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Yet more swimming pool physics

Imagine, if your mind can cope with it, Michael Phelps, decked in his speedos, about to dive into a pool of golden syrup.  If the thought isn't too much for you to cope with, now ask yourself what stroke he should swim to get to the other end as quickly as possible.

As explained in my last entry, Phelps in syrup is kind of like a bacterium in water. Movement is pretty difficult. And it's more than just because it's sticky in there, there is a deep physics reason as to why this should be.  In 'Life at Low Reynolds Number', Edward Purcell explains that movements that preserve time-reversal symmetry will get you nowhere if you have the misfortune to fall into a vat of syrup. Time-reversal what?  Let me explain.

Imagine a swimmer kicking her legs, or a scallop opening and closing its shell. If you were to take a movie of these actions, and play the movie backwards, it would look the same as if you were to play it forwards. You couldn't tell the difference. That's called time-reversal symmetry. Now, in a conventional swimming pool, kicking your legs will get you down the length, and on the seabed rapid opening and closing of its shell will get the scallop away from hungry starfish (see photo by my grandfather). But in syrup it won't.

Purcell explains that a movement with time-reversal symmetry cannot get you anywhere at low Reynolds number (the sticky realm that bacteria inhabit). After one cycle of movement is finished, you are back where you started - any movement the scallop gets from opening its shell is exactly cancelled by the movement it gets when closing it.  That means (i) Bacteria cannot employ a scallop-style open-close mechanism to propel themselves, and (ii) if you fall into a vat of syrup thrashing around won't help you - you'll need to start thinking physics to escape.

To get yourself somewhere, you need a motion that looks different if you were to play a film of it backwards. One way to do this is to corkscrew - if you continually revolve yourself clockwise then the film of that played backwards would show you going anticlockwise - that is, you've broken the time-reversal symmetry. And that is what some bacteria do - they have corkscrew shaped flagella which they continually rotate in the same direction. That's bizarre because they need to have a joint that allows free rotation - not an easy thing to engineer in  something large, let alone something a few microns in size.  And that's all because of physics.

Knowing this, I shall be entering the 100 metres syrup freestyle at the  London Olympics, and fully intend to win it, swimming clockwise-corkscrew.

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