386653 History Dependent Shape of a Pinned Droplet on an Incline
The diverse and complex shapes of raindrops on a window beautifully illustrate the difficulty in predicting the shape of a capillary surface under the influence of surface tension and gravity. Considering the toy problem of a droplet on an incline, we resolve the basic question how to predict the shape of pinned droplets. Answering this question immediately leads to a prediction of the threshold force, viz. the inclination angle, that is required for the droplet to roll off.
In this talk, we present a theoretical model that takes local pinning of the contact line into account. In contrast to seminal papers in this field, which either fix the shape of the contact line or the contact angle variation around it, both these parameters are predicted by our model. This is done for increasing values of the inclination angle until we no longer obtain a solution, which is indicative for roll-off. To verify that our model correctly predicts droplet shapes and roll-off angles, we compared the predictions with constrained energy minimization calculations performed with Surface Evolver and show that they are in excellent agreement.
One of our most interesting findings is that the evolution of the contact line is very different for droplets that start the tilting process with different initial widths and the roll-off angle cannot be predicted without taking into account this history dependence. In fact, we show that one only needs to know this initial width together with the liquid and solid properties to accurately predict the roll-off angle.
From a practical point of view, the results of our study can be used in the design of surfaces for a wide variety of applications, ranging from windscreens without wipers to solar panels with higher water repellency.