The transport theorem for an interface evolving across a fixed region (Q1891521)

Summary: The kinematics of interfaces is studied by means of methods and tools taken from the geometry of manifolds. As interfacial motion, i.e., a time-family of embedded submanifolds, is represented by means of an isotopy of a parameter manifold in the ambient space. The notion of superficial form is used to formalize the concept of density of extensive physical quantities; for superficial forms, a normal derivative operator is defined in terms of the Lie derivative operator. With this machinery, the proof of a transport theorem for interfaces that evolve across a fixed region of the ambient space turns out to be completely analogous to the classical proof of Reynolds Transport Theorem.