WHAT is the perfect swimming stroke? The answer, if you are stuck in a viscous fluid, is to change your shape quite drastically to haul yourself along. This kind of stroke could one day help microscopic robots swim faster and more efficiently through the human body.
To an extremely small swimmer, such as a bacterium, water feels thick and goopy. It is the equivalent of a person trying to swim through peanut butter. At such a small scale it becomes impossible to glide through water like a fish. And as physicists Frank Wilczek and Alfred Shapere discovered in 1989, if you swim without gliding then only the shape of your stroke, not how fast you do it, governs how far you go.
Now Joseph Avron, Kenneth Oded, and Omri Gat of the Technion in Haifa, Israel, have worked out the ideal stroke for one special case 鈥� a two-dimensional swimmer in a flat pool. They used some sophisticated geometry in their calculation, and had to define a new kind of drag coefficient. The conventional drag coefficient applies only to rigid shapes, so they worked out how to define a measure of the overall drag during a stroke where the swimmer changes shape.
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And their swimmer has to be highly elastic. They found that the most efficient stroke, with the least drag, means passing through a particular sequence of shapes from a long oval via a triangle to a broad oval and back again (see Diagram). The triangular stages are crucial to progress: the base of the triangle serves as an anchor to pull the narrow apex in behind it and then push a new tendril forward. The researchers compare the motion to walking, where the foot on the ground serves as an anchor for the rest of the body.
This will not be the last word on ideal swimming strokes. In this calculation, the fluid is two-dimensional, and a restricted set of shapes was tried out. 鈥淭he model we used was chosen for its theoretical merit: we could do explicit calculations with it,鈥� says Gat. It might still be possible to improve the efficiency of the stroke by tweaking the shape of the triangles, for instance, but Gat believes any new solution will still use the same anchor concept, as would the ideal stroke in three dimensions.
Several groups around the world are already experimenting with swimming robots whose microscopic descendants may one day travel through the body to take pictures or deliver medicines.
Boris Rubinsky of the University of California, Berkeley, who works on small swimming robots, says finding the most efficient way to travel is an important design criterion. Rubinsky says that it would be very easy for him to design a shape-changing robot to perform the stroke Gat and his colleagues prescribe. However the problems of providing a power supply, and making the robots microscopic, remain to be overcome.