This contribution aims to theoretically describe the most common cases of mass and molar density inversions, as they can be observed in multi-component fluid mixtures in sub-critical phase equilibrium. These phenomena - also known as barotropy - affect the relative position of phases in a gravitational field for the case of mass barotropy, while the total population of species along the interfacial length is drastically affected for the case of molar barotropy. Rigorous and analytical relationships are developed here to detect both mass and molar density inversions ending at the critical points of mixtures. These conditions, which are useful to describe the existence and persistence of density inversions, are then applied to unequivocally demonstrate that mass and molar barotropy are physically independent phenomena. Qualitative evidence pointing to that conclusion is discussed at the light of the global phase diagram of van der Waals mixtures composed by molecules of different size. Particularly, it has been established that molar density inversions appearing in feasible temperature ranges are sensitive to differences between the molecular hard core volumes of the constituents, a conclusion that is well supported by experimental results. Mass density inversions, in contrast, depend not only on the molecular size but also in the molecular weights of the constituents, in such a way that mixtures may exhibit mass barotropy without exhibiting molar inversions, and vice versa. Analytical relationships for establishing the slope of density inversions on a P-T projection have also been obtained both for mass and molar barotropy. From the comparison with the temperature slope of the three-phase line, we conclude about the possibility of observing density inversions between immiscible liquid phases or between a liquid and a gas phase. (C) 2015 Elsevier B.V. All rights reserved.