  Radio emission models of colliding wind binaries (CWBs) have been discussed
by Dougherty et al. (2003). We extend these models by considering the temporal
and spatial evolution of the energy distribution of relativistic electrons as
they advect downstream from their shock acceleration site. The energy spectrum
evolves significantly due to the strength of inverse-Compton (IC) cooling in
these systems, and a full numerical evaluation of the synchrotron emission and
absorption coefficients is made. We have demonstrated that the geometry of the
WCR and the streamlines of the flow within it lead to a spatially dependent
break frequency in the synchrotron emission. We therefore do not observe a
single, sharp break in the synchrotron spectrum integrated over the WCR, but
rather a steepening of the synchrotron spectrum towards higher frequencies. We
also observe that emission from the wind-collision region (WCR) may appear
brightest near the shocks, since the impact of IC cooling on the non-thermal
electron distribution is greatest near the contact discontinuity (CD). We show
that the thermal emission from a CWB can mimic a thermal plus non-thermal
composite spectrum if the thermal emission from the WCR becomes comparable to
that from the unshocked winds, and obtain a number of insights relevant to
models of closer systems such as WR140. Finally, we apply our new models to the
very wide system WR147. The acceleration of non-thermal electrons appears to be
very efficient in our models of WR147, and we suggest that the shock structure
may be modified by feedback from the accelerated particles. (Abridged).
