Three-Dimensional Lattice Boltzmann Simulations of Droplet Wetting States on Bi-Gaussian Layered Surfaces

Real engineering surfaces commonly exhibit multiscale, hierarchically layered roughness; however, the independent contributions of the upper and lower roughness components in bi-Gaussian layered surfaces (bi-Gaussian surfaces), as well as their coupled effects on wetting behavior, remain insufficiently understood. In this study, a numerical investigation of droplet wetting behavior on bi-Gaussian surfaces is conducted based on bi-Gaussian surface theory. Gaussian and bi-Gaussian surfaces with well-controlled statistical characteristics are generated using a moving average-fast Fourier transform (MA-FFT) algorithm. A color-gradient lattice Boltzmann multiphase model is then employed to systematically simulate the quasi-static wetting dynamics of droplets, with particular emphasis on elucidating how morphological parameters of bi-Gaussian surfaces govern wetting behavior. The results indicate that, for Gaussian-distributed rough surfaces (Gaussian surfaces), droplet wetting is predominantly governed by the global root-mean-square roughness S_q, exhibiting a clear monotonic dependence. In contrast, for bi-Gaussian surfaces, the predictive capability of the global S_q deteriorates significantly. Further decoupled analysis reveals a triple-dominant mechanism underlying layered wetting behavior. The interlayer separation Z_u serves as the primary driving factor that induces the transition of the effective supporting layer from the lower substrate to the upper roughness layer, thereby controlling wetting state transitions. The spiky morphology of the upper Gaussian structure provides the dominant mechanical support for the droplet, while the roughness of the lower Gaussian layer regulates the sensitivity of the wetting transition. Specifically, the lower-layer roughness modulates the sensitivity of the apparent contact angle to the interlayer separation by altering the amplitude of substrate height fluctuations. These findings clarify the wetting behavior of rough surfaces commonly encountered in engineering applications and provide fundamental guidance for understanding complex wetting phenomena on real surfaces, as well as for the rational design of surfaces with tailored wetting properties.