Scale plays a major role in locomotion. Swimming microorganisms, such as bacteria and spermatozoa, are subjected to relatively small inertial forces compared to the viscous forces exerted by the surrounding fluid. Such low-level inertia makes self-propulsion a major challenge. Now, scientists have found that the direction of propulsion made possible by such inertia is opposite to that induced by a viscoelastic fluid. These findings have been published in EPJE by François Nadal from the Alternative Energies and Atomic Energy Commission (CEA), in Le Barp, France, and colleagues. This study could help to optimise the design of self-propelled micro- and nanoscale artificial swimming machines to improve their mobility in medical applications.
Streamlines, velocity field, and magnitude of the share of the propelling flow attributed to the low level inertial force, in the case of touching spheres.
Credit: © Nadal et al.
The authors focus on two joined spheres of different radii - dubbed a dumbbell - rotating in a model fluid. They first use simulation to study the effect of a small-scale inertial force on the dumbbell's propulsion. They then compare it with results from theoretical calculations describing locomotion.
They demonstrate that despite the geometrical asymmetry, such a dumbbell cannot self-propel in a pure Newtonian fluid - which is a model fluid whose viscosity does not change with its flow rate - in the absence of inertia. This is because of the underlying laws of physics. If a dumbbell rotating in the counter-clockwise direction propels upwards in the absence of inertia, it would have to move downwards when rotating in the counter-clockwise direction. As both problems are mirror-image symmetric from each other, their propulsion should occur in the same direction and thus without inertia a rotating dumbbell cannot self-propel.
Furthermore, the study shows that a rotating dumbbell propels with the large sphere due to inertial forces in the fluid and the small sphere ahead in a pure viscoelastic fluid. With this in mind, the authors then derive the optimal dumbbell geometry for a self-propelling small-scale swimmer.