Textile Structure
how cloth is put together
What cloth is

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.
14 min read 6 figures Structure before fibreMeasured, not claimedExactly this many

Worth reading first: A yarn's voids are not enough · How high a cloth wicks · What water does to a thread.

How high a cloth wicks established that a woven cloth has two capillary systems and that they are a factor of twenty to a hundred apart: the hole between four threads lifts 119 millimetres and the channel inside the yarn lifts 6.37 metres. The pore that wicks is the pore that leaks read the same two against a hydrostatic head and found the rise set by the finest pore and the leak by the coarsest.

Both are about heights — how far water climbs, how hard it is pushed back. Neither asks the question a person holding a wet towel is actually asking, which is how much water is in it.

That question has three answers rather than two, because a cloth has a third reservoir the wicking arithmetic never needed. Water inside the fibre is not in a pore at all: it is taken into the cellulose’s own substance, it is what regain measures, and it is the property cotton is sold on.

It is also a twentieth of the total.

Three reservoirs, one construction

Every one of the three follows from numbers already computed for every cloth in the table.

Inside the fibre is the regain times the dry mass — 8.5 per cent for cotton at standard conditions, and saturated rather more. It does not drain and it is the only one of the three that changes the fibre’s own size, which is what water does to a thread.

Between the fibres is the yarn’s own void volume: a yarn at a packing factor of 0.6 is two fifths air, and that air is the channel system the wicking arithmetic gives a radius of 2.3 micrometres.

Between the yarns is the open area times the cloth’s thickness — the holes four threads bound, a hundred micrometres or so across and a cloth-thickness deep.

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.
Fig. 1 For four cloths of this collection’s own table, the share of a saturated cloth’s water in each of the three places. A sheeting at 155 grams a square metre holds 113 per cent of its own weight: 7.5 per cent of it inside the fibre, 39 between the fibres and 54 between the yarns. An open muslin holds 183 per cent and keeps 71 of it in its holes.

The fibre’s own water is between a twentieth and a thirteenth of what a cloth holds, across every cloth in the table, and the two geometric reservoirs hold the rest. That is the essay’s claim and it does not depend on a single quantity that is not already in the cloth’s specification.

A fortyfold range of regain is an eight-point range of absorbency

The consequence is easiest to see by changing the fibre and nothing else.

One construction in four fibres, and what each holds. The same cloth construction spun from four fibres whose regains run from four tenths of a per cent to sixteen, with the water each holds as a share of its own dry weight. cotton, regain 8.5 per cent: 113 per cent; wool, regain 16.0 per cent: 121 per cent; viscose, regain 13.0 per cent: 117 per cent; polyester, regain 0.4 per cent: 105 per cent. A fortyfold range of regain gives a 16-point range of absorbency, because the fibre's own water is a small part of the total and the geometry is the same in every row. What the bars cannot show is the contact angle, which decides whether the geometry fills at all and which is where a polyester actually differs.
Fig. 2 One construction spun from four fibres whose regains run from four tenths of a per cent to sixteen. Cotton holds 113 per cent of its dry weight, wool 121, viscose 117 and polyester 105. A fortyfold range of regain gives an eight-point range of absorbency, because every pore in every row is the same size.

A polyester cloth of the same construction holds 105 per cent of its own weight where a cotton one holds 113. That is not the difference anybody would predict from the fibres’ regains, which differ by a factor of twenty-one, and it is not the difference anybody’s experience of a polyester towel reports either.

The arithmetic is right and the experience is right, and the gap between them is the whole of what this account does not cover. What separates a cotton towel from a polyester one is not how much the geometry could hold; it is whether the geometry fills. A fibre with a contact angle above ninety degrees does not draw water into a two-micrometre channel at all — the Laplace pressure runs the wrong way — so a polyester cloth with a perfectly good pore system simply does not use it, and the hairs decide the sign of that before the water reaches the pores.

So the honest statement is a separation rather than a debunking. The capacity is geometry and the filling is chemistry, they are independent, and a specification that quotes one has said nothing about the other. Regain is a good predictor of absorbency in practice because it correlates with a low contact angle, not because the water it measures is much of the answer.

Which pore drains, and which does not

The three reservoirs do not empty together, and the order is fixed by the pores rather than by how much each holds.

