Wicking — the series · Textile Structure

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.

part 1 · applied

A front on a thread with 8 per cent crimp. Three rows at one scale. The top row is the warp end laid out straight, with the wetted front marked at four equal quarters of its own length — which is where Washburn's law puts it at four times whose square roots are evenly spaced. The middle row is the same thread crimped at 8 per cent, so it covers 92.6 per cent of the paper the straight one did. The bottom row is the cloth, and the four fronts on it are the four above pulled back by 1.08. A coefficient is a length squared over a time, so it comes down by 1.1664 — exactly (1 + c)², with no property of the liquid or the fibre in it. The thread's thickness is not drawn and neither is the liquid: a meniscus in a 2.33 µm pore is finer than any line on this canvas.

Wicking is slower along a crimped thread

A front travelling up a warp end travels the thread's path, which is longer than the cloth by exactly the crimp. So the wicking coefficient measured on the fabric is the yarn's own divided by (1 + c)² — 14.3 per cent lost at eight per cent crimp, whatever the liquid.

part 2 · applied

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.

part 3 · finishing

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.

part 4 · applied

A wick reaches its ceiling in the time its cloth takes to dry

A drying cloth lifts water to a steady height and no further, and the question left was how long it takes to get there. The answer has no permeability and no surface tension in it. Where gravity is small the front climbs as the ceiling times the root of one minus a decaying exponential, and the exponential's time is the cloth's own pore water divided by the rate its faces lose water — the time the room would take to dry it. In an ordinary room that is half an hour, and the front is nine tenths of the way up in fifty-three minutes.

part 5 · applied

How high a strip wicks a finite supply, in four rooms. The steady height of the fine pore system's wicking front against the supply of sweat at the strip's foot, both on logarithmic scales, for a sheeting-weight strip in four rooms. Below each room's capacity the height is the supply over twice the evaporation from each face, a line of slope one that no cloth property moves. It meets the room's drying ceiling at the capacity — 43 g/(m·h) at 20 g/m²·h, ceiling 1064 mm; 100 g/(m·h) at 100 g/m²·h, ceiling 501 mm; 204 g/(m·h) at 400 g/m²·h, ceiling 255 mm; 400 g/(m·h) at 1500 g/m²·h, ceiling 133 mm — and past it the strip takes no more. The marks along the bottom are four sweat rates from rest to hard work, fed from a contact patch 50 mm tall.

A sweating cloth wicks as high as the room can dry it

Every wicking height so far has had its foot in unlimited water. Skin is not a reservoir: it supplies sweat at a rate, and a cloth fed at a rate stands where the supply equals what its faces lose — the supply over twice the evaporation, with no pore, fibre or thickness in it. The cloth decides only when it has had enough, and it says so all at once: the holes between its yarns stay empty until the fine pores are carrying ninety-nine per cent of what they can.

part 6 · applied

How tall a skin contact can be before its cloth floods. The tallest patch of skin contact whose cloth keeps the holes between its yarns empty, against the sweat rate, on logarithmic axes, for a sheeting-weight cloth in rooms evaporating 20, 100, 400, 1500 g/m²·h from each face. The patch evaporates from its outer face only and hands its surplus to the free cloth above, which spreads it until the fine system's capacity; so a contact floods when it is taller than 98.9% of that capacity over the surplus. Below the room's own evaporation rate no contact of any size floods. In an ordinary room a run floods any contact taller than 247 mm and hard work any taller than 90 mm.

Wicking borrows drying area from the cloth that is not touching

A shirt is fed with sweat across the whole of the skin it touches, not at the foot of a strip. Through its own thickness the cloth could pass sweat a hundred thousand times faster than a body makes it, so a patch pressed flat never lacks capacity; what it lacks is drying area, because it can give water to the room only from its outer face. Pressed flat everywhere, it floods as soon as the sweat exceeds the room's evaporation — light work, in an ordinary room. With free cloth above the contact, wicking carries the surplus to faces that are not touching, and the sweat decides how much area it needs: three times the contact's at a run, whatever the contact's size.

part 7 · applied