Water tells two fibres apart

This collection carries three material tables. A density per fibre, a set of mechanical constants — modulus, tenacity, fineness, spinning translation, friction — and now a set of water constants.

Put cotton and viscose beside each other in the first two and something uncomfortable appears. Both are cellulose, so both have a density of 1.52 grams per cubic centimetre. Both are given a modulus of 8 gigapascals, because both are reported in the same range. Both have a fineness of 1.7 decitex.

So a 20 tex yarn of either has the same diameter to the last figure: 0.1671 millimetres. And a diameter is where every geometric result on this site starts.

What “identical” actually costs #

It is worth spelling out how far the identity reaches, because it is further than it first looks.

A diameter decides the cover factor at any sett, so both fibres give the same cover. It decides the jamming sett, so both jam at the same thread count. It goes into Peirce’s geometry as the thickness, so both give the same crimp at the same construction, the same weave angle, the same cloth thickness and the same position on the constant-thread-length locus.

The bending rigidity of a yarn is a modulus times a second moment, and this collection’s bracket runs from a free bundle of fibres to a coherent rod. Both ends are functions of the modulus, the fibre count and the diameter, and all three are the same. So the bending bracket is the same, and therefore the drape, the cantilever bending length, the shed tension and the beat-up force.

The shear locking angle is a diameter over a pitch, so that is the same. The pore between four threads is a function of the diameters and the setts, so the wicking is the same. The crossover length under a capstan grip is a friction coefficient, a wrap angle and a breaking load — and only the last of those differs.

Everything this collection computes about the structure of a cloth is the same number for the two fibres. The only place they part company dry is in strength, where cotton’s tenacity of 0.35 newtons per tex is nearly twice viscose’s 0.20.

Where water gets in #

Water separates them twice, and the two separations are independent.

Swelling. Viscose widens by thirty-five per cent in water against cotton’s twenty, and lengthens by four and two tenths per cent against cotton’s one and two tenths. That is 1.75 times as much transverse swelling and three and a half times as much axial.

Strength. Cotton is one of the very few fibres that is stronger wet — a ratio of about 1.10, reported between 1.05 and 1.20. Viscose loses half: a ratio of about 0.50, reported between 0.40 and 0.60. So a wet viscose yarn is at 0.45 of a dry cotton one’s strength where a dry viscose yarn is at 0.57 of it.

Those two facts are not a small addition to a table. They are the first thing this collection carries that distinguishes two materials its geometry treats as one, and they do so through exactly the door the geometry left open.

Cotton gets stronger wet, and that is genuinely odd #

Nearly every fibre that absorbs water loses strength when it does, and for an obvious reason: water gets between the molecular chains, the secondary bonds that were holding them to each other are replaced by bonds to water, and the fibre softens.

Wool loses fifteen per cent, silk eighteen, nylon twelve, viscose fifty. Cotton gains ten.

The accepted explanation is that a cotton fibre is not a bundle of parallel chains but a set of spiralling fibrils with a lumen down the middle, and that its dry failure is not a simultaneous failure of the whole section but a progressive one starting at the weakest place. Water lets the fibrils slide against each other slightly, which lets load redistribute away from a weak spot before it fails, and the gain from redistribution beats the loss from softening.

That is a structural explanation of a material property, which is worth noting on a site that keeps insisting structure comes before fibre. The one entry in the fibre table that runs against every other entry runs that way because of how the fibre is put together, one level down.

Flax does the same thing more strongly — about fifteen per cent stronger wet — and flax is the most highly organised of the natural cellulosics. Cotton and flax being the two fibres that gain, and both being cellulosic and both being fibrillar, is the kind of pattern that a table of ten fibres cannot establish and can only suggest.

What the two separations do to a cloth, separately #

The two are independent and it is worth following each through a fabric on its own, because they land in different places.

The swelling lands in the geometry. A viscose cloth’s critical swelling is the same as a cotton cloth’s of the same construction — the condition is about thread lengths and thickness and knows nothing about the fibre — but the swelling that has to be accommodated is 1.75 times larger. So a viscose cloth of the sheeting’s construction is very far past its boundary rather than a little past it, and would be compacted correspondingly harder.

Run the crossing-cover arithmetic on viscose and it crosses at 0.306 rather than cotton’s 0.230, which means a much wider band of viscose constructions grows rather than shrinks. That is a counterintuitive consequence of a fibre famous for shrinking, and the resolution is that the shrinking viscose garments in the world are knitted or loosely woven and are shrinking for the frictional reasons the relaxation ladder is about rather than the geometric ones here.

