Textile Structure
how cloth is put together
Concept

Dye affinity — where it appears

How strongly a fibre takes a dye out of the bath: the ratio of the dye held in a unit of fibre to the dye in the liquor beside it at equilibrium. A high affinity slows the dye's advance into a yarn, so it decides how deep a short dip reaches.

Named by 6 essays across one field — each of them below, with the objects they name alongside it.

One dip, two yarns: the same depth of dye. The cross-section of two cotton yarns drawn to one scale after a 20-second dip in a bath whose dye the fibres take up 10 times as strongly as the liquor holds it, each fibre shaded by the dye that reached its distance from the surface. 20 tex: 118 fibres, 167.1 µm across, dyed to 19.7 µm — 24% of its radius and 42% of its section; 74 tex: 435 fibres, 321.4 µm across, dyed to 18.2 µm — 11% of its radius and 21% of its section. The depth in micrometres is the same for both because a dip dyes a depth; the share is not, because the coarse yarn has more section behind the same ring. The fibres are drawn on a lattice and the count is computed; the affinity is an assumed value and every depth moves with its square root.

A dip dyes a depth, not a share

A yarn dyed after spinning is a cylinder the dye has to diffuse into through the liquor between its fibres, and the fibres slow it by taking dye out of the liquor as it passes. A twenty-second dip therefore dyes to a depth, some tens of micrometres, and that depth is almost the same in a fine yarn and a coarse one. So the same dip that colours two fifths of a shirting yarn's section colours a fifth of a denim warp's; eight dips deepen the shade eightfold and leave the ring where it was; and a tighter yarn rings more thinly, because packing closes the pores faster than it narrows the yarn.

finishing · Dyeing A ring-dyed yarn worn flat, step by step. One cotton yarn dyed in a ring 20% of its radius deep, cut flat from the top by an abrader to five depths: worn to 10% of the radius, 1.9% of the yarn has gone and 0% of its width is white; worn to 20% of the radius, 5.2% of the yarn has gone and 0% of its width is white; worn to 30% of the radius, 9.4% of the yarn has gone and 39% of its width is white; worn to 45% of the radius, 16.8% of the yarn has gone and 58% of its width is white; worn to 70% of the radius, 31.2% of the yarn has gone and 74% of its width is white. The olive line is the cut face and the red bar above it is the part of the face that has reached the undyed core. Nothing is white until the cut passes the ring, and then the white arrives quickly. The section is a circle and the ring's edge is drawn sharp; a real yarn is neither, and its fibres migrate, so the core's edge is ragged.

A ring-dyed yarn whitens all at once

Rub a yarn that is dyed in a ring, and for a while nothing shows. The abrader takes off blue fibre, the cut face is blue, and the yarn looks as it did. Then the cut reaches the undyed core, and the white arrives with a vertical tangent, as the square root of the wear past the ring: one per cent of the radius more and an eighth of the width is white. A ring a fifth of the radius deep hides the first five per cent of the yarn's loss and shows half its width white by thirteen. A yarn dyed through never shows white at all. Denim's high-contrast fading is that threshold, drawn over a cloth.

finishing · Dyeing A 50 tex yarn after 1, 4, 8 dips into a fibre that fills. The cross-section of a 50 tex cotton yarn after 1, 4, 8 twenty-second dips, each fibre shaded by the dye fixed at its distance from the surface, on one scale of shade for all three. The fibre's room for dye is finite and one dip at the bath's strength fills 20% of an empty fibre's, so each dip meets less affinity near the surface than the last and carries its dye further in. after 1 dip: ring 14% of the radius deep, the surface 20% full; after 4 dips: ring 18% of the radius deep, the surface 59% full; after 8 dips: ring 24% of the radius deep, the surface 83% full. With room to spare every dip would leave the first dip's 14%. The share is assumed; nothing here measures it.

