Hierarchical fractal surface patterns for enhanced gypsum scaling resistance in membrane distillation: A computational fluid dynamics analysis

Gypsum scaling remains a significant barrier to widespread industrial implementation of membrane distillation (MD) in challenging water treatment applications. This study introduces microscale fractal-based patterns for direct contact membrane distillation (DCMD), incorporating hierarchical geometries within a single length domain to enhance scaling resistance. Using computational fluid dynamics (CFD) coupled with population balance modeling for gypsum crystallization, we systematically evaluated fractal-patterned membranes through a 2 × 2 factorial design investigating pattern direction (indentation vs. protrusion) and orientation (0° vs. 45°) effects. Indentation patterns achieved the highest pure water flux (∼20.0 LMH), demonstrating 35–37 % enhancement over unpatterned baselines, while maintaining nearly identical pressure drops (∼110 Pa/m) across all fractal configurations. Under gypsum scaling conditions, 45° orientations consistently outperformed 0° alignments. The optimal 45° indentation fractal pattern maintained superior flux stability throughout 16-h scaling tests, and comparative analysis against ridge-groove patterns revealed fundamental design trade-offs: although ridge-groove initially achieved higher flux (∼22 LMH), it suffered catastrophic >90 % flux decline versus fractal patterns' sustained performance. Wall shear stress analysis demonstrates that fractal geometries generate more uniform stress distributions through hierarchical, multi-scale flow disruption, effectively eliminating stagnation zones where crystal nucleation preferentially occurs. The findings advance MD implementation in challenging water treatment scenarios through strategic hydrodynamic engineering.