  We present a model for the creation of non-thermal particles via diffusive
shock acceleration in a colliding-wind binary. Our model accounts for the
oblique nature of the global shocks bounding the wind-wind collision region and
the finite velocity of the scattering centres to the gas. It also includes
magnetic field amplification by the cosmic ray induced streaming instability
and the dynamical back reaction of the amplified field. We assume that the
injection of the ions and electrons is independent of the shock obliquity and
that the scattering centres move relative to the fluid at the Alfv\'{e}n
velocity (resulting in steeper non-thermal particle distributions). We find
that the Mach number, Alfv\'{e}nic Mach number, and transverse field strength
vary strongly along and between the shocks, resulting in significant and
non-linear variations in the particle acceleration efficiency and shock nature
(turbulent vs. non-turbulent). We find much reduced compression ratios at the
oblique shocks in most of our models compared to our earlier work, though total
gas compression ratios that exceed 20 can still be obtained in certain
situations. We also investigate the dependence of the non-thermal emission on
the stellar separation and determine when emission from secondary electrons
becomes important. We finish by applying our model to WR 146, one of the
brightest colliding wind binaries in the radio band. We are able to match the
observed radio emission and find that roughly 30 per cent of the wind power at
the shocks is channelled into non-thermal particles.
