Packing Fibres Into Flocs

Flocs are stochastic clumps of fibres created by elastic, frictional and hydrodynamic forces. A reasonable premise is that a floc will be a local densification above the ambient random structure. Recent work of Parkhouse and Kelly [31] obtained a limiting cylinder packing density, c_vol^floc, say, by starting from the random structure and adding cylinders until no more could be fitted:

$$c_{vol}^{floc} = 2\, \frac{\log A}{A}$$ (9)

But for random structures we have:

$$c_{vol} = \frac{n_{contacts}}{2A}$$ (10)

It follows that our estimate of fibre contacts per fibre in a floc is:

$$n_{contacts}^{floc} = 4\, \log A$$ (11)

 

$$c_{vol}^{floc} = 2\, \frac{\log A}{A}$$ (12)

Which is roughly what is observed.