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Shubham Anand1, Jens Elgeti1, Gerhard Gompper1

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Flagellated microswimmers actively move towards areas of higher viscosity, a behavior termed positive viscotaxis. This response is influenced by flagellar properties and can lead to unique drifting trajectories in complex environments.

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Area of Science:

  • Biophysics
  • Fluid dynamics
  • Microbiology

Background:

  • Microorganisms and artificial microswimmers navigate environments using external cues.
  • Understanding flagellar propulsion is key to microswimmer behavior.
  • Near-surface dynamics are crucial for many microswimmer species.

Purpose of the Study:

  • Investigate the viscotaxis of eukaryotic flagellated microswimmers.
  • Analyze behavior in linear viscosity gradients in 2D.
  • Characterize the influence of flagellar parameters on reorientation.

Main Methods:

  • Modeling flagella as semi-flexible filaments with traveling waves of curvature.
  • Utilizing resistive-force theory for flagellar propulsion.
  • Employing numerical simulations and analytical theory.

Main Results:

  • Demonstrated positive viscotaxis: flagella reorient towards higher viscosity.
  • Quantified rotational velocity dependence on gradient strength, beat amplitude, speed, and wavelength.
  • Observed trochoid-like trajectories in response to asymmetric wave forms and gradients.
  • Found that flagellar deformability significantly reduces viscotatic response.

Conclusions:

  • Beating flagella exhibit robust positive viscotaxis.
  • Viscotatic response is universally described by a function of the sperm number.
  • Asymmetric flagellar dynamics can lead to complex gradient-perpendicular trajectories.