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Inertial swimming in an Oldroyd-B fluid
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
Summary
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.
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.
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