A fibre that fills dyes deeper with every dip

Dipped eight times, a ring-dyed yarn is darker than after one dip but no deeper — if its fibres have room for all the dye they are offered. They do not: every dip's dye occupies some of the fibre's room, the next dip meets less affinity near the surface, and dye that is taken up less travels further before it is taken. How much further depends on one number the dip arithmetic never needed — the share of an empty fibre's room one dip fills — and eight dips turn that number into a ring 1.15 times deeper at five per cent and 1.68 times deeper at twenty.

finishing · Dyeing A 50 tex yarn after eight dips, with its pores open and filling. The cross-section of a 50 tex cotton yarn after eight twenty-second dips into a fibre one dip fills by 20%, each fibre shaded by the dye fixed at its distance from the surface, on one scale of shade. open pores: the ring 24% of the radius deep, the surface 83% full; the dark shade's pigment, all in the pores: the ring 22% of the radius deep, the surface 83% full; pores 90% filled at a full fibre: the ring 16% of the radius deep, the surface 83% full. One dip leaves 14%. The middle section is the most a dark denim's indigo could clog its pores, every grain placed in them; the right is a clog no denim's pigment is large enough to make.

Indigo is too little to close the pores it dyes through

Each dip of a fibre that fills carries its dye deeper, because the dye already fixed near the surface leaves less room there. But indigo is fixed as a solid, and some of it sits in the pores the next dip has to travel through, so a heavily dyed skin should also hold the next dip back. The two pull opposite ways, and which wins is decided by how much pigment there is. A dark denim's indigo, every grain of it placed in the pores, fills at most a fifth of them at the surface and takes back about a seventh of the ring's deepening — under two micrometres. The surface fills at the same rate whatever the pores do, so two cross-sections still tell the two effects apart.

finishing · Dyeing The ring across eight dips, for each fibre. The ring's depth after each of eight twenty-second dips, where an empty fibre left in the bath for good would fill by 20% a dip. instant fibre: 14.0% after one and 23.5% after eight; τ = 20 s: 13.0% after one and 19.6% after eight; τ = 100 s: 23.1% after one and 26.1% after eight; τ = 400 s: 35.5% after one and 36.6% after eight. An instant fibre earns its ring by saturating the skin dip by dip. A slow one starts near its final depth, since it never fills its skin.

A slow fibre starts its ring deep

Every account of an indigo dip here lets a cotton fibre take its dye at once. Give the fibre a clock of its own and the ring does not simply run deeper, which is what the question seemed to ask. A clock of a few seconds makes the ring shallower, by nearly a fifth at most, and only past about twenty-six seconds does it run deeper than an instant fibre's. Two sections tell the accounts apart that one cannot: an instant fibre earns its ring dip by dip, from 14 to 23.5 per cent of the radius over eight dips, and a fibre with a hundred-second clock starts at 23 and ends at 26.

finishing · Dyeing A yarn's dye leaving the bath and after it has been aired. The dye held across the outer radius of a 50 tex cotton yarn after a dip, for a fibre with a 20 second clock, on leaving the bath and after 60 seconds' airing with an oxygen front that would reach the axis in 300 seconds. Half-strength depth goes from 13.2 to 10.8 per cent of the radius, and the surface rises to 0.82, with total dye 0.216 and 0.215. The front is swept and not measured. What the chart cannot show is how fast oxygen actually arrives at a wet yarn.

The air moves a ring outward and adds no dye

A rope-dyed yarn leaves the bath with liquor in its pores and oxidises in the air from the outside in. A fibre with its own clock might be expected to keep taking up dye there and deepen its ring. The oxygen front is a sink, though, and liquor runs out to it faster than fibres can drink. So an aired ring is shallower than the ring that left the bath at every front computed, by more for a slower front and most for a slow fibre, and no dye is added at all. Nearly all of it happens in the first few seconds, so a longer airing buys nothing the shorter one had not.

finishing · Dyeing

Named alongside it

The objects these essays reach for when they reach for this one.

Ring dyeingDenimFibreInter fibre poreAbrasionYarn diameterDiffusionFibre migrationPacking factorYarn count

All concepts