Hydrodynamic function of biomimetic shark skin: Effect of denticle pattern and spacing

The structure of shark skin has been the subject of numerous studies and recently biomimetic shark skin has been fabricated with rigid denticles (scales) on a flexible substrate. This artificial skin can bend and generate thrust when attached to a mechanical controller. The ability to control the manufacture of biomimetic shark skin facilitates manipulation of surface parameters and understanding the effects of changing denticle patterns on locomotion. In this paper we investigate the effect of changing the spacing and arrangement of denticles on the surface of biomimetic shark skin on both static and dynamic locomotor performance. We designed 3D-printed flexible membranes with different denticle patterns and spacings: (1) staggered-overlapped, (2) linear-overlapped, and (3) linear-non-overlapped, and compared these to a 3D-printed smooth-surfaced control. These 3D printed shark skin models were then tested in a flow tank with a mechanical flapping device that allowed us to either hold the models in a stationary position or move them dynamically. We swam the membranes at a frequency of 1 Hz with different heave amplitudes (from 1 cm to 3 cm) while measuring forces, torques, self-propelled swimming speed, and cost of transport (COT). Static tests revealed drag reduction of denticle patterns compared to a smooth control at low speeds, but increased drag at speeds above 25 cm s^-1. However, during dynamic (swimming) tests, the staggered-overlapped pattern produced the fastest swimming speeds with no significant increase in the COT at lower heave values. For instance, at a heave frequency of 1 Hz and amplitude of 1 cm, swimming speed of the staggered-overlapped pattern increased by 25.2% over the smooth control. At higher heave amplitudes, significantly faster self-propelled swimming speeds were achieved by the staggered-overlapped pattern, but with higher COT. Only the staggered-overlapped pattern provides a significant swimming performance advantage over the smooth control and the other two denticle patterns. Quantitative hydrodynamic comparisons among skin models where control over manufacture allows alteration of design parameters provides a useful experimental tool for future work on the considerable natural diversity of shark skin denticles both among species and on different body locations.