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The prototypical diffuse-interface model that describes multi-component flowsis the Navier-Stokes Cahn-Hilliard model (NSCH). Over the last decades manyNSCH models have appeared that claim to describe the same physical phenomena,yet are distinct from one another. In a recent article [M.F.P. ten Eikelder,K.G. van der Zee, I. Akkerman, and D. Schillinger, Math. Mod. Meth. Appl. S.33, pp 175-221, 2023.] we have established a unified framework of virtually allNSCH models. The framework reveals that there is only a single consistent NSCHmodel that naturally emanates from the underlying mixture theory. In thecurrent article we present, verify and validate this novel consistent NSCHmodel by means of numerical simulation. To this purpose we discretize adivergence-free velocity formulation of the NSCH model usingdivergence-conforming isogeometric spaces. We compare computations of ourconsistent model to results of existing models from literature. The predictivecapability of the numerical methodology is demonstrated via three-dimensionalcomputations of a rising bubble and the contraction of a liquid filament thatcompare well with experimental data.

The divergence-free velocity formulation of the consistent Navier-Stokes  Cahn-Hilliard model with non-matching densities, divergence-conforming  discretization, and benchmarks