Microcapsule Rupture Force & Payload Release 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. The 9 inputs are read from the form on every keystroke: Capsule Diameter, Wall Thickness, Wall Material Strength, Payload Fill Fraction, Payload Density, Capsule Density, Applied Rubbing Pressure, Contact Area per Rub and Treated Garment Area.
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 Single Capsule Rupture Force together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Rupture Pressure, Applied vs Rupture Pressure, Capsules Burst per Rub, Payload Released per Rub and Rubs to Depletion — 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 Single Capsule Rupture Force 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 — Capsule and Application & Use. 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 Single Capsule Rupture Force in the dark results panel — that is the headline figure, expressed in µN.
4. Check the supporting rows underneath (Rupture Pressure, Applied vs Rupture Pressure, Capsules Burst per Rub, Payload Released per Rub and Rubs to Depletion) 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 Single Capsule Rupture Force before a trial is booked, so machine time and material in Specialized Chemistry & Advanced Dye Physics are committed against a calculated figure rather than an estimate.
• Costing and quotation — Single Capsule Rupture Force 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 Capsule Diameter) shows how much of the gap in Single Capsule Rupture Force each variable explains.
• Teaching and study — the accepted ranges bracket normal Specialized Chemistry & Advanced Dye Physics practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Rupture is treated as all-or-nothing at the threshold, with the fraction burst rising linearly up to it — real capsule populations have a wall-thickness distribution and rupture progressively across a range of pressures, so partial release begins well below the nominal threshold. Rubs to depletion also assumes each rub finds fresh capsules, which a repeated rub in one place does not, and it ignores the capsules lost to laundering and abrasion between wearings. Phase-change capsules must survive rather than rupture, so for those the useful reading is the pressure ratio staying comfortably below one under garment pressures.
• Every input is bounded to the range normal practice occupies (Capsule Diameter 1 to 200 µm, Wall Thickness 0.01 to 10 µm and Wall Material Strength 0.2 to 200 MPa, 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