Motivated by studies of the diffusion of a gas mixture in a Stefan tube, we present a hierarchy of mass transfer models with the species momentum balance and the species continuity equations as the basis. The simplifying conditions and the constitutive equations that lead to the equations of the mixture momentum balance approach are obtained. Further, the form that these equations should take for a multicomponent mixture is derived. These equations are shown to be a generalization of the Meyer–Kostin equations used to study binary diffusion in a Stefan tube. Additional simplifications that result in the so called classic approach to diffusion are identified. © 2016 Elsevier Ltd