  In the present work, we propose a consistent and conservative model for
multiphase and multicomponent incompressible flows, where there can be
arbitrary numbers of phases and components. Each phase has a background fluid
called the pure phase, each pair of phases is immiscible, and components are
dissolvable in some specific phases. The model is developed based on the
multiphase Phase-Field model including the contact angle boundary condition,
the diffuse domain approach, and the analyses on the proposed consistency
conditions for multiphase and multicomponent flows. The model conserves the
mass of individual pure phases, the amount of each component in its dissolvable
region, and thus the mass of the fluid mixture, and the momentum of the flow.
It ensures that no fictitious phases or components can be generated and that
the summation of the volume fractions from the Phase-Field model is unity
everywhere so that there is no local void or overfilling. It satisfies a
physical energy law and it is Galilean invariant. A corresponding numerical
scheme is developed for the proposed model, whose formal accuracy is 2nd-order
in both time and space. It is shown to be consistent and conservative and its
solution is demonstrated to preserve the Galilean invariance and energy law.
Numerical tests indicate that the proposed model and scheme are effective and
robust to study various challenging multiphase and multicomponent flows.
