I asked whether printer inks were vegan, but tattoo ones must be different since they are used on/in skin.
So, are tattoo inks vegan (not containing animal-related products)?
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Tattoo inks may be vegan, but many are not. In addition, the standard transfer paper contains lanolin (wool fat), so that's not vegan either.
Here's a full explanation (edited) from bitesize vegan website
Tattoo ink is formed of a pigment, which gives the ink its color, suspended within a carrier solution. The pigment is usually derived from plants or metal. Now, what my astute commenter was referring to with the bone bit of his comment, however, is black ink, also called “bone black” which can–but doesn’t always–contain charcoal and soot derived from the charred bones of animals.
Carrier solutions generally contain purified water, ethyl alcohol, propylene glycol and glycerine and may also contain witch hazel. For vegans, it’s the glycerine we have to watch out for. It can be from either plants or from animal fats depending on the company.
Aside from bone char pigment and glycerine carrier solutions, there are other animal bits in tattoo inks to keep an eye out for. Some inks also use gelatin and shellac.
Luckily there are plenty of vegan inks on the market, some of which have the bonus of being non-toxic.
Outside of the ink itself, other elements of the tattoo process can be animal-laden. Many artists use vaseline or petroleum jelly during tattooing to help their tattoo machine glide more easily. petroleum jelly itself can by and large be considered animal-free, although it’s a byproduct of the oil industry, which is a bit concerning, and the vaseline brand itself can contain bone char depending on the country and definitely tests on animals.
One lesser-known hidden animal product in the tattoo experience is the lanolin in transfer paper, which comes from sheep’s wool. You see when you get a tattoo, unless you have a badass free-hander, your artist will draw the image out on what looks like tracing paper and apply it to your glistening moist skin to leave an outline to follow. This allows you and your artist to work out ideal positioning and allows you a bit of a preview.
Luckily, there is a vegan transfer paper out there by Reprofx.
So, go to a tattoo place that explicitly advertises itself as vegan (and that you trust), if you are concerned about these things.