Which Is the Motion State of a Droplet on an Inclined Hydrophilic Rough Surface in Gravity: Pinned or Sliding?

Abstract

The motion state of a droplet on an inclined, hydrophilic rough surface in gravity, pinned or sliding, is governed by the balance between the driving and the pinned forces. It can be judged by the droplet’s shape on the inclined hydrophilic rough surface and the droplet’s contact angle hysteresis. In this paper, we used the minimum energy theory, the minimum energy dissipation theory, and the nonlinear numerical optimization algorithm to establish Models 1–3 to calculate out the advancing/receding contact angles (θa/θr), the initial front/rear contact angles (θ1−0/θ2−0) and the dynamic front/rear contact angles (θ1−*/θ2−*) for a droplet on a rough surface. Also, we predicted the motion state of the droplet on an inclined hydrophilic rough surface in gravity by comparing θ1−0(θ2−0) and θ1−*(θ2−*) with θa(θr). Experiments were done to verify the predictions. They showed that the predictions were in good agreement with the experimental results. These models are promising as novel design approaches of hydrophilic functional rough surfaces, which are frequently applied to manipulate droplets in microfluidic chips.