We propose a theoretical framework to derive a consistent set of equations describing sedimentation, i.e. diffusion induced by the gravity (centrifugal) field, in a multi component system. This procedure starts from the combined 1) mass conservation law, 2) equation of motion, 3) volume continuity equation and 4) Nernst-Planck flux formulae. The method known as bi-velocity or Darken model is based on the postulate of a unique transport mechanism for volume and mass. The concentration profile in the equilibrium state is found by solving the nonlinear set of equations. Example applications of this theory applied to Bi-Sb system is evidence of sedimentation of substitutional atoms in condensed matter via diffusion mechanisms.