DO CYANOBACTERIA SWIM USING TRAVELING SURFACE-WAVES

Bacteria that swim without the benefit of flagella might do so by gene rating longitudinal or transverse surface waves. For example, swimming speeds of order 25 mu m/s are expected for a spherical cell propagati ng longitudinal waves of 0.2 mu m length, 0.02 mu m amplitude, and 160 mu m/s speed. This problem was solved earlier by mathematicians who w ere interest ed in the locomotion of ciliates and who considered the u ndulations of the envelope swept out by ciliary tips. A new solution i s given for spheres propagating sinusoidal waveforms rather than Legen dre polynomials. The earlier work is reviewed and possible experimenta l tests are suggested.