New apparatus and methods are provided for the uniform mixing and dispersion of highly viscous flowable pastes, such apparatus comprising a body with a flow passage that is kept full of the material by pumping it under pressure. The passage is of constant flow cross-sectional area along its operative length and the ratio of its dimensions at right angles to one another changes cyclically and repeatedly along its length between a lower value and a higher value. In each stage each increase in ratio produces spreading deformation of the material from a compact mass to a thin sheet moving between closely spaced passage surfaces, and viscous shear in the material, while each decrease returns the moving material to a compact mass; the passage preferably has from 10 to 25 stages. Preferably, a rotatable core member extends through the passage so that it is annular, its rotation increasing the shear in the material above a minimum required for rheological plastic flow to facilitate the flow through the passage. The core member is rotated at a speed within the range 0.05 to 2000 RPM, preferably in the range 0.1 to 100 RPM.