Beyond the Mean-flow: A Spectral-Dynamic Approach to Unraveling the Physics of Droplet Capture in Fog Harvesting Meshes
Fog harvesting efficiency with mesh collectors is governed by complex interactions between droplet inertia and geometry-induced flow structures. Although previous studies have primarily relied on mean-flow metrics, the present work introduces a spectral-dynamic framework to examine an important but often overlooked control on droplet capture. A two-way coupled Eulerian-Lagrangian model is used to simulate droplet-laden flow (2-40 microm) across five representative mesh geometries. The results show that capture efficiency correlates not only with the magnitude of velocity fluctuations, but also with their spectral distribution and persistence. Frequency-domain analysis indicates that mesh geometry redistributes fluctuation energy across pore and obstruction regions, thereby defining a characteristic flow timescale. By comparing this flow timescale with the droplet response time, a dynamic matching parameter, {\Pi}= droplet response time/flow time scale, is introduced. The highest capture efficiency occurs when {\Pi} is order unity, corresponding to sustained droplet-flow interaction in the near-mesh region. Geometries that generate broadband, moderately amplified spectral content (e.g., triangular mesh) increase droplet residence time and interception probability, whereas geometries with either weak or highly localized fluctuations reduce performance through insufficient forcing or premature bypass. A physics-inspired correlation for capture efficiency is proposed based on this condition. The study therefore provides mechanistic design guidance, rather than a definitive optimum, for geometry optimization in fog-harvesting meshes.