Capillary torque in a liquid bridge between two angled filaments

Capillary torque is induced when a liquid bridge forms between two angle-positioned filaments. This paper aims to study the dependency of such capillary torque upon the filament orientation angle, filament spacing, contact angle, and liquid volume through detailed numerical simulation using a surface finite element scheme. Numerical results show that for hydrophilic liquid with contact angle below 90° and at given liquid volume as well as filament spacing, the surface energy of the system grows nonlinearly with increasing filament orientation angle from 0° (parallel filaments) to 90° (cross-positioned filaments). Accordingly, the capillary torque induced by the distorted liquid bridge increases from a torque-free state at 0° to the peak value and then decreases to the second torque-free state at 90°. At fixed filament orientation angle, the capillary torque grows with the liquid volume while decreases rapidly with increasing either contact angle or filament spacing. The peak value of capillary torque depends upon both the geometries and wetting property of the liquid bridge-filament system. A family of characteristic curves in terms of capillary torque with the filament orientation angle is determined at varying volume of liquid bridge, filament spacing ratio, and contact angle. The results and concepts developed in work are applicable for the study of wetting and spreading of liquids in fiber networks, microfluidics-based microstructural assembly, biological cell operation, etc.