Wet Processing
On a range the same water works in every box. That, and not the box count, is what a row of separate baths cannot match.
— %
Share of what entered the range that leaves on the cloth
The cascade assumes the impurity is free in the liquor and partitions between cloth and bath by dilution alone. That is a fair account of alkali, salt, sizing agent and hydrolysed dye in the liquor, and a poor one of anything held by affinity: back-stained dye on cellulose, or dye that has struck an elastane or polyamide component, does not leave because the water is cleaner, and needs temperature, a soaping agent or a reduction clear that this model knows nothing about. Stage efficiency is the input that decides everything and the one with no textbook value: it falls with speed, with heavy constructions and with any box where the cloth floats rather than being worked, and a range running fast on a thick fabric can drop below 50 percent while its nameplate still says six boxes. Take carry-over from the machine by weighing cloth before and after the nip rather than from a handbook, because the wash ratio is the water divided by it and every result here moves with that division. The comparison against separate baths discounts both arrangements by the same stage efficiency, so it isolates the flow direction and nothing else. The least-water figure is the water at which the target is exactly met, with no margin for a mangle that drifts or a box that channels.
Counter-Current Washing Range: Stages, Wash Ratio & Water — free, with the formula and a worked example, at Textile School.