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Research Papers

Intersurface Adhesion in the Presence of Capillary Condensation

[+] Author and Article Information
Jianfeng Sun, Sinan Müftü

Department of Mechanical and
Industrial Engineering,
Northeastern University,
Boston, MA 02115

April Z. Gu

Department of Civil and
Environmental Engineering,
Northeastern University,
Boston, MA 02115

Kai-Tak Wan

Department of Mechanical and
Industrial Engineering,
Northeastern University,
Boston, MA 02115
e-mail: ktwan@coe.neu.edu

1Present address: Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 6, 2018; final manuscript received March 11, 2018; published online April 4, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(6), 061009 (Apr 04, 2018) (5 pages) Paper No: JAM-18-1077; doi: 10.1115/1.4039621 History: Received February 06, 2018; Revised March 11, 2018

An elastic sphere adheres to a rigid substrate in the presence of moisture. The adhesion–detachment trajectory is derived based on the Hertz contact theory that governs the contact mechanics and Laplace–Kelvin equation that governs the water meniscus at the interface. The intersurface attraction is solely provided by the Laplace pressure within the meniscus. Interrelation between the applied load, contact radius, and approach distance is derived based on a force balance. The resulting “pulloff” force to detach the sphere exceeds the critical load in the Derjaguin–Muller–Toporov (DMT) limit which only holds at saturated moisture. The new model accounts for the finite size of water molecules that is missing in virtually all classical models.

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References

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Figures

Grahic Jump Location
Fig. 1

An elastic solid is deformed from a spherical geometry (dashed curve) into Hertz profile (solid curve). The uniform Laplace pressure bounded by the meniscus exerts traction on the sphere in addition to the applied load.

Grahic Jump Location
Fig. 2

Adhesion of an elastic sphere with an elastic modulus E = 1.0 GPa in the presence of moisture: (a) Contact radius as a function of applied load for RH = 5%, 15%, 25%, 35%, 45%, 65%, 85%, and 95% based on the present model (dark curves). At RH = 5%, external tension shrinks the contact area along ABCDO and causes “pulloff” under fixed load at C. Fixed grips continues along CD. At D, a point contact is left and “pulloff” occurs at O. The gray curve shows the locus of fixed load “pulloff”. The Bradley's model is essentially the horizontal axis since contact radius is always zero. The DMT model (red dashed curve) is based on the surface tension of water and “pulloff” occurs at D. The JKR model (blue dashed curve) shows “pulloff” under fixed load at P and “pulloff” under fixed grips at P'. (b) Applied load as a function of approach distance for RH = 5%, 25%, 45%, 65%, 85%, and 95% based on the present model (dark curves). Detachment proceeds along CDH. “Pulloff” under fixed load occurs at C and under fixed grips at H. The “pulloff” locus are shown as gray curves, along with the DMT and JKR models. The Bradley's model is identical to the present model under external tension.

Grahic Jump Location
Fig. 3

“Pulloff” as a function of relative humidity: (a) applied tension, −F(RH), and (b) contact radius a(RH), under fixed load (c.f. gray curve CD in Fig. 2(a)); and (c) approach distance, δ(RH) under fixed load (c.f. gray curve CD in Fig. 2(b)) and 䆆(RH) under fixed grips (c.f. gray curve of negative horizontal axis in Fig. 2(b)).

Grahic Jump Location
Fig. 4

Deformed profile at the contact edge exposed to moist air in the absence of an applied load F = 0. Minimum thickness of liquid water is set to be 8.4 Å (dashed line). At RH = 40%, the profile changes abruptly at the circle marked, indicating the meniscus or cohesive zone edge. The JKR and DMT limits are shown as dashed curves.

Grahic Jump Location
Fig. 5

“Pulloff” force under fixed load as a function of relative humidity, showing the present model (solid curve for RH > 30% and dashed curve for RH < 30%), theoretical results from Refs. [8], [9], and [14], measurements from Refs. [5] and [9]. Note that the two experimental data at RH = 0% and 45% from Ref. [9] neither fall into the main trend of this work and others nor match with the theory from the same paper.

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