Oil Repellency Grade from Critical Surface Tension

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 3 inputs are read from the form on every keystroke: Critical Surface Tension, Zisman Slope and Target Grade.
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 Oil Repellency Grade together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Surface Tension at that Grade, Margin over the Critical Tension, Next Grade Liquid Tension, Step to the Next Grade, Target Grade Liquid Tension, Critical Tension the Target Needs, Reduction Required, Grades Short and Contact Angle at the Target Liquid — 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 Oil Repellency Grade 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 — Surface and Specification. 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 Oil Repellency Grade in the dark results panel — that is the headline figure, expressed in AATCC.
4. Check the supporting rows underneath (Surface Tension at that Grade, Margin over the Critical Tension, Next Grade Liquid Tension, Step to the Next Grade, Target Grade Liquid Tension, Critical Tension the Target Needs, Reduction Required, Grades Short and Contact Angle at the Target Liquid) 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 Oil Repellency Grade before a trial is booked, so machine time and material in Finishing, Coating, Lamination & Functional Performance are committed against a calculated figure rather than an estimate.
• Costing and quotation — Oil Repellency Grade 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 Critical Surface Tension) shows how much of the gap in Oil Repellency Grade each variable explains.
• Teaching and study — the accepted ranges bracket normal Finishing, Coating, Lamination & Functional Performance practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• AATCC 118 is a pass or fail against each liquid in turn and the grade is the highest one that does not wet within thirty seconds; it is not a measurement of critical surface tension, and deriving one from the other in either direction is an inference. The inference is sound in principle and rough in practice, because the standard also depends on how the drop is placed, on surface roughness and on the presence of any hydrophilic contaminant, all of which move the observed grade without moving the chemistry. The Zisman relation is a linear fit of the cosine of contact angle against liquid surface tension, and its whole construction puts the contact angle at zero when the two tensions are equal - which is why a liquid only just above the critical value gives a small angle and a marginal pass. Read a small contact angle at the target grade as a warning that the grade will not survive a soiled or abraded surface. Textile surfaces are also rough and porous, so the wetting they show is Cassie-Baxter rather than the ideal Young behaviour Zisman assumes; roughness helps a repellent surface and hurts a wettable one, which is why a napped fabric can grade above a smooth one carrying the identical finish.
• Every input is bounded to the range normal practice occupies (Critical Surface Tension 8 to 45 mN/m, Zisman Slope 0.005 to 0.2 per mN/m and Target Grade 1 to 8 AATCC, 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