Dye Exhaustion & Fixation Percentage Calculator

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. Put the three readings on one basis before anything else. Because all the outputs are ratios, the unit cancels — but only if the same instrument, wavelength, cell and dilution produced them, and only if they refer to the same volume of liquor. Where the soap bath volume differs from the dyebath, convert each reading to dye mass (concentration x volume) and enter masses rather than concentrations.
2. Subtract the residual from the initial to get the dye that left the liquor. That is a transport figure and nothing more. It counts every molecule that moved onto or into the fibre, whether it formed a covalent bond with cellulose, sat there by substantivity, or was mechanically trapped between fibres in the yarn.
3. Soaping separates the two populations. A boiling soap or detergent wash removes hydrolysed and unreacted dye held only by substantivity; what survives it is covalently bonded. The dye recovered in that liquor is washedOffConcentration, so the measurement is only as good as the soaping — an under-run soap cycle flatters the fixation number and the fastness test finds the difference later.
4. Subtract the soaping loss from the exhausted quantity to get the fixed dye, then take the two ratios. Dividing by the applied dye gives commercial yield; dividing by the exhausted dye gives reaction efficiency with the transport step removed.
5. Read the two fixation figures together, because the gap between them is the whole diagnosis. Low fixation on applied with high fixation on exhausted is an exhaustion problem — salt, liquor ratio, temperature, preparation. Low fixation on exhausted means the dye got in and did not bond, which is alkali profile, bath pH, dye condition or temperature.
6. Total dye to effluent is simply the complement of fixation on applied: residual bath plus soaping liquor. Scaled by the dye charged it sizes the colour and salt load leaving the dyehouse, which is usually the number the environmental side of the business wants rather than the yield.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

Exhaustion of 88% reads as a good dyeing, but only 82 of the 100 units are on the cloth once soaping is finished, and the honest efficiency figure is the 93.18% fixation on exhausted — 6.8% of everything the fibre picked up was hydrolysed dye that had to be washed back out. Note also that two thirds of the 18 points of loss is drop-bath dye, not soaping dye, so an effluent colour problem here is fixed at the exhaustion end, not by adding soaping cycles. Entering 100 as the initial concentration is worth doing deliberately: the other two fields then read directly as percentages of dye charged.

How to use it

1. Work through the input groups in order — Bath Concentration. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Exhaustion in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Fixation on Dye Applied, Fixation on Dye Exhausted, Unfixed Dye Washed Off and Total Dye to Effluent) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Dye selection trials — ranking reactive brands at the same depth, liquor ratio and salt. Fixation on exhausted is the fair comparison, because exhaustion on its own can be bought with more electrolyte and tells you little about the dye's reactivity.
• Wash fastness investigation — a batch that stains the adjacent cotton in a laundering test almost always shows a wide gap between exhaustion and fixation on applied, which moves the enquiry to hydrolysis and soaping rather than to the fastness test itself.
• Effluent and ETP loading — totalDyeLost multiplied by the kilograms of dye charged gives the dye mass to drain per batch, which is what a colour-removal step (coagulation, ozone, adsorption) has to be sized against, alongside the salt and COD it arrives with.
• Dye cost per kilogram of fabric — unfixed dye is bought, applied and thrown away. Moving fixation on applied from 70% to 82% on a 4% owf recipe cuts the dye needed for the same on-cloth depth by roughly one seventh, before counting the shorter wash-off.
• Salt and alkali optimisation — running one shade at stepped salt levels and plotting exhaustion against fixation on exhausted shows the point where more electrolyte stops buying yield and only adds chloride or sulphate to the effluent.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• Reactive dyes on cotton typically fix 60-80% of what is applied. The unfixed balance is hydrolysed dye that loads the effluent and must be soaped off.
• Every input is bounded to the range normal practice occupies (Dye Before Dyeing 0.01 to 100000 units, Dye Left in Bath 0 to 100000 units and Dye Removed by Soaping 0 to 100000 units, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Standards and further reading

• ISO 105-C06 and AATCC 61 — colour fastness to domestic and commercial laundering. This is the test the fixation figure is predicting; dye that exhausted but never bonded shows up as staining of the adjacent multifibre.
• ISO 105-X12 and AATCC 8 — colour fastness to rubbing and crocking. Unfixed surface dye fails wet rubbing before it fails washing, so it is the quicker confirmation after a low fixation result comes off this calculation.
• ASTM E169, general techniques of ultraviolet-visible quantitative analysis, covers the practice behind all three concentration readings entered here: a calibration curve on the dye as supplied, readings kept inside the linear absorbance range, and consistent cell and dilution handling. There is no product standard for dyebath exhaustion itself — mill labs run this to their own dyehouse method.
• ISO 7887 — water quality, examination and determination of colour. Applied to the drop bath and soaping liquor when totalDyeLost has to be reported to the ETP as effluent colour rather than as dye mass.

Questions people ask