Superhydrophobic Finish Contact Angle & Roll-off Predictor

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 7 inputs are read from the form on every keystroke: Intrinsic Contact Angle, Solid Contact Fraction, Wenzel Roughness Factor, Contact Angle Hysteresis, Droplet Volume, Liquid Surface Tension and Liquid Density.
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 Apparent Contact Angle together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Wenzel State Angle, Roll-off Tilt Angle, Solid Contact, Droplet Radius and Retention Force — 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 Apparent Contact Angle 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 Droplet. 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 Apparent Contact Angle in the dark results panel — that is the headline figure, expressed in °.
4. Check the supporting rows underneath (Wenzel State Angle, Roll-off Tilt Angle, Solid Contact, Droplet Radius and Retention Force) 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 Apparent Contact Angle 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 — Apparent Contact Angle 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 Intrinsic Contact Angle) shows how much of the gap in Apparent Contact Angle 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

• The Cassie state is metastable, and that is the practical problem with superhydrophobic textiles rather than a footnote to it. Pressure, impact, condensation within the texture or a surfactant in the water can all collapse the drop into the Wenzel state, at which point the same surface becomes more wettable than a smooth one would have been — which is why the Wenzel angle is shown alongside. A Wenzel result of 180 degrees means the roughness term is out of range and that state is simply not defined for this combination. Roll-off assumes a drop large enough for gravity to matter and a uniform texture; small drops pin regardless of angle. Durability is the other omission — texture that survives a laboratory drop rarely survives abrasion and laundering.
• Every input is bounded to the range normal practice occupies (Intrinsic Contact Angle 60 to 130 °, Solid Contact Fraction 0.5 to 60 % and Wenzel Roughness Factor 1 to 12 r, 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