Could a penguin swim in treacle?

You may think that it could move just the same as it does in water. Maybe it just goes slower? Or takes longer to get up to speed? To understand this scenario we have to look at an issue known as the scallop theorem.

Swimming has evolved independently a number of times, and different creatures employ very different techniques. Penguins swim by flapping their flippers, a motion that can be thought of as ‘flying’ in water. A scallop swims by opening its shell slowly and snapping it shut quickly, forcing water out of the shell opening. For both of these examples, the dominant forces are inertial.

Depending on the viscosity and density of the fluid, and size and speed of the swimmer, inertial forces may be insignificant compared to viscous forces. Such a regime is called the viscous limit, and the scallop theorem concerns movement in this limit. It says that to swim in this regime, the swimmer must perform a motion that doesn’t trace the same path if time is reversed. Reverse time and a scallop is still just opening and closing, exactly the same. Flapping is also useless – a penguin in the viscous limit would simply move forward and back by the same amount as its flippers move one way and then the other.*

Bacteria – the Olympic swimmers of nature


Bacteria cell structure

So how does anything move in the viscous limit? Having lived in this regime for billions of years, bacteria have solved this problem with remarkable style. The bacterial flagellum (a tail connected to a biological motor, well worth reading about in its own right) propels the bacterium by rotating the tail in a corkscrew motion. Turn time backwards and you can clearly see that it’s rotating in the other direction – it is not invariant under time reversal, and therefore it can produce movement in the viscous limit.

Going back to the penguin, the question is whether it is in the viscous limit. That depends on the size of the penguin, the speed it moves its flippers and the density and viscosity of treacle. As with many problems in the real world, the penguin in this scenario doesn’t conveniently slot into one extreme or the other. The answer is therefore that it probably could swim by flapping, but that viscous forces would have a big impact.

Question your assumptions

These examples (and my failure to choose a clear-cut one) serve to illustrate an important point. Living our lives in an environment dominated by inertial forces, our physical intuition fails us when we stray into this alien world. As scientists and engineers, having a sense of how a system works without calculating it is a very important skill. But what comes next is equally important – you must scrutinise your assumptions, and ask yourself if you’ve made any without realising. I chose the penguin example hoping that it would illustrate that it couldn’t swim in treacle despite your gut feeling that it could, and it was only when I calculated the Reynolds number that I realised I was wrong. I had wrongly assumed that the penguin in treacle would be in the viscous limit.

One of the best phrases you can read on an exam paper is ‘you may assume x is negligible’, but life isn’t an exam, and no one has carefully set up the problem for you. Physical intuition is invaluable, but it’s a skill to be wielded with caution and as part of a thorough, logical approach to understanding the situation you’re faced with.

*I've conveniently assumed the penguin doesn't rotate its flippers at all between the forwards and backwards flap. A motion that slices through the fluid in one direction and pushes it with a flat surface in the other would indeed work.

Isobel Ashbey

I am a Physicist in the Applied Science group, working across projects for consumer, industrial and energy clients. I have a particular interest in Biophysics and the human body but enjoy working on any projects with an Applied Physics element, including fibre optics, electromagnetism and thermodynamics.