title: The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young's and Young-Laplace equations.
abstract: Many physical problems require explicit knowledge of the equilibrium shape of the interface between two fluid phases. Here, we present a new numerical method which is simply implementable and easily adaptable for a wide range of problems involving capillary deformations of fluid-fluid interfaces. We apply a simulated annealing algorithm to find the interface shape that minimizes the thermodynamic potential of the system. First, for completeness, we provide an analytical proof that minimizing this potential is equivalent to solving the Young-Laplace equation and the Young law. Then, we illustrate our numerical method showing two-dimensional results for fluid-fluid menisci between vertical or inclined walls and curved surfaces, capillary interactions between vertical walls, equilibrium shapes of sessile heavy droplets on a flat horizontal solid surface, and of droplets pending from flat or curved solid surfaces. Finally, we show illustrative three-dimensional results to point out the applicability of the method to micro- or nano-particles adsorbed at a fluid-fluid interface.
authors.affiliation: Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, Utrecht 3584 CE, The Netherlands.
authors.forename: Giuseppe
authors.initials: G
authors.lastname: Soligno
authors.affiliation: Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, Utrecht 3584 CC, The Netherlands.
authors.forename: Marjolein
authors.initials: M
authors.lastname: Dijkstra
authors.affiliation: Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, Utrecht 3584 CE, The Netherlands.
authors.forename: René
authors.initials: R
authors.lastname: van Roij