Methods and apparatus for controlling the movement of materials having different physical properties when one of the materials is a fluid. The invention does not rely on flocculation, sedimentation, centrifugation, the buoyancy of the materials, or any other gravity dependent characteristic, in order to achieve its desired results. The methods of the present invention provide that a first acoustic wave is propagated through a vessel containing the materials. A second acoustic wave, at a frequency different than the first acoustic wave, is also propagated through the vessel so that the two acoustic waves are superimposed upon each other. The superimposition of the two waves creates a beat frequency wave. The beat frequency wave comprises pressure gradients dividing regions of maximum and minimum pressure. The pressure gradients and the regions of maximum and minimum pressure move through space and time at a group velocity. The moving pressure gradients and regions of maximum and minimum pressure act upon the materials so as to move one of the materials towards a predetermined location in the vessel. The present invention provides that the materials may be controllably moved toward a location, aggregated at a particular location, or physically separated from each other.