Methods of imparting color to nylon substrates

A continuous method of contacting an active agent to a linear synthetic polymeric substrate to impart a color to the linear synthetic polymeric substrate, the method comprising:

• contacting an active agent precursor solution with a cation exchange resin (CER), the contacting forming a treated active agent precursor solution;
• diluting a first portion of the treated-active agent precursor solution to form an active agent solution;
• contacting the active agent solution with the polymeric substrate at a treatment temperature and for a treatment time;
• and
• adding a second portion the treated-active agent precursor solution to the active agent solution to maintain a concentration of the active agent in the active agent solution;
• wherein:
• the polymeric substrate comprises a polyamide polymeric material;
• the active agent precursor solution comprises an active agent comprising an acid dye selected from the group consisting of an anthraquinone acid dye, an azo acid dye, and a triphenylmethane acid dye;
• the CER comprises sulfonic acid functional groups;
• a concentration of the active agent in the active agent precursor solution is in a range from 10 g/L to 50 g/L;
• wherein a mass concentration of the active agent in the active agent precursor solution is in a range from 400% to 1000% relative to a mass concentration of the active agent in the active agent solution;
• and
• a ΔE of the polymeric substrate is less than that of an otherwise identical continuous method comprising contacting the active agent solution with the cation exchange resin instead of contacting the active agent precursor solution with the cation exchange resin.