TY - JOUR T1 - Computer simulations of phase field drops on super-hydrophobic surfaces JF - Journal of Computational Physics Y1 - 2017 A1 - Livio Fedeli KW - Multigrid KW - Phase field KW - Quasi-Newton KW - Super-hydrophobicity AB -

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

VL - 344 UR - http://www.sciencedirect.com/science/article/pii/S002199911730356X ER - TY - JOUR T1 - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JF - ESAIM: Mathematical Modelling and Numerical Analysis Y1 - 2013 A1 - Cacace, S. A1 - Antonin Chambolle A1 - Antonio DeSimone A1 - Livio Fedeli PB - EDP Sciences VL - 47 ER - TY - JOUR T1 - Metastable equilibria of capillary drops on solid surfaces: a phase field approach JF - Continuum Mechanics and Thermodynamics Y1 - 2011 A1 - Livio Fedeli A1 - Turco, Alessandro A1 - Antonio DeSimone AB -

We discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

VL - 23 UR - https://doi.org/10.1007/s00161-011-0189-6 ER - TY - CONF T1 - A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena T2 - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Y1 - 2010 A1 - Antonio DeSimone A1 - Livio Fedeli A1 - Turco, Alessandro ED - Hackl, Klaus AB -

We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

JF - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials PB - Springer Netherlands CY - Dordrecht SN - 978-90-481-9195-6 ER -