Out-of-Contact Elastohydrodynamic Deformation due to Lubrication Forces

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Out-of-Contact Elastohydrodynamic Deformation due to Lubrication Forces

Yumo Wang, Charles Dhong, and Joelle Frechette

Phys. Rev. Lett. 115, 248302 – Published 10 December 2015

Abstract

We characterize the spatiotemporal deformation of an elastic film during the radial drainage of fluid from a narrowing gap. Elastic deformation of the film takes the form of a dimple and prevents full contact to be reached. With a thinner elastic film the stress becomes increasingly supported by the underlying rigid substrate and the dimple formation is suppressed, which allows the surfaces to reach full contact. We highlight the lag due to viscoelasticity on the surface profiles, and that for a given fluid film thickness deformation leads to stronger hydrodynamic forces than for rigid surfaces.

Received 15 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.248302

Authors & Affiliations

Yumo Wang¹, Charles Dhong¹, and Joelle Frechette^1,2,*

¹Chemical and Biomolecular Engineering Department, Johns Hopkins University, Baltimore, Maryland 21218, USA
²Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA

^*jfrechette@jhu.edu

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Vol. 115, Iss. 24 — 11 December 2015

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Figure 1
Schematics (not to scale) of (a) the elastohydrodynamic problem with labeled variables (inset: Kelvin-Voigt model for elastomer viscoelasticity), and (b) material layers and properties.
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Figure 2
(a) Experimental and theoretical spatiotemporal surface profile during approach at $V = 137 nm / s$ . The black solid lines correspond to theoretical predictions treating the PDMS films as a viscoelastic solid. Time stamps are I: $t = 3.8$ , II: $t = 8.8$ , III: $t = 13.8$ , IV: $t = 18.8$ , V: $t = 23.8$ , VI: $t = 33.8$ , and VII: $t = 53.8 s$ . Dashed lines are for the positions of the corresponding undeformed sphere. (b)–(e) Temporal central separation for (b) $V = 69 nm / s$ , (c) $V = 355 nm / s$ , (d) $164 nm / s$ , and (e) $V = 137 nm / s$ . (b)–(c) Effect of drive velocity. (d)–(e): Effect of film thickness. Black solid lines are the same as in (a), dashed lines are Reynolds’ theory. Red solid lines are predictions treating the elastomer as an elastic solid. Black arrows are the time for dimple formation. $h_{\infty}$ is the long time predictions (central $d h / d t < 1 % V$ ). (d): Approach of a thinner PDMS coating ( $T = 10.9 μ m$ , $R = 1.10 cm$ ), black rigid line represents predictions for $E = 84 MPa$ . Yellow line represents the predictions for $E = 1 MPa$ . Inset of (d) shows shape of fringes for thin (10.9) and thick ( $330 μ m$ ) PDMS film during the approach with $h_{center} = 150 nm$ and the inset of (e) shows the effect of viscosity of PDMS on initial surface profile.
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Figure 3
(a) Growth of barrier ring radius ( $r_{b}$ ). Squares, $V = 69$ ; circles, $V = 137 nm / s$ . $t_{d}$ ( $s$ ) is the time elapsed after center curvature of the elastomer becomes negative. Black solid lines, $r_{b} = \sqrt{R V t_{d} / 2}$ . Vertical dashed lines indicate when the motor stopped. (b) Radial cumulative force (%) as a function of $r / R$ for $V = 137 nm / s$ . The roman numerals represent the same times as those of Fig. 2. Solid lines correspond to the relative cumulative force results from a spherical indenter with the same load as that in EHD (dashed lines), calculated from Hertz contact mechanics. (c) Center point (solid) and edge (open) separation after dimple formation (circles, $V = 137$ ; squares, $V = 69 nm / s$ ). Inset: Corresponding interference fringes for $V = 69 nm / s$ . Solid arrows: motor stop time for $V = 137$ and $V = 69 nm / s$ . (d) Schematic showing formation and relaxation of dimples with a barrier ring $r_{b}$ .
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Figure 4
Repulsive elastohydrodynamic force as a function of central separation $h$ . Circles, $V = 69$ ; squares, $V = 137$ ; triangles, $V = 355 nm / s$ . Dashed lines, predictions for rigid surfaces; solid lines, predictions for compliant surfaces treating the elastomer as a viscoelastic solid. Inset: corresponding force as a function of time.
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