Is there a mob cap in minecraft?

Right now I'm currently in snapshot 14w21b and I'm working to built a slime farm. I played last night and made a huge slime farm in a slime chunk using the chunkfinder.com app, and I gave it Nearly TEN LAYERS and not one spawned! I do have around 20 cows in my world but I have lit up alot of the caves though. I'm working towards lighting more caves but does that app even work? I had to reload my world and am doing it in a chunk where I've lit up more caves so I hope it works… Those suckers are the most important creatures in the game… At least what they drop.

Slimes and cows are different types of mobs, so it wouldn't be affected by each other. You're just unlucky at the moment. Slimes are a hostile mob, while cows are a passive mob, so mob caps for each are different. I made a mine once, saw a single slime mob once and never saw it again. Mad another mine, found billions of slimes. You may need to make it in another area.

There's not really a cap, just a limit to what your computer can handle. You're just being unlucky, slimes are a pain like that.