  Due to the potential application of regulating droplet shape by external
fields in microfluidic technology and micro devices, it becomes increasingly
important to understand the shape formation of a droplet in the presence of an
electric field. How to understand and determine such a deformable boundary
shape at equilibrium has been a long-term physical and mathematical challenge.
Here, based on the theoretical model we propose, and combining the finite
element method and the gradient descent algorithm, we successfully obtain the
droplet shape by considering the contributions made by electrostatic energy,
surface tension energy, and gravitational potential energy. We also carry out
scaling analyses and obtain an empirical critical disruption condition with a
universal scaling exponent 1/2 for the contact angle in terms of normalized
volume. The master curve fits both the experimental and the numerical results
very well.
