There are a wide variety of ink chemistries used to print textile materials. The fiber content of the material will dictate which ink can be used. Some inks work on a variety of fiber types while others only work on specific fiber types.
In general terms, dyes are soluble and have an affinity to the substrate to which they are applied. Pigments on the other hand are non-soluble and have no affinity to material.
A third category has some characteristics of each of the primary two, and is called a dispersed dye.
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