A consistent and conservative model and its scheme for N-phase-M-component incompressible flows

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