The head each of a cloth's two pore systems holds against. Jurin's height for each cloth's two pores: the channels between the fibres inside a yarn, a couple of micrometres across, and the holes four threads bound, a hundred or so. muslin: 6.37 metres and 0.111; sheeting: 6.37 metres and 0.163; poplin: 6.37 metres and 0.140; duck: 6.37 metres and 0.084. The two differ by a factor of forty to seventy-five, so a cloth lifted out of water loses everything between its yarns before it loses anything inside them — the draining order is fixed by the pores and not by how much each holds. What the chart cannot show is the contact angle, which is taken as nought and which every height is proportional to the cosine of.
Fig. 3 Jurin’s height for each cloth’s two pores. The channels inside the yarn hold against 6.37 metres of water; the holes between the yarns against 0.08 to 0.16 metres. The two differ by a factor of forty to seventy-five, so everything between the yarns leaves before anything between the fibres does.

A cloth lifted out of water loses its cloth-scale water first. Gravity acting over a cloth’s own height — a hundred millimetres of hanging towel is a head of a hundred millimetres — exceeds what the hundred-micrometre holes hold and is a fortieth of what the two-micrometre channels hold. So the fifty-four per cent that was between the yarns drips out, the thirty-nine per cent between the fibres stays, and the seven per cent inside the fibre stays until the cloth is dried.

That has a consequence for how a towel is used and it is the opposite of the way absorbency is usually discussed. The water a towel takes off a body is the water in its holes, which is the reservoir that fills fastest and empties fastest; the water in its yarns is a reserve it cannot easily give up, and the water in its fibres is not available at all. A towel waccount out is a towel with its holes emptied and its yarns still full.

It also explains why a damp cloth feels damp long after it has stopped dripping: the quantity remaining is the two fine reservoirs, which hold against any head a hand can apply and which only evaporation removes.

A towel holds more water and a smaller multiple of itself

The construction absorbency is actually sold in is a pile, and the arithmetic says something about it that the specification does not.

What a pile buys a towel, and what it costs the ratio. A sheeting ground with a pile adding a stated multiple of its yarn, with the water it holds drawn two ways: as a share of its own dry weight, which is how absorbency is quoted, and in absolute grams a square metre. at 1 times the yarn it holds 113 per cent of its weight, 175 grams a square metre; at 3 times the yarn it holds 73 per cent of its weight, 337 grams a square metre; at 5 times the yarn it holds 64 per cent of its weight, 499 grams a square metre; at 7 times the yarn it holds 61 per cent of its weight, 661 grams a square metre. The ratio falls and the absolute rises, because a pile adds yarn and the voids inside it while adding nothing to the cloth's own holes. What the curves cannot show is the space between the loops of a real pile, which is a fourth reservoir this model has no term for and which is probably the largest one a towel has.
Fig. 4 A sheeting ground with a pile adding a stated multiple of its yarn, drawn two ways: the water it holds as a share of its own dry weight, and in grams a square metre. At five times the yarn it holds 64 per cent of its weight where the plain ground held 113, and 499 grams a square metre where the ground held 175.

Adding pile raises the water held and lowers the ratio. The reason is in which reservoirs a pile adds to: it multiplies the yarn, and therefore the void volume inside the yarn and the regain in the fibre, and it adds nothing at all to the cloth’s own holes, which are a property of the ground’s construction. So the dry mass rises in proportion to the pile and the water rises more slowly.

A towelling specification quotes grams a square metre and an absorbency as a percentage, and by this arithmetic the second falls as the first rises for a fixed ground. Two towels of the same absorbency ratio and different weights hold quite different amounts of water, and the heavier is the better towel by the measure that matters.

The model is missing the largest term here and it is worth saying so before anybody uses these numbers. A real pile’s loops stand off the ground and the space between them is a fourth reservoir, coarser than any of the three and probably larger than all of them, which this arithmetic has no term for. What the pile curve establishes is the direction and the mechanism, not the size.

What it does to the collection’s own wet arithmetic

Three earlier results treat a wet cloth as a cloth with water in it, and the three reservoirs say which of them is about which water.

