, D. W. , and Wong, C. , 2006, “ Optimizing Geometrical Design of Superhydrophobic Surfaces for Prevention of Microelectromechanical System (MEMS) Stiction,” Electronic Components and Technology Conference, pp. 1–7.
Hariri, A. , Zu, J. , and Ben Mrad, R. , 2007, “ Modeling of Wet Stiction in Microelectromechanical Systems (MEMS),” J. Microelectromech. Syst., 16(5), pp. 1276–1285. [CrossRef]
Sammoura, F. , Hancer, M. , and Yang, K. , 2011, “ The Effect of Surface Chemistry on MEMS Stiction in an Ultralow-Humidity Environment,” J. Microelectromech. Syst., 20(2), pp. 522–526. [CrossRef]
Liu, C. , Chou, B. C. , Tsai, R. C. F. , Shen, N. Y. , Chen, B. S. , Cheng, E. C. , Tuan, H. C. , Kalnitsky, A. , Cheng, S. , and Lin, C. H. , 2011, “ MEMS Technology Development and Manufacturing in a CMOS Foundry,” 16th International Solid-State Sensors, Actuators and Microsystems Conference (TRANSDUCERS), pp. 807–810.
Tas, N. R. , Mela, P. , Kramer, T. , Berenschot, J. , and van den Berg, A. , 2003, “ Capillarity Induced Negative Pressure of Water Plugs in Nanochannels,” Nano Lett., 3(11), pp. 1537–1540. [CrossRef]
Mukhopadhyay, S. , Roy, S. S. , D'Sa, R. A. , Mathur, A. , Holmes, R. J. , and McLaughlin, J. A. , 2011, “ Nanoscale Surface Modifications to Control Capillary Flow Characteristics in PMMA Microfluidic Devices,” Nanoscale Res. Lett., 6(1), pp. 1–12. [CrossRef]
Aristoff, J. M. , Duprat, C. , and Stone, H. A. , “ Elastocapillary Imbibition,” Int. J. Non-Linear Mech., 46(4), pp. 648–656. [CrossRef]
Washburn, E. W. , 1921, “ The Dynamics of Capillary Flow,” Phys. Rev., 17(3), pp. 273–283. [CrossRef]
Fisher, L. R. , and Lark, P. D. , 1979, “ An Experimental Study of the Washburn Equation for Liquid Flow in Very Fine Capillaries,” J. Colloid Interface Sci., 69(3), pp. 486–492. [CrossRef]
Van Honschoten, J. , Escalante, M. , Tas, N. , Jansen, H. , and Elwenspoek, M. , 2007, “ Elastocapillary Filling of Deformable Nanochannels,” J. Appl. Phys., 101(9), p. 094310. [CrossRef]
Van Honschoten, J. , Escalante, M. , Tas, N. , and Elwenspoek, M. , 2009, “ Formation of Liquid Menisci in Flexible Nanochannels,” J. Colloid Interface Sci., 329(1), pp. 133–139. [CrossRef] [PubMed]
Dimitrov, D. , Milchev, A. , and Binder, K. , 2007, “ Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas–Washburn Equation,” Phys. Rev. Lett., 99(5), p. 054501. [CrossRef] [PubMed]
Bhushan, B. , and Dugger, M. , 1990, “ Liquid-Mediated Adhesion at the Thin Film Magnetic Disk/Slider Interface,” ASME J. Tribol., 112(2), pp. 217–223. [CrossRef]
Grobelny, J. , Pradeep, N. , Kim, D. I. , and Ying, Z. C. , 2006, “ Quantification of the Meniscus Effect in Adhesion Force Measurements,” Appl. Phys. Lett., 88(9), p. 091906. [CrossRef]
Yang, S. H. , Nosonovsky, M. , Zhang, H. , and Chung, K. H. , 2008, “ Nanoscale Water Capillary Bridges Under Deeply Negative Pressure,” Chem. Phys. Lett., 451(1), pp. 88–92. [CrossRef]
Yang, S. , Zhang, H. , Nosonovsky, M. , and Chung, K. H. , 2008, “ Effects of Contact Geometry on Pull-Off Force Measurements With a Colloidal Probe,” Langmuir, 24(3), pp. 743–748. [CrossRef] [PubMed]
Nosonovsky, M. , and Bhushan, B. , 2008, “ Capillary Effects and Instabilities in Nanocontacts,” Ultramicroscopy, 108(10), pp. 1181–1185. [CrossRef] [PubMed]
Rabinovich, Y. I. , Esayanur, M. S. , Johanson, K. D. , Adler, J. J. , and Moudgil, B. M. , 2002, “ Measurement of Oil-Mediated Particle Adhesion to a Silica Substrate by Atomic Force Microscopy,” J. Adhes. Sci. Technol., 16(7), pp. 887–903. [CrossRef]
Rabinovich, Y. I. , Adler, J. J. , Esayanur, M. S. , Ata, A. , Singh, R. K. , and Moudgil, B. M. , 2002, “ Capillary Forces Between Surfaces With Nanoscale Roughness,” Adv. Colloid Interface Sci., 96(1), pp. 213–230. [CrossRef] [PubMed]
Rabinovich, Y. I. , Esayanur, M. S. , and Moudgil, B. M. , 2005, “ Capillary Forces Between Two Spheres With a Fixed Volume Liquid Bridge: Theory and Experiment,” Langmuir, 21(24), pp. 10992–10997. [CrossRef] [PubMed]
