In this paper, we revise the structure of the residue curve maps (RCM) theory of simple evaporation from the point of view of Differential Geometry. RCM are broadly used for the qualitative analysis of distillation of multicomponent mixtures within the thermodynamic equilibrium model. Nevertheless, some of their basic properties are still a matter of discussion. For instance, this concerns the connection between RCM and the associated boiling temperature surface and the topological characterization of the distillation boundaries. In this paper we put in evidence the Riemannian metric hidden behind the thermodynamic equilibrium condition written in the form of the van der Waals-Storonkin equation, and we show that the differential equations of residue curves have formal gradient structure. We discuss the first non-trivial consequences of this fact for the RCM theory of ternary mixtures. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.