Nonwovens
Crowding rises with the square of aspect ratio. That single fact is why wetlaid is a short-fibre, low-consistency process.
— N
Fibres sharing the volume swept by one fibre length
The crowding number is a suspension property and says nothing about what the wire, the dewatering profile or the shear in the slice then do with it - two machines at the same crowding number can form very differently, and a well-designed hydraulic headbox will beat a poor one at identical stock. Read it as the constraint the machine has to work against rather than as a prediction of formation. Note that the tool will often report a crowding number far above the target at the consistency the flow actually requires, and that is not an error in the arithmetic: it is the central tension of wetlaid, where the consistency needed to lay a given basis weight through a given slice at a given speed is frequently well above the consistency the fibre length can tolerate. The resolutions are all structural - a wider slice, a slower wire, shorter fibre, or dilution with a correspondingly larger white-water system - and the tool exists to make the size of the gap explicit before a machine is bought. Jet-to-wire ratio here is a geometric result of flow and slice opening rather than a setting; on a real machine it is trimmed by slice adjustment and by headbox pressure, and a ratio far from unity in either direction orients fibre in the machine direction and costs cross-direction strength. Fibre length is taken as a single value, while a real furnish has a distribution, and the longest tail of that distribution drives flocculation more than the mean does.
Wetlaid Headbox Flow, Jet-to-Wire Ratio & Crowding Number — free, with the formula and a worked example, at Textile School.