Could you please be more specific? What kinds of liquids are you dealing with? What is the length scale of the interface – µm, cm, km? What do you do to the interface to deform it?

In small systems, interface shapes are governed by surface tension(s); the systems try to minimize interface areas (subject to constraints w.r.t. to material balance and apparatus geometry). In large systems, gravity may also play a role.

1- scale: small system (µm)

2- any kind of liquid

3- liquid-liquid interface deformations induced by radiation pressure from a laser or any kind of forces