Nucleation Rate of Capillary Bridges Between Multi-Asperity Surfaces
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Nucleation Rate of Capillary Bridges Between Multi-Asperity Surfaces Emrecan Soylemez1, Maarten P. de Boer1 and W. Robert Ashurst2 1
Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA, U.S.A.
2
Department of Chemical Engineering, Auburn University, Auburn, AL, U.S.A.
ABSTRACT A microcantliever based crack healing experiment is described and utilized in order to study the capillary nucleation rate for typical MEMS surfaces. An advanced test chamber that allows exquisite environmental control is also described and used in this study. Crack healing experiments prove to be a viable experimental technique to investigate the dynamics of capillary nucleation. The effective capillary nucleation time for the multi-asperity surface of microcantilever samples appears to increase logarithmically with adhesion energy. INTRODUCTION Capillary bridge formation between two nearby surfaces in humid environments is a ubiquitous phenomenon. For example, this phenomenon can be observed in studies of granular materials1, friction2, insect adhesion3, head/disk system involving stiction4, soil mechanics5, nanolithography6, colloidal physics7 and micro-electromechanical systems (MEMS) devices8. Adhesion of contacting surfaces in MEMS is a prominent failure mechanism. Capillary forces are the strongest contributors to adhesion forces, and lead to stiction. While equilibrium capillary adhesion energies of water have been widely studied 9, there is a lack of understanding of capillary adhesion dynamics. A better understanding of capillary adhesion dynamics may provide useful insight into reliability issues of MEMS devices with moving parts that utilize impacting surfaces. For example, a variety of alcohol vapors significantly reduce or perhaps eliminate wear in sliding micromachined contacts10. However, these vapors may increase adhesion due to capillary forces. When contacting surfaces are exposed to the unsaturated vapor of a condensable substance, the substance may spontaneously condense into a liquid state and form curved menisci that can fill in regions between surfaces separated by a small gap11. Consequently, the curved meniscus induces a pressure difference across the liquid-vapor interface. The expression relating the pressure to the meniscus curvature is known as Young-Laplace equation12, οܲ ൌ
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(1)
Here, re is the effective radius of curvature of the meniscus, and JL is the surface tension of the liquid13. Under thermodynamic equilibrium, the value of re can be found from the Kelvin equation14, ଵ
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ோౝ ்୪୬ሺΤ౩ ሻ ఊಽ ౣ
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(2)
Here, rK is the Kelvin radius, Rg is the ideal gas constant, T is temperature, p is the vapor pressure, ps is the saturated vapor pressure, and Vm is the molar volume of the liquid substance.
3
The surface forces apparatus (SFA) and the atomic force microscope (AFM) have been used to measure equilibrium capillary forces. These techniques can be used to quantify the maximum capillary force (at contact), but not the full force-distance curve15. The SFA mea
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