Context : In massive-star binary systems , the interaction of the strong stellar winds results in a wind collision region between the stars , which is limited by two shock fronts .
Besides the nonthermal emission resulting from the shock acceleration , these shocks emit thermal ( free-free ) radiation detectable at radio frequencies that increase the expected emission from the stellar winds .
Observations and theoretical studies of these sources show that the shocked gas is an important , but not dominant , contributor to the total emission in wide binary systems , while it plays a very substantial role in close binaries .

Aims : The interaction of two isotropic stellar winds is studied in order to calculate the free-free emission from the wind collision region .
The effects of the binary separation and the wind momentum ratio on the emission from the wind-wind interaction region are investigated .

Methods : We developed a semi-analytical model for calculating the thermal emission from colliding stellar winds .
Assuming radiative shocks for the compressed layer , which are expected in close binaries , we obtained the emission measure of the thin shell .
Then , we computed the total optical depth along each line of sight to obtain the emission from the whole configuration .

Results : Here , we present predictions of the free-free emission at radio frequencies from analytic , radiative shock models in colliding wind binaries .
It is shown that the emission from the wind collision region mainly arises from the optically thick region of the compressed layer and scales as \sim D ^ { 4 / 5 } , where D is the binary separation .
The predicted flux density S _ { \nu } from the wind collision region becomes more important as the frequency \nu increases , showing higher spectral indices than the expected 0.6 value ( S _ { \nu } \propto \nu ^ { \alpha } , where \alpha = 0.6 ) from the unshocked winds .
We also investigate the emission from short-period WR+O systems calculated with our analytic formulation .
In particular , we apply the model to the binary systems WR 98 and WR 113 and compare our results with the observations .
Our theoretical results are in good agreement with the observed thermal spectra from these sources .

Conclusions :