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.
Highlights
The study of the motion states of droplets on an inclined, hydrophilic rough surface in gravity is a fundamental problem in the mechanics of wetting and spreading [18,19,20,21,22,23,24,25], which facilitates a better understanding of how to manipulate a droplet on a rough surface
Method of the Droplet: Pinned or Sliding the droplet stays on an inclined, hydrophilic rough surface, we can predict the
If θ1−0 < θa and θ2−0 > θr, the droplet is pinned; If θ1−0 ≥ θa and θ2−0 ≤ θr, the droplet is sliding; If θ1−0 < θa and θ2−0 ≤ θr, the droplet is contracting—we went to Step 4 and further judged the motion state of the droplet; If θ1−0 ≥ θa and θ2−0 > θr, the droplet is stretching—we went to Step 5 and further judged the motion state of the droplet
Summary
The study of the motion states of droplets on an inclined, hydrophilic rough surface in gravity is a fundamental problem in the mechanics of wetting and spreading [18,19,20,21,22,23,24,25], which facilitates a better understanding of how to manipulate a droplet on a rough surface. A small droplet on an inclined hydrophilic rough surface has two main motion states: pinned and inchworm sliding. Predicting the motion state of a droplet on an inclined, hydrophilic rough surface is more complicated and difficult, because it concerns the surface inclination, the droplet shape, the droplet’s contact angle hysteresis, and the dynamic behavior of the droplet’s three-phase contact line
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