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Inertial swimming in an Oldroyd-B fluid.

N Ali1, M Sajid2

  • 1Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan. nasir.ali@iiu.edu.pk.

The European Physical Journal. E, Soft Matter
|April 25, 2025
PubMed
Summary
This summary is machine-generated.

Fluid inertia enhances self-propelling sheet motion in complex fluids like Oldroyd-B and Maxwell fluids, unlike Newtonian fluids. Adjusting oscillation frequency or Deborah number optimizes swimming speed for these non-Newtonian fluids.

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Area of Science:

  • Fluid dynamics
  • Non-Newtonian fluid mechanics
  • Biophysics

Background:

  • Self-propelling objects in fluids are crucial in biological and engineering applications.
  • Understanding the role of fluid inertia and viscoelasticity in locomotion is key.
  • Previous studies often focused on Newtonian or second-order fluids.

Purpose of the Study:

  • To investigate the impact of fluid inertia on a self-propelling inextensible waving sheet in an Oldroyd-B fluid.
  • To analyze swimming velocity and rate of work done by the sheet.
  • To compare the behavior in Oldroyd-B, Maxwell, and Newtonian fluids.

Main Methods:

  • Analytical calculation of swimming velocity and work rate for small wave amplitude.
  • Analysis in the limit of small wave amplitude relative to wavelength.
  • Comparison across different fluid models (Oldroyd-B, Maxwell, Newtonian) and Reynolds numbers.

Main Results:

  • Newtonian fluid: Swimming speed decreases monotonically with increasing Reynolds number (R).
  • Oldroyd-B fluid: Swimming speed initially increases to a maximum then decreases asymptotically with R.
  • Maxwell fluid: Swimming speed increases monotonically with R. Limiting speeds differ across fluid types.

Conclusions:

  • Fluid inertia supports swimming sheet motion in complex (Oldroyd-B, Maxwell) fluids, contrary to Newtonian fluids.
  • Energy consumption at fixed speed is lower in Oldroyd-B than Newtonian fluids.
  • Maximum swimming speed can be achieved by tuning oscillation frequency or Deborah number.