Phase-Field Simulations of Capillary Interactions Between Rough Surfaces
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At a small enough length scale, surfaces are always rough, regardless whether they are generated by nature or via artificial process. When two such surfaces are placed close enough, the water molecules in the humid air are absorbed and hence form capillary bridges. Theories for adhesive interactions typically use simple cohesive laws, which are good models for Van-der-Waals interactions but may not be appropriate for capillary adhesion. We here construct a phase-field model that explicitly represents water present between two contacting rough interfaces. We show results obtained with this model on synthetic, computer-generated, self-affine rough interfaces. In quasi-static simulation, we observe the merging and splitting of droplets under the normal and shear movement of the interfaces. The overall force is dominated by the perimeter of the droplet, indicating the importance of a detailed understanding of droplet morphology.