What a Pool Table Can Teach You About Unstirring the Coffee  
     
  By KENNETH CHANG for The New York Times
     When cream is stirred into coffee, it is no surprise to see the swirls of white and brown become tan. It would be a shock if stirring in the opposite direction separated the liquid back to the original brown and white swirls.
      Physicists describe the stirring of coffee, as well as the billowing of smoke, the flow of heat, the decay of buildings and many other phenomena as "irreversible."
      The second law of thermodynamics essentially says that disorder increases. In the long term, this means that the universe will inevitably fall apart. In the short term, it means that you cannot unstir your coffee.
      Yet the basic physics of the universe does not demand the second law; it includes no such notion of irreversibility. And an experiment, described in the current issue of the journal Nature, shows that stirred liquids can be unstirred in some cases.
      Two physicists, David J. Pine of New York University and Jerry P. Gollub of Haverford College in Pennsylvania set up a device consisting of two concentric cylinders. In the gap, about a tenth of an inch wide, they poured a liquid with the viscosity of honey and hundreds of thousands of tiny beads of the same density as the liquid, so that they floated within in the liquid without rising or falling. The researchers traced the motion of about 60 of the balls that were dyed black.
      The researchers turned the inner cylinder clockwise - dragging along the liquid and the balls - and then turned it counterclockwise back to its original position. When the amount of turning was small, the balls all returned to virtually the same positions where they started. This behavior occurred only because the fluid was viscous.
      For a slightly greater degree of turning, then the balls started jostling around instead of ending up back at their starting positions. "The particles move all over the place," Dr. Pine said.
      The stirring had become irreversible.
      " What it implies is there is a sharp transition" between reversible and irreversible flows, said Troy Shinbrot, a professor of biomedical engineering at Rutgers University who was not involved in the research but did write an accompanying commentary in Nature.
      Dr. Pine and Dr. Gollub enlisted two other scientists, John F. Brady of the California Institute of Technology in Pasadena, Calif., and Alexander M. Leshansky at the Technion-Israel Institute of Technology, to help explain what was going on.
      Dr. Pine said they believed that the stirring became irreversible when the balls were significantly affected by more than one of their neighbors.
      For example, if the cue ball bounces off only one other ball, it is easy to imagine a pool shark making the reverse shot. But if the cue ball bounces off more than one other ball, then the shot becomes much more difficult to reverse.
      Stirring is not just a theoretical interest, either. The same phenomenon is important in manufacturing drugs, refining oil and understanding the movement of the Earth's interior.