Theoretical and Numerical Constant Mean Curvature Surface and Liquid Entry Pressure Calculations for a Combined Pillar–Pore Structure

Abstract

Modern microfabrication techniques have led to a growing interest in micropillars and pillar–pore structures. Therefore, in this paper a study of the liquid entry pressure of a hydrophobic pillar–pore structure and the corresponding liquid–gas interface shape for the pressurized liquid is presented. We theoretically analysed the constant mean curvature problem for the rotationally symmetric case and determined an analytical expression for the liquid entry pressure of a hydrophobic pillar–pore structure. Furthermore, the shape of the liquid–gas interface as well as a formula for the location of the minimum were derived. The results are useful for designing geometries with specific properties, such as preventing or facilitating liquid intrusion into rough structures. We compared these results to multiphase lattice Boltzmann simulations where equilibrium contact angles in the range of 157∘ to 102∘ were tested. In our further analysis, we compared theoretical findings from previous works to our lattice Boltzmann simulations. The presented cases can serve as a benchmark for the development and validation of numerical multiphase models.

Validating the Transition Criteria from the Cassie–Baxter to the Wenzel State for Periodically Pillared Surfaces with Lattice Boltzmann Simulations

“…Zheng et al used a force balance approach to derive a general expression to calculate the critical pressure for a liquid film on an arbitrary periodically pillared structure and found good agreement with numerical simulations. Jäger et al were able to confirm their results with multiphase LB simulations. In the critical state, according to F z = normalΔ p normalc normalr normali normalt ( A normalc − A ) + γ l cos ( α 0 ) ︸ p r o j e c t i o n a l o n g z ‐ normala normalx normali normals = 0 Rearranging gives normalΔ p normalc normalr normali normalt = prefix− γ l cos ( α 0 ) A c − A …”

“…Zheng et al used a force balance approach to derive a general expression to calculate the critical pressure for a liquid film on an arbitrary periodically pillared structure and found good agreement with numerical simulations. Jäger et al were able to confirm their results with multiphase LB simulations. In the critical state, according to Rearranging gives …”