A yarn’s voids are not enough asks whether a yarn’s air can absorb its fibres’ swelling, and finds it cannot: a cotton yarn is forty per cent air and its fibres gain forty-four per cent of area, so the yarn itself must grow. That is about the second reservoir and about the first, and the third does not enter — the swelling happens inside the yarn and the cloth’s holes are spectators.

A wet cloth is set closer than it was woven and the swelling a cloth cannot take are about what the grown yarn does to the cloth’s geometry. Those consume the third reservoir: a swelling yarn closes the holes, so the reservoir that holds most of a wet cloth’s water is the one that shrinks when the cloth gets wet.

That is a genuine circularity in the reading and it is worth naming rather than resolving. The open area used here is the dry cloth’s, so the hole volume is the volume before the yarns swell into it. A wetted cotton’s cover rises by an eighth, which takes a sheeting’s open area from 24.5 per cent to something under 20, and the hole reservoir with it. So the largest of the three shares is computed at the wrong moment, and the correction runs against it: a saturated cloth holds rather less between its yarns than its dry construction says, and the fibre’s share of the remainder is correspondingly larger than a twentieth.

Working the two together — the swelling that closes the holes, the water that has to be somewhere while it closes them — is a fixed point rather than a calculation, and it has not been solved here. What can be said is the direction and a bound: the hole reservoir is between its dry value and its wetted one, a range of about a fifth, and the fibre’s share is between a twentieth and a sixteenth of the total.

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. voile at 58 grams a square metre holds 278 per cent of its own weight, 3.1 per cent of it in the fibre; muslin at 99 grams a square metre holds 183 per cent of its own weight, 4.6 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; sheeting at 155 grams a square metre holds 113 per cent of its own weight, 7.5 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.
Fig. 5 The same three shares over five cloths sorted by openness. A voile keeps most of its water between its yarns and a sheeting keeps rather less, so the correction for the swelling that closes those holes is largest exactly where the reservoir is largest. The fibre’s own share moves the other way and stays small throughout.

Why the shares are so alike across the table

Four quite different cloths give three shares that vary less than they might, and the reason is a cancellation worth naming.

The fibre’s share is almost a constant. It is the regain over the sum of the three volumes divided by the dry mass, and both the numerator and the largest part of the denominator scale with the yarn — so a heavier cloth has more bound water and proportionally more void volume, and the ratio hardly moves. Across the four cloths it runs from 4.6 per cent to 7.5, on cloths whose weights differ by a factor of two.

The other two trade with the open area and with nothing else. The void volume is the yarn’s, so it rises with the cloth’s weight; the hole volume is the open area times the thickness, so it falls as the cloth closes. A muslin at 38 per cent open keeps 71 per cent of its water in its holes and a sheeting at 24 per cent keeps 54.

So the three-way split is really a one-parameter family, and the parameter is the open area. A cloth’s reservoirs are decided by how open it is and almost nothing else — which is the same conclusion the cover factor reaches about half the other properties of a cloth, arriving at a volume rather than at a shadow.

The absorbency a specification quotes is the wrong one twice

Absorbency is sold as a percentage of dry weight, and the arithmetic says that number is the wrong one in two independent ways.

It divides by the thing a buyer is not choosing. A towel’s job is to take water off a body, which is a quantity in grams and not a ratio. Dividing by the towel’s own weight rewards a light towel for being light — and by the pile arithmetic a light towel holds a higher percentage and less water. The ratio and the quantity move in opposite directions across the range a towel is actually made in, so the specification is not merely imprecise; it ranks backwards.

And it measures the reservoir that leaves first. A test that saturates a specimen and lets it drip is measuring what remains after the coarsest reservoir has partly emptied, and how much has emptied depends on how long it dripped and how high it hung. That is a head, the head is a metre or two of test rig, and the three reservoirs’ thresholds straddle it — so a standard test’s result sits on the steep part of a staircase and is sensitive to the rig.

