Textile Structure
how cloth is put together
Series

Permeability — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. What a muslin passes, against how closely it is set. A muslin's air permeability at 100 Pa as the sett is closed from 6.9 to 34.2 threads per centimetre, with the two paths separated. The channels between the threads carry 8285 mm/s at the open end and 1330 at the close one, and they go to zero when the cloth jams. The threads themselves carry 1.7 to 6.4 mm/s and never go to zero at all, because a thread is sixty per cent fibre whatever the sett is. Extended to a cloth with no channel left, that path is 8.1 mm/s — a floor set by the yarn rather than by the construction, and a specification asking for less has asked for a fabric that cannot be woven from this yarn at any sett.

    A cloth stops having holes before it stops passing air

    Close a woven cloth up and the channels between its threads shut. What passes through it does not go to zero, because a thread is sixty per cent fibre and forty per cent air and stays that way whatever is done to the construction. So a fabric's permeability has a floor, the floor belongs to the yarn rather than to the weaver, and no sett on any loom reaches it.

    part 1 · applied
  2. Where Poiseuille's rule starts being true of a cloth. Every account of a fabric's air permeability quotes the fourth power: flow down a channel goes as the fourth power of its width, so a small change of sett is a large change of flow. That is Poiseuille's result and it is about the viscous drop. A channel through a cloth is about as long as it is wide and the air in it is moving fast, so most of the pressure goes on giving that air its kinetic energy instead — and the inertial term does not depend on the hole's size at all. Plotted against cover, the viscous share of the drop runs from 1.0 per cent in an open muslin to 61.6 in a close one, passing half at a cover of 0.571. Quoting the fourth power alone below that is wrong by a factor rather than by a correction: at the open end it overstates the flow 98-fold.

    The fourth power is a close cloth's rule

    Every account of a fabric's air permeability quotes the same thing: flow down a channel goes as the fourth power of its width, so a small change of sett is a large change of flow. That is Poiseuille's result, it is about the viscous drop, and in an open cloth the viscous drop is two per cent of the pressure. The rule becomes true as the cloth closes, and where it starts being true is a number.

    part 2 · setting
  3. Four ways of closing a muslin, and the floor under all of them. The same muslin at four states: as woven, calendered to 3:1, wetted so its fibres swell by 20 per cent, and with the channel between its threads gone altogether. Air permeability at 100 Pa falls from 3505 mm/s to 8.1 — a factor of 434 — and stops there. The last figure is not a cloth with no holes in it: it is a cloth whose only remaining path is through the threads, which are sixty per cent fibre whatever is done to the construction. That number is the floor, it is a property of the yarn, and no sett reaches it. Note that the two middle routes are not in a fixed order: a 3:1 calender closes more than this swelling and a 2:1 calender closes less, so which is the stronger depends on how far each is taken.

    A windproof cloth is at its yarn's limit

    Windproof is a threshold on air permeability, and it is the only fabric specification on this site that the construction cannot settle. No weavable sett of an ordinary shirting yarn gets within two hundred times of it, layering the cloth barely helps because the resistance is inertial rather than viscous, and the floor set by the yarn's own porosity lands on the same order as the threshold with a fivefold bracket around it.

    part 3 · applied
  4. Where a muslin's air goes, as the cloth is set closer. A permeability computed from the average hole says nothing about which holes the air uses, and once the holes have a spread the answer is: not many of them. Two curves, both over the same population of holes — the share of the flow carried by the widest tenth, and how few of the holes carry half of it. At 16 ends per centimetre the cloth is nearly democratic: the widest tenth takes 12% and half the air needs 45% of the holes. At 44 the widest tenth takes 53% and half the air goes through 8.8%. Both inputs move together as the cloth closes — the spread in the holes rises because the spacing is fixed and the diameter is not, and the exponent rises because the pressure drop stops being inertial — so the concentration rises faster than either.

    Half the air goes through a tenth of the holes

    A permeability computed from the average hole says nothing about which holes the air uses. Once the threads have a spread, the answer is: not many of them — and in a close cloth, half the flow leaves through less than a tenth of the openings.

    part 4 · setting

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