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Optimal propulsive flapping in Stokes flows.

Loïc Was1, Eric Lauga

  • 1Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla CA 92093-0411, USA.

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Summary
This summary is machine-generated.

This study reveals optimal flapping motion for microscopic propulsion. The figure-eight pattern, similar to insect flight, is efficient across all Reynolds numbers.

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Area of Science:

  • Fluid dynamics
  • Biophysics
  • Robotics

Background:

  • Swimming fish and flying insects use flapping for thrust.
  • Microscopic organisms often use wavelike deformations.
  • Flapping motion with two degrees of freedom can theoretically generate net forces at all Reynolds numbers.

Purpose of the Study:

  • To compute the optimal flapping kinematics of a rigid spheroid in Stokes flow.
  • To analyze force generation and energetics of flapping motion.
  • To derive optimal flapping kinematics as a function of flapper shape and motion amplitude.

Main Methods:

  • Exact analytical solution for hydrodynamics, force generation, and energetics.
  • Analytical computation of the gradient of flapping efficiency.
  • Numerical derivation of optimal flapping kinematics.

Main Results:

  • Optimal flapping kinematics were derived for a rigid spheroid in Stokes flow.
  • Flapping efficiency gradient was computed analytically.
  • Optimal kinematics showed weak dependence on flapper shape.
  • Observed kinematics resemble the figure-eight motion of insect wings.

Conclusions:

  • Flapping motion is a potentially viable propulsion mechanism across all Reynolds numbers.
  • Optimal flapping kinematics are robust with respect to flapper shape.
  • The study provides insights into efficient propulsion for micro-scale systems.