Membrane distillation (MD) is a thermally driven separation process that is operated below boiling point. Since the performance of MD modules is still comparatively low, current research aims to improve the understanding of the membrane structure and its underlying mechanisms at the pore level. Based on existing realistic 3D membrane geometries (up to 0.5 billion voxels with $39\mathrm{nm}$ resolution) obtained from ptychographic X-ray computed tomography, the D3Q27 lattice Boltzmann (LB) method was used to investigate the interaction of the liquid and gaseous phase with the porous membrane material. In particular, the Shan and Chen multi-phase model was used to simulate multi-phase flow at the pore level. We investigated the liquid entry pressure of different membrane samples and analysed the influence of different micropillar structures on the Wenzel and Cassie–Baxter state of water droplets on rough hydrophobic surfaces. Moreover, we calculated the liquid entry pressure required for entering the membrane pores and extracted realistic water contact surfaces for different membrane samples. The influence of the micropillars and flow on the water-membrane contact surface was investigated. Finally, we determined the air–water interface within a partially saturated membrane, finding that the droplet size and distribution correlated with the porosity of the membrane.

Microfabrication techniques allow the development and production of artificial superhydrophobic surfaces that possess a precisely controlled roughness at the micrometer level, typically achieved through the arrangement of micropillar structures in periodic patterns. In this work, we analyze the stability and energy barrier of droplets in the Cassie–Baxter (CB) state on such periodic patterns. In addition, we further develop a transition criterion using the CB equation and derive an improved version which allows predicting for which pillar geometries, equilibrium contact angles, and droplet volumes the CB state switches from a metastable to an unstable state. This enables a comparison with existing experiments and three-dimensional multiphase Lattice Boltzmann simulations for different pillar distances, two contact angles, and two droplet volumes, where a good agreement has been found.

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.