Abstract Propagation of acoustic waves in non-isothermal dense media produces radiation-pressures whose nature is analyzed here. The case of a flux of thermal — rather than acoustic — energy can be analogously treated, and a molecular theory of thermal diffusion is accordingly formulated. p]The special case of thermal diffusion occurring within the liquid-filled channels of a thin partition — “thermodialysis” — is quantitatively analyzed within the frame of reference of the radiation-pressure approach. p]Some apparatuses developed for the experimental study of thermodialysis are described. The results obtained are discussed and shown to be in accord with the theoretical expectations.