Recent measurements of the viscosity of polydimethylsiloxane (PDMS) melts swollen with dissolved carbon dioxide at 50 and 80 degrees C by Gerhardt et al. have shown that classical viscoelastic scaling factors can be employed to superpose the viscosity curves for CO2-swollen melts onto the viscosity curve for pure PDMS at the same temperature and pressure. Here a free volume expression for the viscosity of a diluted polymer melt is combined with equation-of-state theories for the volumetric properties of PDMS-CO2 mixtures to develop models for the CO2 concentration-dependent viscoelastic scaling factors, Both the Sanchez-Lacombe and Panayiotou-Vera equations-of-state are investigated for this purpose. The predicted viscoelastic scaling factors are found to be in very good agreement with the data of Gerhardt et al. The model predictions show that mixing of gaseous carbon dioxide into the swollen PDMS phase is highly non-ideal, and that significant free volume is added to the melt upon carbon dioxide dissolution. The free volume added to the melt by dissolved carbon dioxide is the principal mechanism for viscosity reduction, relative to pure PDMS, in this system.