Is she dipped in honey? Cuz that would be just GREAT!

Are you sure this is supposed to be Rei?

I just looked it up, and the artist's caption for this pic is "アヤナミたん", so it's definitely Ayanami.

Oh, there's also the note:

"悶絶！　LCLがネバネバしてるよ！　の巻。"

Basically, Rei is upset that LCL fluid is so sticky. So it's definitely not honey, but apparently has about the same consistency. Which is not something I remember from the series.