Imagine the following situation: I have a thin stationary water film, like a soap bubble, suspended inside a large ring. I throw a small loop of string onto the film and punch a hole inside it. How can I describe the motion of the hole in the water film bounded by the loop of string? The surface tension of the surrounding film will tend to minimize the ratio between the length of the boundary and the circumference, so the hole will disk shaped. Furthermore, if the weight of the string that bounds the hole is smaller than the weight of a water film with the surface given by the inside of two, then the effective mass of the hole will be negative, i.e. if the film is subject to a gravitational field, then the hole will tend to move upwards.
What is the correct way to describe such a system? How can I derive its equations of motion?