Beyond viscous friction: the role of extensional friction in directional droplet transport on structurally anisotropic surfaces.

HYPOTHESIS: The solid-liquid friction between droplet and solid surface plays a critical role in interfacial and surface flows. Recent studies on plant surfaces with anisotropic structures, such as Crassula muscosa and Oryza sativa (rice), demonstrate their remarkable capability to drive directional liquid transport. While the classical two-dimensional Furmidge equation is widely used to describe droplet sliding on inclined surface, it fails to capture the variations in solid-liquid friction on structurally anisotropic substrates. To elucidate the underlying mechanical mechanism, this study investigates the friction force components during droplet sliding along different paths. By incorporating the extensional friction term that accounts for capillary bridge deformation, a three-dimensional Furmidge equation is developed.

EXPERIMENTS: Biomimetic surfaces with rectangular ridge arrays replicating rice leaf topographies were fabricated. Owing to the structural anisotropy of the surfaces, distinct contact angles and run-off angles were observed when the viewing direction was aligned perpendicular or parallel to the groove orientation.

FINDINGS: The proportional relationship between extensional friction at receding contact line and viscous friction in boundary layer is calculated by the three-dimensional Furmidge equation across different motion paths. The results are compared with the predictions of other solid-liquid friction models. The findings reveal that directional transport stems from differences in extensional friction at low capillary numbers (2.77 × 10-6 to 5.75 × 10-6), and explain why the maximum static friction exceeds kinetic friction. This work reveals the intrinsic mechanical linkage between anisotropic structure and solid-liquid friction components, paving the way for biomimetic surfaces with intelligently tunable anisotropy beyond homogeneous wettability.