Name: CORSINI
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I want to thank you for helpfull informations on this site and your blog.
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Is there any comparative study of deep water fabric dyeing versus inkjet fabric printing?

I have googled this without serious help

I don't know of any comparative study. I am ignorant of the processes currently being used in the textile industry, and can comment only on those processes which are used by artists and small-scale crafters. Perhaps I can give you some alternative terms with which to search further, though.

'Deep water fabric dyeing' is known in English as vat dyeing or as immersion dyeing. (In small-scale craft uses, immersion dyeing can be done with a high water ratio for solid colors, or a low water ratio for mottled colors; the latter is frequently referred to as low water immersion dyeing, or LWI.)

I don't know much about the use of inkjet printers in the printing of commercial fabrics. Any sort of dye can be used in an inkjet printer, in theory, and often pigments are used instead. To compare this process to immersion-dyed fabric, you must find out exactly what is in the inks that are used. You may find more information on the different types of dyes that exist on "About Dyes". Any of them could be used in one form of printing or another.

Quilt artists commonly use ordinary paper printers to print on fabric that has been specially prepared with a product that allows printer ink, whether made from dyes or pigments, to stick to the fabric so permanently that the fabric may be laundered. The product most commonly used for this purpose in the US is called Bubble Jet Set. It seems to me that commercial processes would be more likely to use true dyes, which attach directly to the fabric without the use of such a binder.

It is interesting to note that the dyes in inkjet inks can be made from disperse dyes, so that prints made from them on paper can be sublimated onto synthetic fibers such as polyester, using a heat-transfer process. Some inkjets are used to print with food-safe dyes in order to make designs to be placed directly onto food. In this case, only a limited number of dyes can be used, since only a few dyes have been approved for use in food. Food dyes are acid dyes and actually work fairly well to dye protein fibers such as wool, but heat setting is required.