Optimization of Patterned Surfaces for Improved Superhydrophobicity Through Cost-Effective Large-Scale Computations

The growing need for creating surfaces with specific wetting properties, such as superhyrdophobic behavior, asks for novel methods for their efficient design. In this work, a fast computational method for the evaluation of patterned superhyrdophobic surfaces is introduced. The hydrophobicity of a surface is quantified in energy terms through an objective function. The increased computational cost led to the parallelization of the method with the Message Passing Interface (MPI) communication protocol that enables calculations on distributed memory systems allowing for parametric investigations at acceptable time frames. The method is demonstrated for a surface consisting of an array of pillars with inverted conical (frustum) geometry. The parallel speedup achieved allows for low cost parametric investigations on the effect of the fine features (curvature and slopes) of the pillars on the superhydophobicity of the surface and consequently for the optimization of superhyrdophobic surfaces.Comment: 18 pages, 18 figure

The normal field instability under side-wall effects: comparison of experiments and computations

We consider a single spike of ferrofluid, arising in a small cylindrical container, when a vertically oriented magnetic field is applied. The height of the spike as well as the surface topography is measured experimentally by two different technologies and calculated numerically using the finite element method. As a consequence of the finite size of the container, the numerics uncovers an imperfect bifurcation to a single spike solution, which is forward. This is in contrast to the standard transcritical bifurcation to hexagons, common for rotational symmetric systems with broken up-down symmetry. The numerical findings are corroborated in the experiments. The small hysteresis observed is explained in terms of a hysteretic wetting of the side wall.Comment: accepted to New Journal of Physic

Optimization of patterned surfaces for Improved superhydrophobicity through cost-effective large-scale computations

The pattern design of superhydrophobic surfaces can be significantly aided by computations that predict the Cassie–Baxter (CB) to Wenzel (W) transition, which is responsible for the break-down of superhydrophobic behavior. We present a computational framework for the optimization of patterned surfaces based on the energy barriers of the CB–W transitions which comprises the following elements: (a) design of structured surface patterns, for example, arrays of pillars, with parameterized geometric features such as size, pitch, slope, and roundness. (b) Computation of the wetting states with a modified Young–Laplace equation that facilitates the introduction of solid/liquid interactions for complex surface patterns and has significantly lower computational cost than other commonly used methods, such as the volume-of-fluid, phase-field, and so forth. (c) Incorporation of the modified Young–Laplace in the simplified string method, allowing the calculation of the minimum energy paths of wetting transitions which, apart from the energy barriers, also reveal the transition mechanisms (CB failure modes). (d) Accommodation of large-scale problems with good parallel performance and scalability on multicore-distributed memory systems using fast iterative solvers and the Message Passing Interface communication protocol. We demonstrate the computational framework with a shape optimization study of inverted conical frustum pillars. The optimization objective function is the resistance to the CB–W transition, which is quantified by the energy barrier—a relatively large energy barrier suggests improved superhydrophobicity. We also report the parallel performance, in terms of parallel speedup for problems ranging from three hundred thousands to 12 million degrees of freedom, solved using up to 40 processing cores