Is there any applications of conformal mapping in fluid dynamics or precisely in the field of bubble dynamics?
The complex variable technique of conformal mapping is a useful intermediate step that allows for complicated airfoil flow problems to be solved as problems with simpler geometry. Using conformal mapping technique, the fluid flow around the geometry of an airfoil can be analyzed as the flow around a cylinder whose symmetry simplifies the needed computations. Because the functions that define the fluid flow satisfy Laplace’s equation, the conformal mapping method allows for lift calculations on the cylinder to be equated to those on the corresponding airfoil.
Sure, but you need the system to be quasi-2d, e.g. a Hele-Shaw cell. Check out the recent paper by Giovanni Vasconcelos:
"Multiple bubbles and fingers in a Hele-Shaw channel: complete set of steady solutions"
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9945270&fileId=S0022112015004693
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