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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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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