Polyester Oligomer Deposition Risk & Safe Drop Temperature

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. The 11 inputs are read from the form on every keystroke: Fabric Weight, Liquor Ratio, Extractable Oligomer in Fibre, Dyeing Temperature, Time at Temperature, Bath Drop Temperature, Release Rate Constant, Release Reference Temperature, Release Doubling Interval, Solubility at 20 degC and Solubility Doubling Interval.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Safe Drop Temperature together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Bath Volume, Extractable Oligomer in Batch, Fraction Released, Oligomer in Liquor, Solubility at Dyeing Temperature, Solubility at Drop Temperature, Bath Capacity when Hot, Bath Capacity at Drop, Mass at Risk of Depositing and Deposit per kg of Fabric — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

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

The tool loads with this case already solved — the Safe Drop Temperature shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Batch, Dyeing Cycle and Solubility Curve. 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 Safe Drop Temperature in the dark results panel — that is the headline figure, expressed in degC.
4. Check the supporting rows underneath (Bath Volume, Extractable Oligomer in Batch, Fraction Released, Oligomer in Liquor, Solubility at Dyeing Temperature, Solubility at Drop Temperature, Bath Capacity when Hot, Bath Capacity at Drop, Mass at Risk of Depositing and Deposit per kg of Fabric) 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

• Process planning — establishing Safe Drop Temperature before a trial is booked, so machine time and material in Dyeing, Printing, Color Management & Chemical Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Safe Drop Temperature is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Fabric Weight) shows how much of the gap in Safe Drop Temperature each variable explains.
• Teaching and study — the accepted ranges bracket normal Dyeing, Printing, Color Management & Chemical Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Both curves here are engineering approximations with the right shape rather than measured constants for a particular dye system: oligomer release is treated as first order with a doubling interval, and solubility as an exponential in temperature. The absolute masses should be read as indicative, but the comparison the tool is built for - deposit against drop temperature - depends on the shape of the solubility curve rather than on its calibration, and that comparison is robust. Dispersing agents and oligomer-specific auxiliaries raise the effective solubility substantially and are the usual chemical answer where a hot drop is not possible; their effect belongs in the 20 degree solubility figure, which is why it is an input rather than a constant. Reduction clearing removes oligomer already deposited but does nothing about the mechanism, and a machine that deposits every batch will foul its heat exchanger whatever the fabric is cleared with. Texturised and microfibre polyester expose far more surface and release more oligomer than the same weight of flat yarn, so the extractable content should rise with fineness. Nothing here models the oligomer that recrystallises inside the fibre rather than in the bath, which is a different fault presenting as a dull or hazy shade rather than as white specks.
• Every input is bounded to the range normal practice occupies (Fabric Weight 5 to 5000 kg, Liquor Ratio 2 to 40 :1 and Extractable Oligomer in Fibre 0.1 to 5 %, 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.

Questions people ask