What a pile buys a towel, and what it costs the ratio. A muslin ground with a pile adding a stated multiple of its yarn, with the water it holds drawn two ways: as a share of its own dry weight, which is how absorbency is quoted, and in absolute grams a square metre. at 1 times the yarn it holds 183 per cent of its weight, 181 grams a square metre; at 3 times the yarn it holds 96 per cent of its weight, 285 grams a square metre; at 5 times the yarn it holds 78 per cent of its weight, 389 grams a square metre; at 7 times the yarn it holds 71 per cent of its weight, 493 grams a square metre. The ratio falls and the absolute rises, because a pile adds yarn and the voids inside it while adding nothing to the cloth's own holes. What the curves cannot show is the space between the loops of a real pile, which is a fourth reservoir this model has no term for and which is probably the largest one a towel has.
Fig. 6 The same pile arithmetic on an open muslin ground rather than a sheeting. It starts higher, because a muslin’s holes hold 71 per cent of its water against a sheeting’s 54, and falls faster, because the pile adds yarn to a cloth whose holes were the larger share. Both curves say the same thing about the specification: the multiple falls while the quantity rises.

The quantity a buyer wants is grams a square metre of water held after a stated head, and every term of it is computable from a construction. That it is computable from a construction and the trade quotes something else is the ordinary shape of the gap between a model and a standard, and it is the same gap a grade and a yield open in the applied field: the standard measures what was cheap to measure, and the decision needs something else.

What was computed, and how

Each cloth’s yarn length in a square metre comes from its setts and its crimps; its dry mass from that and the counts; its fibre volume from the mass and the fibre’s density; its yarn volume from the packing factor. The void volume is the difference. The hole volume is the open area — one minus each system’s cover, multiplied — times the cloth’s own computed thickness. The bound water is the regain times the dry mass. The two pore radii are the hydraulic radii of the two pore systems, and the head each holds against is Jurin’s height at a contact angle of nought.

Five things must hold. Every cloth holds water in all three places, so none of the shares is a rounding. The fibre’s own water is the smallest of the three on every cloth, which is the essay’s claim tested rather than described. The cloth’s pore is more than ten times the yarn’s in radius on every cloth, and the yarn’s therefore holds against more than ten times the head — the two halves of the draining order, tested separately so that a slip in the radius or in Jurin’s height would fail one of them. And an opener cloth holds a larger share of its water in its holes, at every step of the table sorted by open area.

The regains, the fibre densities and the packing factor are quoted; the setts, counts, crimps and thicknesses are each cloth’s own.

Where the model stops

Saturated is not defined here. The three volumes are the geometry filled completely, which is what a cloth pulled out of a bath holds for the moment before it drips. A standard absorbency test measures something else — a stated time, a stated drip, a stated centrifuge — and every one of those is partway down the draining order.

The regain is a standard-conditions figure and a soaked fibre takes more. Cotton’s 8.5 per cent is its regain at sixty-five per cent humidity; in liquid water it takes rather more, so the fibre’s share here is a floor. Doubling it would still leave it the smallest of the three.

The hair layer is not counted. A cloth’s surface is a population of protruding fibre, and the water held among those hairs is outside all three reservoirs — a fourth term, at the coarsest scale of all, which drips fastest and which nothing here computes.

And the pile’s own interstices are missing, which is the same omission one level up and is the one that matters for a towel.

Still open: what a waccount towel actually has left

The draining order is a prediction and it is measurable with a balance and nothing else.

Take a cloth of known construction, saturate it, and weigh it after each of four treatments: dripping under gravity, blotting, wringing, and centrifuging at a stated force. Each of those is a head, and the arithmetic above says what each should remove: gravity over the cloth’s own height removes the holes, a wringing pressure of a few kilopascals removes the holes and some of the yarn, and a centrifuge at a few hundred g begins to reach the two-micrometre channels.

The prediction is a staircase rather than a curve — long flat stretches where a head is between the two pores’ thresholds and nothing further comes out, with steps where a threshold is crossed. A smooth curve would refuse the two-pore model, and a staircase with its steps at 0.1 and 6 metres of head would confirm it in the one place the wicking essays could not, which is the volumes rather than the heights.

Who worked it out

Regain, packing factors and open areas are standard and tabulated. The two pore systems are the reading of a woven cloth built up in the wicking essays. Adding the fibre’s own water to them as a third reservoir, computing the three shares from one construction, and finding the fibre’s the smallest of them were done here.

Where this goes next

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. 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. 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.

Shares its objects with

Essays naming at least two of the same things, that neither author linked.

Named objects

A flat tag is an object no other essay names yet.

MoistureOpen areaPacking factorRegainTwo pore systemsWaterWicking