David Pine of New York University and colleagues at the Haverford College, the California Institute of Technology and the Israel Institute of Technology studied the motion of tiny polymer beads suspended in a viscous fluid trapped between two concentric cylinders held 2.5 millimetres apart. When the team rotated the inner cylinder in one direction and then back again, they found that the beads returned to their starting positions. But the behaviour is only seen if the solution is relatively dilute and the beads are stirred for a short time. At higher concentration and longer times, mixing becomes irreversible.

According to the researchers, the observed behaviour can be explained by collisions between individual beads. Mixing can be reversed if the particles do not collide with each other, which is the case at low concentrations. But as the solution becomes more concentrated -- and more collisions occur -- the process becomes irreversible.

"The irreversibility of these particles may be explained by the extreme sensitivity of their trajectories to imperceptibly small changes of the particle positions," explains Pine. Such perturbations might arise from almost anything – from small imperfections in the particles or by small external forces - and are magnified exponentially because of the motion of other particles suspended in the liquid, he says. Physical systems that exhibit such extreme sensitivity to small perturbations are said to be 'chaotic', which means that their behaviour cannot be determined in advance.

The US-Israel team says that an irreversible flow could be transformed into a reversible one at a predictable point by reducing the number of particles since this makes collisions between the particles less likely. This could be important for scaling up laboratory experiments to industrial levels, which is difficult simply because of the unpredictable behaviour of the particles involved. Possible applications include mixing of pharmaceutical suspensions and the catalysis of petrochemicals in fluid beds. The work could also help in understanding particle migration during ceramic processing and in the culture of blood-making cells.