  We develop a low Mach number formulation of the hydrodynamic equations
describing transport of mass and momentum in a multispecies mixture of
incompressible miscible liquids at specified temperature and pressure that
generalizes our prior work on ideal mixtures of ideal gases and binary liquid
mixtures. In this formulation we combine and extend a number of existing
descriptions of multispecies transport available in the literature. The
formulation applies to non-ideal mixtures of arbitrary number of species,
without the need to single out a 'solvent' species, and includes contributions
to the diffusive mass flux due to gradients of composition, temperature and
pressure. Momentum transport and advective mass transport are handled using a
low Mach number approach that eliminates fast sound waves (pressure
fluctuations) from the full compressible system of equations and leads to a
quasi-incompressible formulation. Thermal fluctuations are included in our
fluctuating hydrodynamics description following the principles of
nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid
finite-volume numerical method developed in our prior work on binary liquid
mixtures, and use it to study the development of giant nonequilibrium
concentration fluctuations in a ternary mixture subjected to a steady
concentration gradient. We also numerically study the development of
diffusion-driven gravitational instabilities in a ternary mixture, and compare
our numerical results to recent experimental measurements in a Hele-Shaw cell.
We find that giant nonequilibrium fluctuations can trigger the instability but
are eventually dominated by the deterministic growth of the unstable mode, in
both quasi two-dimensional (Hele-Shaw), and fully three-dimensional geometries
used in typical shadowgraph experiments.