The strength lands in everything that breaks. The crossover length — the gripped length at which a thread breaks rather than slides, which is how far a cut edge frays — has the breaking load inside a logarithm. So halving a viscose yarn’s strength when it is wet shortens its crossover, which means a wet viscose frays less far than a dry one before the thread gives.

That is the opposite of what a garment does, and the reason is that a real wet viscose does not fray, it tears: the thread that would have been withdrawn breaks in the cloth instead. Which is the same statement read correctly, and a good example of why a length computed at a fixed force needs its question stated before it means anything.

The column that cannot be quoted #

There is a fourth column that would be more useful than any of these and it is not in the table: the wet modulus.

Every bending result in this collection runs on a modulus. The bracket a yarn’s rigidity lies in is a function of it, the drape follows from the rigidity, the shed tension follows from the modulus directly. So the natural question — what does a wet cloth’s bending do — needs a wet modulus, and there is not one to quote.

The reason is not that nobody has measured it. It is that the initial modulus of a fibre is the least reproducible of its mechanical constants even dry: it depends on the strain rate, the gauge length, the conditioning and where on the toe of the curve the tangent is taken, and this collection already carries cotton’s dry modulus as a range of 5 to 12 gigapascals — a factor of two and a half. A wet modulus measured by a different method in a different decade adds its own factor.

So the honest position is that this collection cannot compute what water does to a cloth’s stiffness, and saying so is better than picking a ratio and carrying three-figure answers on it.

What it can do is state the direction, which is not in doubt: every fibre that absorbs water is less stiff wet, cotton included, and the effect is large — a wet wool fibre’s modulus is a fraction of its dry one. So a wet cloth is limper than a dry one by more than its geometry alone would give, and every drape number in this collection is a dry number.

What survives the unknown #

Two results in this ladder survive not knowing the wet modulus, and it is worth being clear about why, because it is the same reason twice.

The wet relaxed construction of a balanced cloth. Where warp and weft are the same count in the same fibre, the two rigidities are equal whatever they are, the energy is symmetric, and the minimum sits at the symmetric state. Six of the eight cloths here are balanced, and their wet shrinkage is a geometric answer with no material constant in it at all. Run at both ends of the bracket and it does not move.

And every result that is a comparison. A wet modulus enters as a multiplier on both sides of any comparison between two constructions in the same fibre, so it divides out. Which of two cloths shrinks more, which drapes more, which locks sooner: all unaffected.

What does not survive is any absolute stiffness quoted wet, and there are none in this collection because it declines to compute them.

Regain, which separates them a third time and matters least #

There is a third water column and it is worth saying why it does the least work here.

Regain is the mass of water a fibre holds at ordinary room conditions as a fraction of its dry mass: cotton 8.5 per cent, viscose 13. So the two do differ, and by half again.

But regain enters this collection at only one place, and it is a bookkeeping one. Every yarn count is a conditioned mass, so the tex number a cloth is specified in already includes the fibre’s standard regain, and the diameter computed from it is a conditioned diameter. Viscose’s higher regain means that a 20 tex viscose yarn has slightly less dry cellulose in it than a 20 tex cotton one — 17.7 grams per thousand metres against 18.4 — and therefore a slightly smaller dry diameter.

That correction is not applied anywhere in this collection, for either fibre, and it is a systematic one of about half a per cent on a diameter. It is small enough to ignore and large enough that ignoring it should be said out loud rather than assumed.

It is also the one place where the two fibres’ identity above is not quite exact. Their conditioned diameters agree to the last figure and their dry ones do not, and which of those a model means is a question nobody usually asks.

The identity is an inconsistency, and it is worth two per cent #

The regain section says the two fibres’ conditioned diameters agree to the last figure and their dry ones do not, and puts the difference at about half a per cent. Working it through properly makes it larger and, more importantly, shows that the agreement is an artefact rather than a coincidence.

A diameter here is computed from a conditioned count and a dry density. That is inconsistent: the mass includes the water and the density does not, so the volume comes out too small.

Doing it consistently means adding the sorbed water’s own volume. For a 20 tex cotton at 8.5 per cent regain, the dry cellulose is 18.43 grams per kilometre occupying 12.13 cubic centimetres, and the 1.57 grams of water occupy 1.57 more — 13.70 against the 13.16 the dry-density route gives. A four per cent error in volume is a two per cent error in the diameter.

Every diameter in this collection computed for a hygroscopic fibre is about two per cent low, and with it every cover factor; every jamming sett is correspondingly high.

