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Abstract: The influence of finite system size on the free energy of a sphericalparticle floating at the surface of a sessile droplet is studied bothanalytically and numerically. In the special case that the contact angle at thesubstrate equals $\pi-2$ a capillary analogue of the method of images isapplied in order to calculate small deformations of the droplet shape if anexternal force is applied to the particle. The type of boundary conditions forthe droplet shape at the substrate determines the sign of the capillarymonopole associated with the image particle. Therefore, the free energy of theparticle, which is proportional to the interaction energy of the originalparticle with its image, can be of either sign, too. The analytic solutions,given by the Green-s function of the capillary equation, are constructed suchthat the condition of the forces acting on the droplet being balanced and ofthe volume constraint are fulfilled. Besides the known phenomena of attractionof a particle to a free contact line and repulsion from a pinned one, weobserve a local free energy minimum for the particle being located at the dropapex or at an intermediate angle, respectively. This peculiarity can be tracedback to a non-monotonic behavior of the Green-s function, which reflects theinterplay between the deformations of the droplet shape and the volumeconstraint.



Autor: J. Guzowski, M. Tasinkevych, S. Dietrich

Fuente: https://arxiv.org/







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