On the importance of material frame-indifference and lift forces in multiphase flows

In this paper, we discuss the importance of the Principle of Material Frame-Indifference, sometimes referred to as Objectivity, in multiphase flows. We first give a brief account of the formulation of a two-phase mixture and then indicate where and how this principle should be utilized. We will then give a brief review of the meaning of this principle in continuum mechanics and how it has been used in various fields of physics. We also give examples of frame-indifferent and frame-dependent constitutive relations which have been used in multiphase flow studies. The importance of lift forces is also discussed. Finally, we derive a general constitutive relation which is frame-invariant and general enough to be used in many applications.