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The hydrodynamics of a self-propelling swimmer undergoing intermittent S-start swimming are investigated extensively with varying duty cycle$$DC$$, swimming period$$T$$, and tailbeat amplitude$$A$$. We find that the steady time-averaged swimming speed$$\bar {U}_x$$increases directly with$$A$$, but varies inversely with$$DC$$and$$T$$, where there is a maximal improvement of$$541.29\,\%$$over continuous cruising swimming. Our results reveal two scaling laws, in the form of input versus output relations, that relate the swimmer's kinematics to its hydrodynamic performance: swimming speed and efficiency. A smaller$$DC$$causes increased fluctuations in the swimmer's velocity generation. A larger$$A$$, on the other hand, allows the swimmer to reach steady swimming more quickly. Although we set out to determine scaling laws for intermittent S-start swimming, these scaling laws extend naturally to burst-and-coast and continuous modes of swimming. Additionally, we have identified, categorized and linked the wake structures produced by intermittent S-start swimmers with their velocity generation.
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Dynamics of a self-propelled compound droplet
A recent experiment by Wanget al.(Soft Matt., vol. 17, 2021, pp. 2985–2993) shows that a self-propelled compound drop in a surfactant-laden solution can autonomously change its motion from a straight line to a spiraling trajectory, enhancing its capability for chemical detection, catalytic reaction and pollutant removal in a large fluid region. To understand the underlying physics of this peculiar motion, we develop a two-dimensional minimal model to study the swimming dynamics of a compound droplet driven by a self-generated Marangoni stress. We find that, depending on the Péclet number ($$Pe$$) and the viscosity and volume ratios of the two compound phases, the drop can swim in a variety of trajectories, including straight lines, circles, zigzag curves and chaotic trajectories. The drop moves in circles when its two components have comparable volumes. Otherwise, it shows other types of motions depending on$$Pe$$. Our simulation results for the circular motion at small$$Pe$$are qualitatively comparable to the experiment. The transition between zigzag and circular trajectories is mainly determined by the orientation of high-order modes with respect to the drop's swimming direction. For most compound drops, the speed decays as$$Pe^{-1/3}$$at high Péclet numbers as it does for a single-phase drop. A drop with two equal components undergoes a run-and-reorient motion due to the competition between the even and odd modes.
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- Award ID(s):
- 2135617
- PAR ID:
- 10578846
- Publisher / Repository:
- Published by Cambridge University Press: 03 November 2023
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 952
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.891
