Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session X06: Biofluids: General Locomotion II
8:00 AM–10:36 AM,
Tuesday, November 21, 2023
Room: 102B
Chair: Xuanhong An, San Jose State University
Abstract: X06.00008 : Dispersion Relations for Undulatory Locomotion in Nematodes
9:31 AM–9:44 AM
Presenter:
Christopher J Pierce
(Georgia Institute of Technology)
Authors:
Christopher J Pierce
(Georgia Institute of Technology)
Lucinda Peng
(Georgia Institute of Technology)
Daniel Irvine
(Georgia Institute of Technology)
Xuefei Lu
(Georgia Institute of Technology)
Hang Lu
(Georgia Institute of Technology)
Daniel I Goldman
(Georgia Tech)
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'>λ style='mso-bidi-font-style:normal'>2f∝λ2, implying that a single ‘dispersion relation’ governs undulatory wave propagation despite differences in the form of external resistive forces. To explain this, we derived a theoretical dispersion relation for swimming in a fluid by regarding the nematode as a viscoelastic beam in a low-Re, Newtonian fluid, following Fang-yen et al (PNAS, 2010). Our model shows that to maintain force balance, waves must obey the observed scaling relation. Furthermore, experimentally derived model parameters lead to good quantitative agreement with the model. Surprisingly we find that the addition of elastic terms to the external drag has no effect on the real part of the dispersion relation, instead modifying the imaginary part. This implies that the presence of elasticity does not affect the f-λ scaling relation but can influence the 'evanescent' decay of undulations over time. Overall, we find that mechanical constraints arising from the structure of the equations of motion lead to common dispersion relations across different environments. This may help nematodes maintain consistent speeds by managing the tradeoff between wave efficiency (set by λ) and undulation speed (set by f) across terrains.
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