  We propose a variant of the $\theta$-scheme for diffuse interface models for
two-phase flow, together with three new linearization techniques for the
surface tension. These involve either additional stabilizing force terms, or a
fully implicit coupling of the Navier-Stokes and Cahn-Hilliard equation. In the
common case that the equations for interface and flow are coupled explicitly,
we find a time step restriction which is very different to other two-phase flow
models and in particular is independent of the grid size. We also show that the
proposed stabilization techniques can lift this time step restriction. Even
more pronounced is the performance of the proposed fully implicit scheme which
is stable for arbitrarily large time steps. We demonstrate in a Taylor flow
application that this superior coupling between flow and interface equation can
render diffuse interface models even computationally cheaper and faster than
sharp interface models.
