HP has a limited number of DesignJet printers that use pigment based color inks, the rest take dye based colors. Black ink is frequently pigment based. This site has a list of cartridge numbers for different types of printers that are pigment based.
http://www.oddparts.com/ink/faq19.htm
Here's some general info:
http://www.castleink.com/_a-printer-inks.html Keep in mind, these sites are talking about ink on paper, not fabric. The reason color inks are dye based is so they are smooth, thin, blendable, flowing, and cheap to produce...iow, water soluble, what you don't really want for washable fabric use.
There is a great article by Gloria Hansen, a quilt and mixed-media artist, on the subject of inkjet printing on fabric.
http://www.gloriahansen.com/articles.php?p=1&ID=3 See if that helps answer some of your questions. Please note, it was written in 2003.