Be it dry food, moist food, or a piece of chicken I throw to them. They do it for about 30 to 60 seconds.
Pets Stack Exchange is a question and answer site for pet owners, caretakers, breeders, veterinarians, and trainers. It only takes a minute to sign up.Sign up to join this community
Cats basically live repeating the usual sequence: hunting (identify the prey, follow, chase, kill bite, dissect, ingest), grooming, sleeping.
So it is normal behaviour for a cat to clean himself after eating and before sleeping.
Even when they don't have obvious leftover food on their paws or face they clean their face by first licking their paws and then cleaning their face with their paws (and then cleaning their paws again - having wet paws helps to clean the face).
It is also worth noting that the absence of grooming or excessive grooming can be pathological and you should consult your vet if you notice drastic change in your cat's grooming behaviour.