Level set/Phase field with mass addition

Hello all,

I am trying to combine the level set/phase field method with mass addition, but I couldn't find a way to implement it. I saw that the level set/phase field examples in gallery basically follow mass conservation, but I wonder how could I apply boundary shape change at the same time? I've tried to add a moving mesh or deformed geometry module, but failed to evaluate. Anyone could share your experience?

Thanks a lot in advance!