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I'm curious about the physics behind the clumping of wet hair. More specifically, how the amount of water in hair and distance between hairs affect the clumping process. I know intuitively that when the amount of water reaches a level and the hairs are close enough, the liquid bridge formed between hairs can stick hairs together. I wonder is there any quantitative analysis or model of this phenomenon?

My background is computer science and I'm trying to simulate wet hair for visual effects.

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1 Answer 1

There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays

(freely available here, but for some reason I am not allowed to link to it normally: http://211.144.68.84:9998/91keshi/Public/File/34/482-7386/pdf/nature10779.pdf)

They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump together due to the water droplets on the fibers. They quantatively determine when the volume of liquid is sufficiently small to cause spreading between the fibers, thus clumping. The equation itself, without context, is not that useful so I advice you to read the paper and especially Eq. 2 and 3.

What I can explain here is the qualitative picture. They show a phase diagram (see below) which explains whether two fibres with a drop touching the two will have a fully spreading, partially spreading or non-spreading situation. Put in black-and-white, small droplets on long fibers will spread (i.e. clump), large droplets on short fibers don't. This is caused by an interplay between the liquid that energetically favors spreading (due to surface tension) and elasticity of the fibers that energetically favor a straight configuration that promotes non-spreading.

Fig 2d from Duprat et al. 2012 Nature
Fig 2d from Duprat et al. 2012 Nature

The dashed and solid curves in the phase diagram are Eqs. 2 and 3 respectively. So with these equations you should be able to model when hairs will clump.

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