On the Reynolds transport theorem for three phase systems with storage in interfaces

In the paper, the Reynolds transport theorem (RTT) for three phase systems is developed, in terms associated with a moving control volume. The basic tools applied to the derivation are the generalized transport theorem by Truesdell and Toupin, and generalized surface transport theorem by Aris as well as Slattery. The final results referenced to a generic extensive quantity demonstrate the theorem in the integral instantaneous from. As a further illustration of applicability of the theorem relation developed some specific forms are deduced from such as for multiphase systems in terms of fixed control volume, surface systems and homogeneous spatial systems.