A 2D Geometrical Perspective for the Contact Angle Hysteresis

Contact angle and its hysteresis during advancing and receding are probably the most fundamental concepts when two fluids interact with a solid surface. Surface roughness/microstructure affects contact angle hysteresis. Fiber is a common structure used to fabricate functional surfaces. However, a general model for fiber rough surfaces has not been obtained. This work, from a geometrical perspective, derives analytical solutions for the relationships between droplet volume and apparent contact angles and asymptotes for advancing, receding, and equilibrium contact angles on the surface with cylindrical humps. Energy evolution is tracked by calculating the Gibbs free interfacial energy. Results show that the contact angle hysteresis is constrained by geometry when assumptions are met. The advancing, receding, and equilibrium contact angles oscillate and gradually approach the predicted asymptote values with increasing humps. Gibbs free interfacial energy drops upon droplet advancing and receding. This energy cliff would induce droplet vibration, and the energy can be dissipated via fluid internal friction. Lattice Boltzmann method (LBM) simulations and quasi-2D experiments verify these solutions and demonstrate dynamic behaviors during droplet jumps to the next hump. From an energy perspective, the equilibrium contact angle can fall outside the contact angle hysteresis, although geometrically impossible. Energy analysis reveals that the Gibbs free energy at 0° can be order-of-magnitude less than that at other apparent contact angles. 3D experiments confirm that prewetted rough surfaces can reach this more stable configuration devoid of contact angle hysteresis, verifying 2D analytical modeling. Note that the theoretical analysis is based on idealistic assumptions, and the real circumstance may deviate from these assumptions.