Black inks are pretty interesting and it's not 100% clear to me why they "blue." My best guess (and I emphasize this is a guess) is that because the particle sizes in black inks tend to be very small that it's easier for the pigment to diffuse out away from where the ink was embedded. Very small particles scatter blue light and take on a blue-ish tint and so I speculate that might be what's happening here as you move away from the embedded black ink and have a "dilute" concentration of black pigment.

I would definitely encourage folks to get whatever data they can about the inks in their tattoos and hang onto the info. At a minimum, allergic reactions are a known issue with tattoos and can crop up long after tattooing. One big challenge we have is figuring out what the specific allergens are since we don't know 1) what ink was used and 2) what was in the inks. We hope our work can help address #2. If people keep better records of the inks that were used that would go a long way towards addressing #1. -JRS