And it separates the pair before any water is added #

The correction is not the same for the two fibres, because their regains are not. Cotton picks up 2.0 per cent and viscose 2.9, so consistently computed,

a 20 tex viscose yarn is 0.9 per cent thicker than a 20 tex cotton one, dry-room dry.

That is small and it is not zero, and it arrives from the one column the essay treats as bookkeeping. The identity the whole essay is built on is a consequence of an inconsistency: the two fibres share a dry density, they are quoted at a conditioned mass, and using the first with the second erases the difference between them.

So the honest version of the essay’s finding is sharper rather than weaker. The geometry does not quite treat the two fibres as one — it treats them as one only because a conditioned mass has been divided by a dry density. Repair that and the pair separates by a per cent in every geometric result, which is far too small to matter and is not nothing, and the water columns still carry the whole of anything a reader would notice.

Which says how to state a diameter #

The practical form is a rule for the arithmetic rather than a new number.

A diameter computed from a count needs a density at the same regain as the count. Either use the conditioned mass with an effective conditioned density — 1.46 for cotton against cellulose’s 1.52, 1.44 for viscose, 1.26 for wool — or strip the regain out of the count first and use the dry density on the dry mass. The two routes agree; mixing them is what costs the two per cent.

That is exactly the shape of every state complaint in this collection. A mass and a density are both state-dependent, and they have to be quoted in the same state, in the way a thickness and a pressure do and a dimension and a relaxation do.

And it says where the error is largest. Polyester is unaffected and wool is worst, so the correction is biggest precisely for the fibre whose geometry this collection computes least and smallest for the one it computes most confidently — which is a fortunate accident and not a reason to leave it unrepaired.

What was counted, and how #

The diameters are identical, and that is asserted rather than observed. At three counts spanning a factor of six, cotton’s and viscose’s yarn diameters must agree exactly. A later change that gave viscose its own density would break that assertion and should — and the assertion is where it would be noticed, rather than in a figure whose two curves quietly separated.

And the water columns differ by a wide margin. Viscose’s swelling must exceed cotton’s by more than half again; cotton’s wet strength ratio must be above one and viscose’s below 0.7. Both are asserted as inequalities with margins rather than as values, because the values are measurements and the argument is about their relation.

Every working value is inside its own reported range, which is the check that catches a typing error rather than a modelling one, and it runs at import over all ten fibres and all four columns.

Where the model stops #

Nothing here explains either separation. Why viscose swells so much further is a question about how much of the cellulose is crystalline and how much amorphous — regenerated cellulose is far less ordered than native — and this collection does not model that. Why cotton gains strength wet is the fibrillar argument above, which is a description rather than a computation.

The wet-to-dry ratios are applied to a finished yarn. They were measured on fibres and on yarns and the two are not the same number, because a yarn’s strength is its fibres’ strength times a translation efficiency and water changes the friction that translation depends on. Wet fibres grip each other better, so a wet spun yarn should translate slightly better than a dry one, and that is not in the ratio here.

And there is no time in it. A viscose fabric that is wet, dried and wet again is not the same fabric; regenerated cellulose is the classic case of a fibre whose repeated wetting changes it permanently. This collection’s model recovers exactly.

The generalisation #

Two objects a model cannot distinguish are a test of what the model is about.

Cotton and viscose being identical in every geometric result here is not an embarrassment; it is the site’s own thesis stated as a fact. A weave’s behaviour is decided by how it is put together, and two fibres of the same density and the same modulus at the same count are the same input. The model is right to give the same answer, and a model that gave different answers would be smuggling something in.

The interesting question is then what would distinguish them, and the answer is: whatever they differ in. Here that is strength and water, so anything about breaking, fraying, tearing or washing separates them and nothing else does. That is a sharp and checkable prediction, and it is the sort of prediction a model only makes once somebody has noticed that it treats two things as one.

Look for the pairs a model cannot tell apart, and ask what would. It is a cheap way to find out what a model is really a model of.

Who found it, and when #

The wet-to-dry strength ratios are standard and have been tabulated since the 1930s; cotton’s gain and viscose’s loss are both textbook facts and both are widely used — cotton’s is why cotton is the fibre of choice for anything that will be laundered hard, and viscose’s is why a viscose garment is often labelled dry-clean when the same construction in cotton is not.

The fibrillar explanation of cotton’s wet gain is Meredith’s and dates from the 1940s.

What is this collection’s is nothing about the constants and only the observation about its own tables: that the two fibres are indistinguishable to every geometric computation here, so the water columns are carrying the whole of the difference.

Where the ladder goes next #

Into the finishing field, where the two shrinkages a cloth can have — one recoverable and one not — are measured by the same tape and are different mechanisms, and where this collection can now tell them apart.