The Laboratory

Browning has used a rather jaunty rhythm in this poem, which sounds almost comic in contrast to the subject matter. He also has his speaker move jerkily from one thing to another, as if she is distracted by what she sees around her in the chemist's shop.
Everyone's idea of the speaker will be different, but I see her as quite young, rather silly, and obviously with a jealous and vindictive nature.
There is a rather lengthy but comprehensive analysis of the poem here
and a powerpoint presentation which explains the subject matter and language in a simpler way here.
I'd be happy to hear any other ideas about the young woman in the poem, but Browning has certainly created a real character, and a believable setting for her.