Analyzing Changes in Flagellar Shape and Swimming Speed with Varying Fluid Viscosity

Many different microswimmers propel themselves using flagella that beat periodically. The shape of the flagellar beat and swimming speed have been observed to change with fluid rheology. We quantify changes in the flagellar waveforms of Chlamydomonas reinhardtii in response to changes in fluid viscosity using (1) shape mode analysis and (2) a full swimmer simulation to analyze how shape changes affect the swimming speed. By decomposing the gait into the time-independent mean shape and the time-varying stroke, we find that the mean shape of the flagellum changes in response to viscosity, while the time-varying stroke does not. Using the swimmer simulation, we show that the observed change in swimming speed with viscosity is explained by the variations in mean flagellar shape and beat frequency.