Simulations of microscopic propulsion of soft elastic bodies

David Urbanik, Shikhar Mani Dwivedi, Colin Denniston

Using simulations that realistically model both hydrodynamic and elastic behavior, we study the motion of a microscopic, driven elastic sphere immersed in water. We first confirm the "jittery" relaxation recently predicted theoretically for an externally driven elastic sphere. The sphere is then divided in two and each section is driven internally with the two sections 180°out of phase. With periodic and perfectly symmetric driving, the elastic sphere spontaneously breaks symmetry and can attain macroscopic average swimming velocities to the right or left, the direction depending only on the initial state. With asymmetric driving the elastic sphere swims in one direction and the maximum speed is obtained with a 1/3:2/3 split. At high drive frequencies close to elastic resonances of the sphere, the motion can be quite efficient. At low drive frequencies the propulsion speed becomes independent of the elastic constants of the sphere and less efficient, but still substantial. Inertia is found to be an important driver of the behavior despite the small size of the spheres. As we model the full three-dimensional elasticity and compressible hydrodynamics, our simulations give not just qualitative indications but quantitative predictions for the motion.