  We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible
two-phase flows where the mechanisms of chemotaxis, active transport and
reaction are taken into account. The evolution system couples the Navier-Stokes
equations for the volume-averaged fluid velocity, a convective Cahn-Hilliard
equation for the phase-field variable, and an advection-diffusion equation for
the density of certain chemical substance. This system is thermodynamically
consistent and generalizes the well-known ``Model H'' for viscous
incompressible binary fluids. For the initial-boundary value problem with a
physically relevant singular potential in a general bounded smooth domain
$\Omega\subset \mathbb{R}^3$, we first prove the existence and uniqueness of a
local strong solution. When the initial velocity is small and the initial
phase-field function as well as the initial chemical density are small
perturbations of a local minimizer of the free energy, we establish the
existence of a unique global strong solution. Afterwards, we show the
uniqueness of asymptotic limit for any global strong solution as time goes to
infinity and provide an estimate on the convergence rate. The proofs for global
well-posedness and long-time behavior are based on the dissipative structure of
the system and the Lojasiewicz-Simon approach. Our analysis reveals the effects
of chemotaxis, active transport and a long-range interaction of Oono's type on
the global dynamics of the coupled system.
