  In this work, we propose a novel phase-field model for the simulation of
two-phase flows that is accurate, conservative, bounded, and robust. The
proposed model conserves the mass of each of the phases, and results in bounded
transport of the volume fraction. We present results from the canonical test
cases of a drop advection and a drop in a shear flow, showing significant
improvement in the accuracy over the commonly used conservative phase-field
method.
  Moreover, the proposed model imposes a lesser restrictive
Courant-Friedrichs-Lewy condition, and hence, is less expensive compared to
other conservative phase-field models. We also propose improvements on
computation of surface tension forces and show that the proposed improvement
significantly reduces the magnitude of spurious velocities at the interface.
  We also derive a consistent and conservative momentum transport equation for
the proposed phase-field model and show that the proposed model when coupled
with the consistent momentum transport equation results in discrete
conservation of kinetic energy, which is a sufficient condition for the
numerical stability of incompressible flows, in the absence of dissipative
mechanisms. To illustrate the robustness of the method in simulating
high-density ratio turbulent two-phase flows, we present the numerical
simulations of high-density ratio droplet-laden isotropic turbulence at finite
and infinite Reynolds numbers.
