Difference between revisions of "Plateau's laws"

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They can be split into two observations that are true for bubble arrangements in general
 
They can be split into two observations that are true for bubble arrangements in general
  
# Soap films are made of entire smooth surfaces.
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* Soap films are made of entire smooth surfaces.
# The average curvature of a portion of a soap film is always constant on any point on the same piece of soap film.
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* The average curvature of a portion of a soap film is always constant on any point on the same piece of soap film.
  
 
and two further ones which are true if three bubbles are touching each other
 
and two further ones which are true if three bubbles are touching each other
# Soap films always meet in threes, and they do so at an angle of cos<sup>&minus;1</sup>(&minus;1/2) = 120 degrees forming an edge called a Plateau Border.
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*Soap films always meet in threes, and they do so at an angle of cos<sup>&minus;1</sup>(&minus;1/2) = 120 degrees forming an edge called a Plateau Border.
# These Plateau Borders meet in fours at the tetrahedral angle to form a vertex.
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* These Plateau Borders meet in fours at the tetrahedral angle to form a vertex.
  
 
These rules were later examined with the formalisms of geometric measure theory by Jean Taylor. He showed that these experimental rules have a close relation to the stability of the structures.
 
These rules were later examined with the formalisms of geometric measure theory by Jean Taylor. He showed that these experimental rules have a close relation to the stability of the structures.
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See also:
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[[Surface curvature#Minimal surfaces|Plateau's laws]] in [[Surface curvature]] in [[Surface tensions]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].

Latest revision as of 23:13, 24 November 2011

Plateu's laws are a set of rules, formulated in the 19th century by the Belgian physicist Joseph Plateau from experimental observations, that describe the structure of soap films in foams.

They can be split into two observations that are true for bubble arrangements in general

  • Soap films are made of entire smooth surfaces.
  • The average curvature of a portion of a soap film is always constant on any point on the same piece of soap film.

and two further ones which are true if three bubbles are touching each other

  • Soap films always meet in threes, and they do so at an angle of cos−1(−1/2) = 120 degrees forming an edge called a Plateau Border.
  • These Plateau Borders meet in fours at the tetrahedral angle to form a vertex.

These rules were later examined with the formalisms of geometric measure theory by Jean Taylor. He showed that these experimental rules have a close relation to the stability of the structures.


See also:

Plateau's laws in Surface curvature in Surface tensions in Capillarity and wetting from Lectures for AP225.