I'm guessing you are referring to the p trap, like your residential drains at home, the food particles should be displaced as the water runs through the plumbing. If the particles are greasy they might cling to the sides of the plumbing and eventually might back up the system. If the non greasy particles stick around then flush the drain with a larger volume of water like a milk pitcher or a pail and it will disturb the settled particles. That is also good practice when winterising and putting anti freeze in the drains. The grease will need some non caustic attention with a grease remover. In both cases you will get an odour. I often drop an enzyme type treatment in the drains when they can be left for a while during non camping periods.
The bathtub and shower drains will build up from soap scum and hair. That's when you use a flexible cable type rooter with the bristles on the end to move the residue. You can find them at dollar stores etc. about 24" long. With all drains a plunger will also help lift the sludge or disturb it and a flush might do the trick.
Married To The Navigator
2005 Red GMC Duramax 4X4 HD Crew Cab
4" Magnaflow, Banks Air Intake
Firestone Ride Rite Air Springs