Small-scale devices are particularly vulnerable to adverse effects of adhesion because of large surface-area-to-volume ratios. Additionally, small gaps can be easily bridged at high humidity or when there are other contaminant liquids present. The bridging of a portion of the interface by a liquid droplet of given volume, tends to pull surfaces in closer proximity due to the sub-ambient pressures that arise. In turn, regions spanned by the bridge will increase in size and lead to a greater adhesive force. In the present work we develop a model for these effects in the presence of surface roughness. The influence of asperities on the surface is treated by means of a recently-developed multi-scale model that considers the full range of wavelengths comprising the surface profile. In the simulations, two nominally flat rough surfaces with profiles that vary only in one direction are brought together under a prescribed load. A liquid bridge of given volume (per unit depth) is then introduced into the contact, assuming an initial areal coverage. The interface configuration is then iterated until one is found that satisfies the equations of elasticity and capillarity for a given liquid volume. As a result of the simulation, critical values are found for combinations of parameters that delineate stable and unstable conditions.

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