Abstract: Transport processes such as emulsification, mass transfer, dissolution, washing or chemical reaction are carried out by admixing two substantially immiscible fluid phases with a rotary agitator having thereon filamentary elements that occupy 0.1% to 20% of the space to be swept thereby, whose thickness is 10-5000 .mu.m and whose thickness-to-length ratio is 1:5 to 1:5000, there being several thousand such elements on the rotor, that rotates at several thousand rpm, the elements having peripheral speed of at least 30 m/s.-- The operation is improved by also including in the fluid medium solid particles of a size 1-1000 .mu.m.