Textile Structure
how cloth is put together
Series

Water — the series

5 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. A cotton fibre dry and wet. One cotton fibre in its dry state and saturated with water, both drawn at the same scale in both directions. It is 20% wider and 1.2% longer, so its cross-sectional area rises by 44% if the section stays similar to itself. The length difference is drawn and is nearly invisible, which is the point: a swelling that were the same in both directions would make a cloth bigger and change nothing about its structure, and this one changes every ratio of a diameter to a spacing in the cloth. What the drawing cannot show is the section: a cotton fibre is not a cylinder, and the directly measured area swelling of 40% to 42% does not agree with the square of the width change, which is a fact about the fibre.

    What water does to a thread

    A cotton fibre in water is a fifth wider and a hundredth longer. If it grew equally in both directions a wet cloth would simply be a bigger cloth and nothing structural would follow; because it does not, every ratio of a diameter to a spacing in a cloth moves, and they all move the same way.

    part 1 · cloth
  2. A yarn's voids against its fibres' swelling. One cotton yarn's cross-section at a packing factor of 0.60, drawn dry and with every fibre swollen by 20% while the yarn's own outline is held. The fibres now occupy 0.864 of the section, which is above the 0.75 a heavily compacted assembly reaches and above the 0.65 of a spun yarn, so the yarn cannot stay this size: it must grow by at least 7.3%. What the drawing cannot show is disorder — the fibres are laid on a lattice here to make the areas exact, and a real yarn's fibres are neither round nor evenly spaced, which is why the bound is quoted over three packing limits rather than at one.

    A yarn's voids are not enough

    A ring-spun cotton yarn is sixty per cent fibre and forty per cent air, and its fibres gain forty-four per cent of area in water. The obvious thought is that the air takes it. The arithmetic says the air cannot, and gives a floor on how far the yarn itself must grow with no measurement of a yarn in it anywhere.

    part 2 · cloth
  3. One canopy, two opposite outcomes, decided by a sign. What a canopy does to a drop, for sheeting raised 32-fold. A rough surface multiplies the cosine of the intrinsic contact angle by its roughness ratio, which here is 2.0 — a hair is a cylinder and contributes πd of surface for every d of shadow. So a fibre that wets at all is driven to complete spreading, and one that does not is driven to a Cassie state sitting on 32.4% solid and air. The dashed diagonal is what the bare fibre would do; the canopy pushes every point away from ninety degrees, in whichever direction it already lay. Raising is therefore not a wetting treatment or a repellency treatment — it is an amplifier, and which one it turns out to be was settled by the chemistry before the raising machine was switched on. What the figure cannot show is which state a real drop reaches, because both are available near the hinge and the one it finds depends on how it arrived.

    The hairs decide the sign of the wetting

    Raising a cloth is not a wetting treatment and it is not a repellency treatment. It is an amplifier, and which of the two it turns out to be was settled in the dyehouse before the raising machine was switched on — by whether the fibre's own contact angle was above or below ninety degrees.

    part 3 · cloth
  4. Where a wet cloth keeps its water. For four cloths of this collection's own table, the share of the water a saturated cloth holds that sits inside the fibre as regain, between the fibres inside the yarn, and between the yarns in the cloth's own holes. muslin at 99 grams a square metre holds 183 per cent of its own weight, 4.6 per cent of it in the fibre; sheeting at 155 grams a square metre holds 113 per cent of its own weight, 7.5 per cent of it in the fibre; poplin at 100 grams a square metre holds 165 per cent of its own weight, 5.2 per cent of it in the fibre; duck at 207 grams a square metre holds 139 per cent of its own weight, 6.1 per cent of it in the fibre. The fibre's own water — the property cotton is sold on — is a twentieth to a thirteenth of the total, and the other nineteen twentieths are geometry. What the bars cannot show is the hair layer, which holds water outside all three of these and which this arithmetic has no place for.

    A cotton's own water is a twentieth of what a cloth holds

    A wet cloth keeps water in three places and only one of them is the fibre. A sheeting saturated holds 113 per cent of its own dry weight: 7.5 per cent of that inside the cotton as regain, 39 per cent in the channels between the fibres of its yarns, and 54 per cent in the holes four threads bound. The same construction in polyester, whose regain is a fortieth of cotton's, holds 105 per cent — an eight-point difference from a fortyfold one, because absorbency is a geometry with a fibre in it rather than a fibre with a geometry round it.

    part 4 · cloth
  5. The suction water supplies, against the pressure twist supplies. The pressure pressing a yarn's fibres together, against its twist, with the suction inside the menisci of a damp yarn's own pores drawn as a level. The suction is 0.0624 newtons a square millimetre — 2γ over the pore radius of 2.3 micrometres — and it does not depend on the twist at all. The twist's pressure crosses it at about 186 turns a metre, so water is worth as much as the first 186 turns and nothing more: at 600 turns it is 11 per cent of what the twist already supplies. What the chart cannot show is the saturation, at which the suction vanishes because a full yarn has no meniscus in it.

    A wet fibre is stiffer and a wet yarn is not locked

    The intuitive reason a damp cloth stiffens is that water pulls the fibres together — a meniscus is curved, the pressure inside it is below atmospheric, and the suction presses the assembly exactly as twist does. Computed, that suction is worth the first 186 turns a metre of twist and nothing after them: six per cent of what an ordinary yarn's twist already supplies, and nowhere near enough to stop the fibres sliding. What wetting actually does is fatten the fibres, and a fibre's bending rigidity goes as the fourth power of its diameter — so a wet cotton fibre is 2.07 times as stiff with no contact in the argument at all.

    part 5 · cloth

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