A piston-cylinder apparatus was established to measure the solubility and diffusivity of air in dimethyl silicone oils and in hydraulic oils based on the PVT state equation of air and the solution of unsteady one-dimensional diffusion equation. The measured diffusivity-temperature relation can be well fitted by the Arrhenius equation for engineering applications. The correlation between the solute diffusivity D and solvent viscosity mu is examined. In terms of Eyring's activation theory, the activation in the air-silicone-oil diffusion process is quite different from that in the momentum transport of the silicone oil: the activation entropy of the former is positive while that of latter is negative. However, the activation enthalpies of the two processes are in the same order of magnitude, which leads to the observation that D mu/T is roughly constant.