Tian, H. , and Matsudaira, T. , 1993, “ The Role of Relative Humidity, Surface Roughness and Liquid Build-Up on Static Friction Behavior of the Head/Disk Interface,” ASME J. Tribol., 115(1), pp. 28–35. [CrossRef]
Erle, M. A. , Dyson, D. , and Morrow, N. R. , 1971, “ Liquid Bridges Between Cylinders, in a Torus, and Between Spheres,” AIChE J0, 17(1), pp. 115–121. [CrossRef]
Zheng, J. , and Streator, J. L. , 2003, “ A Micro-Scale Liquid Bridge Between Two Elastic Spheres: Deformation and Stability,” Tribol. Lett., 15(4), pp. 453–464. [CrossRef]
Zheng, J. , and Streator, J. L. , 2004, “ A Liquid Bridge Between Two Elastic Half-Spaces: A Theoretical Study of Interface Instability,” Tribol. Lett., 16(1–2), pp. 1–9. [CrossRef]
Megias-Alguacil, D. , and Gauckler, L. J. , 2009, “ Capillary Forces Between Two Solid Spheres Linked by a Concave Liquid Bridge: Regions of Existence and Forces Mapping,” AIChE J., 55(5), pp. 1103–1109. [CrossRef]
Matthewson, M. , 1988, “ Adhesion of Spheres by Thin Liquid Films,” Philos. Mag. A, 57(2), pp. 207–216. [CrossRef]
Matthewson, M. , and Mamin, H. , 1988, “ Liquid Mediated Adhesion of Ultra-Flat Solid Surfaces,” MRS Proceedings, Cambridge University Press, Vol. 119, pp. 87–92.
Poon, C. Y. , and Bhushan, B. , 1996, “ Numerical Contact and Stiction Analyses of Gaussian Isotropic Surfaces for Magnetic Head Slider/Disk Contact,” Wear, 202(1), pp. 68–82. [CrossRef]
Tian, X. , and Bhushan, B. , 1996, “ The Micro-Meniscus Effect of a Thin Liquid Film on the Static Friction of Rough Surface Contact,” J. Phys. D: Appl. Phys., 29(1), pp. 163–178. [CrossRef]
Streator, J. L. , 2002, “ A Model of Mixed Lubrication With Capillary Effects,” Proceedings of the 28th Leeds-Lyon Symposium on Tribology: Boundary and Mixed Lubrication, Science and Applications, Vienna, Austria, Sept. 4–7, 2001, Tribol. Ser., 40, pp. 121–128.
Persson, B. , 2008, “ Capillary Adhesion Between Elastic Solids With Randomly Rough Surfaces,” J. Phys.: Condens. Matter, 20(31), p. 315007. [CrossRef]
Streator, J. L. , and Jackson, R. L. , 2009, “ A Model for the Liquid-Mediated Collapse of 2-D Rough Surfaces,” Wear, 267(9), pp. 1436–1445. [CrossRef]
Streator, J. L. , 2009, “ A Model of Liquid-Mediated Adhesion With a 2D Rough Surface,” Tribol. Int., 42(10), pp. 1439–1447. [CrossRef]
Rostami, A. , and Streator, J. L. , 2015, “ Study of Liquid-Mediated Adhesion Between 3D Rough Surfaces: A Spectral Approach,” Tribol. Int., 84, pp. 36–47. [CrossRef]
Rostami, A. , and Streator, J. L. , 2015, “ A Deterministic Approach to Studying Liquid-Mediated Adhesion Between Rough Surfaces,” Tribol. Lett., 58(1), pp. 1–13. [CrossRef]
Adamson, A. W. , and Gast, A. P. , 1967, Physical Chemistry of Surfaces, Wiley, New York.
Johnson, K. L. , 1985, Contact Mechanics, Cambridge University Press, New York.
Hamrock, B. J. , Schmid, S. R. , and Jacobson, B. O. , 2004, Fundamentals of Fluid Film Lubrication, Marcel Dekker, New York.
Patir, N. , and Cheng, H. , 1978, “ An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication,” ASME J. Tribol., 100(1), pp. 12–17.
Bathe, K. J. , and Wilson, E. L. , 1976, Numerical Methods in Finite Element Analysis, Prentice Hall, Upper Saddle River, NJ.
Jackson, R. L. , and Streator, J. L. , 2006, “ A Multi-Scale Model for Contact Between Rough Surfaces,” Wear, 261(11), pp. 1337–1347. [CrossRef]
Garcia, N. , and Stoll, E. , 1984, “ Monte Carlo Calculation for Electromagnetic-Wave Scattering From Random Rough Surfaces,” Phys. Rev. Lett., 52(20), pp. 1798–1801. [CrossRef]
Green, C. K. , Streator, J. L. , Haynes, C. , and Lara-Curzio, E. , 2011, “ A Computational Leakage Model for Solid Oxide Fuel Cell Compressive Seals,” J. Fuel Cell Sci. Technol., 8(4), p. 041003. [CrossRef]
Johnson, K. L. , Greenwood, J. A. , and Higginson, J. G. , 1985, “ The Contact of Elastic Regular Wavy Surfaces,” Int. J. Mech. Sci., 27(6), pp. 383–396. [CrossRef]
Rostami, A. , and Jackson, R. L. , 2013, “ Predictions of the Average Surface Separation and Stiffness Between Contacting Elastic and Elastic–Plastic Sinusoidal Surfaces,” Proc. Inst. Mech. Eng., Part J, 227(12), pp. 1376–1385. [CrossRef]

