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

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