I'd suggest that the algae ARE the sludge. Lots of algae get pretty sludgey!
Your creature could be a filter feeder. Lots of options there:
- Baleen Whales have lost their teeth and have baleen plates instead.
- Flamingoes. Their ancestors lost their teeth when they became birds. Filter feeding came later.
- There is a pterosaur which evolved to be flamingo-like in its feeding.
- Various crustaceans, such as barnacles and krill use their legs to filter, then pass the food to their mouth. Some types of crab use special mouthparts which act as 'hands' to filter and again pass the food to the mouth.
Alternatively, they could suck the sludge up through a tube. Lots of insects do this to suck the sap of plants by piercing the stem - the tube is called a proboscis, if you want to google for pictures. Pretty much everything in the Hemiptera order have sucking mouthparts: aphids (greenfly), leafhoppers and the like.
A short guide to nose evolution in vertebrates... Fish use their noses for smelling, not for breathing. The amphibian descendants of those fish came out of the water also with a nose which was not involved in breathing. They had these pathways into the body:
- Nostrils --> nasal cavity.
- Mouth --> throat --> lungs.
- Mouth --> throat --> stomach.
This is inefficient - you can't breathe and have a mouth full of food at the same time. That's fine if you quickly swallow prey whole, but no use if you need to take time to chew before swallowing.
A creatures which was one of 'the early amniotes' (sort of intermediate between amphibians and proper reptiles) solved this. It evolved a pathway from nostrils to lungs, so it now had:
- Nostrils --> nasal cavity --> throat --> lungs.
- Mouth --> throat --> lungs.
- Mouth --> throat --> stomach.
So they could now breathe and chew gum at the same time! :-) All reptiles, birds and mammals are descended from that early amniote.