Flow Reversibility Demonstration

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Flow Reversibility Demonstration

• Matthew Ernst
• Union College
• Fluids II

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Design of the Demonstration Apparatus

• Combination of 2 different demonstration designs
  as seen in the Shapiro video.

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How it works - Conceptually

• Low Reynolds Flow
• High viscosity µ 1.519 kg/ms
• Low velocity, small length scale
• Low Re ensures laminar flow
• No turbulence
• All low Re flows are reversible!

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How it works - Conceptually

• No slip at the walls
• Thin sheets or layers of fluid are pulled along
  by the inner cylinder
• Slip or shear between neighboring fluid layers
  develop the Velocity Profile in the annulus
  between the cylinders

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How it works - Mathematically

• Creeping Flow
• Model as Couette Flow
• Executing the Laplacian

(1)
Boundary Conditions U(r, 0) 0 U(a, t) a? U(b,
t) 0 a inner radius b outer radius
(2)
(3)
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How it works - Mathematically

• Solving

(4)
(5)
(6)
(7)
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Diffusion

• Fuzziness of recovered geometry
• Stretching out shape leads to easier diffusion

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References

• Cengel, Y.A., 2006, Fluid Mechanics Fundamentals
  and Applications, McGraw-Hill, New York, NY.
• Acheson, D.J., 1990, Elementary Fluid Dynamics,
  Clarendon Press, Oxford.
• Heller, J.P., Socony Mobile Oil Company Inc.,
  Field Research Laboratory, Dallas Texas.