Figures

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Fig. 1

Liquid flow in a horizontal capillary tube

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Fig. 2

Schematic depiction of the modeled interface

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Fig. 3

Contact between an annular rigid flat and a flexible disk

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Fig. 4

Discrete pressure and deformation elements

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Fig. 5

Equivalency of a pressurized ring to the superposition of a uniform positive pressure circle of radius rj+Δrj/2 with a uniform negative pressure circle of radius rj−Δrj/2

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Fig. 6

Results for the pressure distribution for an external load of Pext=20 N

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Fig. 7

A schematic explanation of the parameters involved in Eq. (7)

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Fig. 8

A numerically generated Gaussian isotropic rough surface

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Fig. 9

Flowchart of the numerical algorithm

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Fig. 10

(a) Liquid film pressure and (b) liquid film thickness versus radial position at time t=0

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Fig. 11

Results for the liquid tensile force and flow rate between the two contacting surfaces versus time

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Fig. 12

(a) Liquid film pressure and (b) liquid film thickness versus radial position at t=0

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Fig. 13

Results for maximum tensile force and average flow rate versus the external load

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Fig. 14

Results for maximum tensile force and average flow rate versus composite surface roughness

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Fig. 15

Results for maximum tensile force and average flow rate versus effective elastic modulus

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Fig. 16

Comparison between results from the numerical model and curve-fit, Eq. (30)

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Fig. 17

Experimental setup used to measure the liquid film radius

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Fig. 18

Spread of liquid film between the contacting surfaces

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Fig. 19

Liquid film radius versus time results as predicted by the numerical model and via experiment for different PSF lubricants

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