Mess, Mess, Messy Mealtimes

I just cleaned up lunch and it made me wonder if anyone has any clever methods of containing the mass of crumbs and sticky goo that seems to explode in the kitchen every time a child eats? We have plastic pocket bibs which are extremely helpful to protect clothes but what about everything that doesn't make it into the bib?

I thought about getting cafeteria trays but wonder if it would be just one more thing to wash?
Ooh, what about an animal trough? Wait, except thats no good either because they don't like their food mixed together. Hmmm.
If you've found something that works-do share! I'm not looking for a miracle here, just something that seems to help. I can only sweep the floor so many times in one day!