The kinematics of multi-phase flows is of crucial importance in developing and optimizing separation processes at laboratory and industrial scales. In this communication, we present a new model to describe the mass and momentum transfer of miscible ternary mixtures. Our model is based on the generalized bracket approach of nonequilibrium thermodynamics and used in combination with the generalized nonrandom two-liquid equation. The viscous drag between the components is formulated in terms of time evolution equations, making a straightforward formulation of boundary conditions possible. We not only account for gravitational effects but also for inertia, which is of practical relevance on various length scales including inertial microfluidics. The proposed general framework can be extended to complex fluids with internal micro-structures or chemical reactions. (C) 2018 Elsevier Ltd. All rights reserved.