Textile Structure
how cloth is put together
Concept

Jurin's law — where it appears

The height at which a column of liquid in a capillary balances its own weight, published by James Jurin in 1718. It gives the equilibrium height and says nothing about how long the liquid takes to get there, which is a different law with a different exponent.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

The sett moves the flux and not the height. A 20 tex cotton yarn woven at every sett from 8 to 34 threads per centimetre. Above: the hole between the threads lifts from 27 to 234 mm as the cloth closes, while the space between the fibres lifts 6.37 m at every one of them — so the cloth's maximum is the flat line, and the sett does not touch it. Below: the permeability of those holes falls by a factor of 292 over the same range. Both curves are monotone, so there is no optimum — only an interval, ending at the jam at 34.6 threads per centimetre.

The sett decides how much, not how high

Every essay on wicking so far has found the sett deciding something. This one finds it deciding nothing at all: a cloth's maximum rise is 6.37 m at eight threads per centimetre and 6.37 m at thirty-four, because the sett cannot reach inside a yarn.

setting · Sett Two pore systems in one cloth — 24 threads per centimetre. A plain weave of 20 tex cotton in section, at 24 threads per centimetre, so the yarn is 167 µm across and the clear hole between two picks is 250 µm. That hole's hydraulic radius is 124.8 µm. Inside the yarn, fibres 14 µm across packed at 0.6 leave spaces of hydraulic radius 2.33 µm — 53 times finer, and by Jurin's law 53 times higher: 6.37 m against 119 mm. The yarn's interior is magnified 6 times and the two discs at the foot are the only part drawn at one scale.

How high a cloth wicks

A woven cloth has two capillary systems and they are a factor of twenty to a hundred apart. The one every diagram draws — the hole between four threads — lifts 119 mm. The one nobody draws, inside the yarn, lifts 6.37 m.

applied · Wicking The coarsest pore and the finest, in one muslin. A muslin's two pore systems asked the same question. Water at a contact angle of 120° is held back by a pore of radius r at a head of 2γ|cos θ|/ρgr, so the hole between four threads — hydraulic radius 134 µm — holds 56 mm of water, and the space between the fibres inside a thread — 2.50 µm — holds 2975 mm. Water takes the cheapest path, so the cloth leaks at the first of them and the second is never asked. Turn the contact angle round to a wetting one and the same two radii give a rise instead, and now it is the finest that decides, because that is the one that lifts highest: 5950 mm. One expression, two ends of a distribution, and the fabric's two properties read opposite ends of it.

The pore that wicks is the pore that leaks

A cloth's water resistance and a cloth's wicking are one expression, read at the two ends of a contact angle. The geometry cannot be chosen to give both, because it is the same geometry; the only thing that decides which a fabric does is a finish. And the two questions do not even read the same pore — a rise is set by the finest and a leak by the coarsest, so the same cloth lifts water three metres and holds it back at fifty-six millimetres.

finishing · Wicking How high each pore system stands while the cloth is drying. The height at which supply up the cloth balances loss from its faces, for the two pore systems, against the evaporation rate. The coarse system between the yarns barely moves — 137 millimetres at the dry end against 109 at the wet — while the fine system between the fibres falls from its sealed-tube height of 6375 millimetres to 52. The two cross at 1553 grams a square metre an hour.

A drying cloth cannot lift what a sealed tube can

Every rise on this account is an equilibrium in a sealed tube, and a garment is neither sealed nor at equilibrium. Balancing the supply up a strip against the loss from its faces gives a quadratic whose width cancels exactly: in an ordinary room the fine system between the fibres stands at 500 millimetres instead of 6.37 metres, keeping 7.9 per cent of what a tube would give it, while the coarse system loses a third of a per cent. The forty-sixfold advantage becomes 3.7, and in a drying wind it reverses.

applied · Wicking

Named alongside it

The objects these essays reach for when they reach for this one.

Hydraulic radiusWickingContact angleInter fibre porePacking factorPermeabilityPoiseuille's lawPore radiusTwo pore systemsWashburn's lawThe Young–Laplace pressureCover

All concepts