If only consider about curvature effect and no external force added, the droplet is going to deform to part of a perfect circle no matter what kind of polygon it starts with.
Here we show an example that starts with a polygon of n=10, and within 2000 iterations (time step from 4x10-5 to 2x10-4) it has already turned to a shape closed to a circle.
Video 1: Model validation without external force [stage 1]
This video includes first 2000 iterations of simulation. From the animation we can observe that the contact angle change very fast until it is close to steady state, and vibrates in a range about 5 degrees. That’s due to the way we calculate the contact angle (see code) and how we add and cut points in the system. Length of bottom segment is always increasing in this stage, showing that the driving force has not been balanced and the whole system is still moving on.
Video 2: Model validation without external force [stage 2]
This video shows iterations from 2000 to 8000. In this part the shape of the droplet gets rounder, and the length of the bottom segment still increases in a relative fast speed. We add an average contact angle after 5000 iterations, and this value shows that the system is approaching to steady state.
Video 3: Model validation without external force [stage 3]
In the last 12,000 iterations the system comes closer to steady state. Shape and contact angle becomes more stable, and the increase of length of bottom segment becomes slower.
After 20,000 iterations, we think the system can be considered as close enough to steady state, and we move on to next stage: adding a uniform force field to all points in the system.
Video 4: Droplet in constant force field
We add every point a same force on positive x-axis. From the video we can see that the droplet evolutions very fast, time step of simulation has always been controlled in a level of 4x10-8. This shows that even after 20000 iterations, the time passed by is only equivalent to a few iterations in the previous videos. That’s also the reason why we only observe huge change in shape but nearly no change about whole droplet movement.
This simulation indicates a lot of potential applications. We can use it to simulate all kinds of filed operation or actions on micro/nano level particles. For example, if we can calculate the distribution of charge on droplet surface under an external electrical filed, we can simulate using a charged tip to drive or deform a micro particle. The program itself still needs to be improved, especially about how to make the simulation more efficient and control the time step, cutting and adding limit of segments in a better way, to make it adapt to various kinds of conditions.
