Asymptotic approach to a rotational Taylor swimming sheet

Abstract

The interaction of a viscous fluid and a circular, pre-stressed active shell is studied in the limit of low Reynolds numbers. A seminal paper of Taylor represents a benchmark for this class of problems. Here, inspired by the same approach, we determine with asymptotic techniques the possible swimming motions of the shell for the particular changes of curvature that it can achieve when actuated. We confirm numerical results obtained previously, and highlight the structure of a problem that turns out to be similar to that of Taylor, and as such represents a simple example of Stokesian swimming.

Keywords

• Stokes flow
• Micromotility
• Morphing shells
• Perturbation series
• Low Reynolds swimming
• Circular disk