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Benard instability

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i understand how one can produce such an effect, but is there any explanations on why these particular shapes appear and is there any significance to them besides then to release extra heat?

 

and can the usual shape structure be altered or does it always make the exact same pattern?

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here's the technical stuff, but since i have no love of mathematics(only use what i need) this stuff is greek to me.

 

http://www.lstud.ii.uib.no/~s1422/ber200/oppgave2/

 

 

basically, in a nutshell it's when a water is heated in a certain way like in a beaker, but the heat is introduced in such a way that it only heats a very thin(top) portion or layer of the water. placing a bunsen burner underneath the beaker will ruin the gig as the heat will be distributed more evenly and then boil.

but if it's(heat) is introduced in such a way that only the top thin layer is heated, it(water) forms a substance like a crust but has a distinct shape of a honecomb.

 

{edit: i think this is better linky} http://www.enseeiht.fr/hmf/travaux/CD0001/travaux/optmfn/hi/01pa/hyb72/rb/rb.htm

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