Interface Equilibrator: Numerical solutions to capillarity and wetting equilibrium and quasi-equilibrium problems

This paper introduces Interface Equilibrator (IE), a new graphical-user-interface software for simulating the equilibrium shape of fluid–fluid interfaces in a wide range of wetting and capillarity problems. IE provides an easy-to-use three-dimensional computer-aided-design environment to define the problem's geometry (i.e., the solid surfaces and the fluids' volumes), by simply loading opportune triangular meshes, and chemistry, by selecting the value of the relevant experimental parameters (e.g., Young's contact angle). No other input is required. Then, IE calculates the fluid–fluid interface's equilibrium shape using a novel numerical methodology, presented in this paper, that consists in an energy-minimization Monte Carlo simulation alongside other built-in automated methods to, e.g., refine the fluid–fluid interface mesh according to its local curvature and polish it. The energy-minimization algorithm is based on a numerical approach introduced a few years ago [Soligno et al., “The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young's and Young–Laplace equations,” J. Chem. Phys. 141, 244702 (2014)] that is generalized here to handle unconstructed meshes with any topology and to include also new types of forces (e.g., due to a rotating system or to a line tension). In addition, several illustrative and scientifically interesting novel results are presented in this paper to demonstrate IE's versatility and capability of addressing a broad spectrum of research problems, relevant for many technological applications, such as microfluidics, fluid management at various length scales, printing, colloids, soldering for chip manufacture, etc. Finally, the paper reports numerous validation tests, where known analytic or numerical solutions are compared with IE's results to verify the correctness and accuracy of IE's calculations.