Squeeze Effects in a Flat Liquid Bridge Between Parallel Solid Surfaces

[+] Author and Article Information
Marie-Hélène Meurisse

Laboratoire de Mécanique des Contacts et des Solides – UMR CNRS/INSA de Lyon 5514, Institut National des Sciences Appliquées de Lyon, 69621 Villeurbanne, FranceMarie-Helene.Meurisse@insa-lyon.fr

Michel Querry

Laboratoire de Mécanique des Contacts et des Solides – UMR CNRS/INSA de Lyon 5514, Institut National des Sciences Appliquées de Lyon, 69621 Villeurbanne, France

J. Tribol 128(3), 575-584 (Mar 14, 2006) (10 pages) doi:10.1115/1.2197525 History: Received July 19, 2005; Revised March 14, 2006

When a liquid lubricant film fractionates into disjointed liquid bridges, or a unique liquid bridge forms between solid surfaces, capillary forces strongly influence the action of the fluid on the solid surfaces. This paper presents a theoretical analytical model to calculate the normal forces on the solid surfaces when squeezing a flat liquid bridge. The model takes into account hydrodynamic and capillary effects and the evolution of the geometry of the liquid bridge with time. It is shown that the global normal force reverses during the squeezing motion except in the case of perfect nonwetting; it is attractive at the beginning of the squeezing motion, and becomes repulsive at small gaps. When the external load is constant, capillary suction tends to accelerate the decrease in gap dramatically.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Geometrical description of sessile drops and liquid bridges: (a) sessile drop with a contact angle less than π∕2rad, (b) sessile drop with a contact angle greater than π∕2rad, (c) diabolo shaped liquid bridge (contact angle less than π∕2rad), (d) roller shaped liquid bridge (contact angle greater than π∕2rad)

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Figure 2

Local shape of Delaunay’s roulettes: (a) elliptic roulettes, ξ0=0, (b) elliptic roulettes, ξ0=π, (c) hyperbolic roulettes, ξ0=0, (d) hyperbolic roulettes, ξ0=π, (e) catenary, (f) circle (e=1)

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Figure 3

Geometrical parameters of liquid bridges bounded by circular meniscus profiles

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Figure 4

Theoretical boundary case of circular menisci corresponding to V¯=V¯adm: (a) diabolo bridge (contact angle less than π∕2), (b) roller bridge (contact angle greater than π∕2)

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Figure 5

Absolute difference between nondimensional curvatures in the middle plane of the bridge, and at the surfaces

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Figure 6

Variations of nondimensional characteristic volumes versus contact angle θ (rad)

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Figure 7

Intensity of the nondimensional capillary force versus the nondimensional volume in the range [V¯0(θ),1000] for different values of contact angle θ (rad); θ⩽π∕2 in (a), θ⩾π∕2 in (b)

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Figure 8

Intensity of normal force versus gap at constant squeezing speed: volume: 10μl; viscosity: 1mPas; surface tension: 70mN∕m; squeezing speed: (a) ḣ=−0.001mm∕s, (b) ḣ=−0.1mm∕s, (c) ḣ=−10mm∕s, (d) ḣ=−1000mm∕s

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Figure 9

Comparison between experiment and theory: volume of water: V=15μl; final gap: 0.05mm; squeezing speed: (a) ḣ=−0.01mm∕s, (b) ḣ=−0.1mm∕s; advancing contact angle (theoretical): (a) 0.48π, (b) 0.499π

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Figure 10

Normal force versus gap at constant squeezing speed, for various contact angles close to π∕2: V=15μl; (a) ḣ=−0.01mm∕s, (b) ḣ=−0.1mm∕s

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Figure 11

Nondimensional volume versus nondimensional time, when squeezing a liquid bridge at constant applied load, for various values of Γ



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