Fibre & Fabric Conditioning Time to Moisture Equilibrium

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 8 inputs are read from the form on every keystroke: Half-Thickness of the Diffusion Path, Bulk Density of the Assembly, Fibre Density, Air Temperature, Initial Regain, Equilibrium Regain at the Standard Atmosphere, Sorption Isotherm Slope and Acceptance Tolerance.
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 Time to Reach Tolerance together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Time Constant, Half-Life, Completion after 24 h, Regain after 24 h, Sorption Capacity Factor, Effective Diffusivity, Assembly Porosity and Water Exchanged per Tonne — 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

Substituting

This is why laboratories condition overnight and why the practice works: 16 hours is comfortably inside a night, and the standard four-hour minimum in the test methods would have left this specimen 6% short of equilibrium.

How to use it

1. Work through the input groups in order — Specimen and Atmosphere & Target. 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 Time to Reach Tolerance in the dark results panel — that is the headline figure, expressed in h.
4. Check the supporting rows underneath (Time Constant, Half-Life, Completion after 24 h, Regain after 24 h, Sorption Capacity Factor, Effective Diffusivity, Assembly Porosity and Water Exchanged per Tonne) 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 Time to Reach Tolerance before a trial is booked, so machine time and material in Fiber Testing, Bale Management & Laboratory Sampling are committed against a calculated figure rather than an estimate.
• Costing and quotation — Time to Reach Tolerance 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 Half-Thickness of the Diffusion Path) shows how much of the gap in Time to Reach Tolerance each variable explains.
• Teaching and study — the accepted ranges bracket normal Fiber Testing, Bale Management & Laboratory Sampling practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• This is a diffusion estimate for a slab exchanging through its faces, so it applies to stacks, flat specimens and open beds. A wound package is a cylinder with a much longer path than its wall thickness suggests, and this will read optimistic for one. The isotherm is treated as linear over the interval travelled, which is reasonable near the standard atmosphere and poor at the extremes where the curve turns sharply. Sorption hysteresis is not modelled: the standards require approach from the dry side precisely because the equilibrium value itself depends on direction. Heat of sorption is ignored - real conditioning warms the specimen slightly and self-retards a little at the start. Where the answer matters, the standards' own criterion of successive weighings remains the acceptance test; this predicts how long to expect before that criterion is met.
• Every input is bounded to the range normal practice occupies (Half-Thickness of the Diffusion Path 1 to 300 mm, Bulk Density of the Assembly 10 to 1200 kg/m3 and Fibre Density 0.7 to 3 g/cm3, 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

• ASTM D1776 - Standard Practice for Conditioning and Testing Textiles: 21 +/- 1 C and 65 +/- 2% RH, with equilibrium declared when successive weighings differ by no more than 0.1%.
• ISO 139 - Textiles, Standard atmospheres for conditioning and testing: 20 +/- 2 C and 65 +/- 4% RH.
• ASTM D2654 - Moisture in Textiles, for the oven-dry and regain determinations this tool works in.
• Crank, J., The Mathematics of Diffusion, for the slab solution; Millington and Quirk (1961) for the porosity exponent.

Questions people ask