SelfPropelling Bodies in Low Reynolds Number Flow

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Self-Propelling Bodies in Low Reynolds Number Flow

• genome.jgi-psf.org/ciona4/

By Jake Zwaik
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Low Reynolds Number Flow

• Reltlt1

• Viscous Forces gtgt Inertial Forces

• Viscous forces dominate the flow

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Effects on the Navier Stokes
Navier Stokes for incompressible flow of a
Newtonian Fluid
Low Reynolds Number Flow
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Resulting affects on Self-Propelling Bodies

• Flow is reversible
• Any reciprocating motion by the propelling body
  will neutralize itself and it wont move
• Time does not matter
• Only the pattern of motion is important

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Examples of Self-Propelling Bodies in Low
Reynolds Flow

• E. Coli
• Re10-4, typical speed 30 microns/sec
• Coasting distance 0.1 angstrom 0.01nm
• Human Version
• Swimming in a pool of molasses
• Cant move any part of body faster than 1 cm/min

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Demonstration

• Two types of propulsion each powered by a
  rubber band
• Rudder reciprocating motion
• Corkscrew non reciprocating motion

• Drawing of rudder motion

• Drawing of corkscrew motion

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Demonstration

• Tank of water µ0.893 x 10-3 kg/ms
• ?1000 kg/m3

• Tank of glycerin µ1 kg/ms
• ?1260 kg/m3

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The Big Idea

• Any propelling body with one degree of body will
  ultimately have a reciprocating motion
• Corkscrew has two degrees of freedom. It can
  translate and rotate. As a result, it has a
  velocity and angular velocity

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References

• Purcell, Edward M. "Life At Low Reynolds Number."
  American Journal of Physics 45 (1976) 3-11. 1
  June 2007 lthttp//brodylab.eng.uci.edu/jpbrody/re
  ynolds/lowpurcell.htmlgt.