Abstract: Methods and apparatus for mixing fluids which pass through a plurality of fluid passageways arranged as a repeating pattern of clusters which form a geometric array are disclosed. The axes of the passageways are offset from the overall flow axis which is essentially perpendicular to the end plane of the array and each passageway is arranged in a predetermined position. The fluid flows through the passageways with a velocity having two components including a mean flow component which is parallel to the flow axis and a nonaxial component which is perpendicular to the flow axis. Although each nonaxial component for those passageways forming any given cluster acts in a direction different from the others, they interact and cooperate with each other to induce the fluid to swirl in a generally orbital fashion around the flow axis while simultaneously advancing along the flow axis downstream of the array.