Hi OP - I'm in a very similar place (got a thread on her somewhere about it) but with the genders reversed (there isn't such an age difference, but that's by-the-by).
It's actually quite telling for me that you've come out of an abusive relationship at a similar time I did. My Ex wasn't physically violent, but for almost a year prior to us splitting I had to put up with a lot of emotional abuse.
I now wonder if it isn't the good feelings you get from the interactions that gets us addicted. I fairly certain, in my instance, the other person is flirting to a certain extent and there seems to be some chemistry. But an all-consuming, turn-you-into-a-teenager crush like wot hits me? No. I think many people can "click" and even flirt and have a mild crush. But most of those will likely forget about it the moment they go home or elsewhere. I've been that person myself in the past.
But in the aftermath of that emotional abuse it doesn't half feel wonderful to experience that honest, joyful chemistry and repartee with someone else again - the kind I once felt with my Ex, especially knowing you're now single and thus open to new relationships.
Also, I've heard it can be a "solution" of the brain gone awry. One theory suggests that your subconscious makes a note of who's been a positive role model in your life. When you're very stressed or feeling unloved, it will then push you towards someone who displays many of the traits these people had. Maybe they have your best friend's smile or that kindly aunt's accent. The point is, your subconscious says "you're feeling bad and to fix this you need someone to make you feel good". In the absence of an actual supportive partner, it reaches for the nearest photofit, believing this amalgam of traits = perfect fit.
Of course, reality, sadly, isn't as simple or co-operative as our subconscious may wish it were. :(