Looking at my computer's fan I can say that a lot of dust is collected on it not less dust should be collected in the lungs, not to mention some inhaled parts of food.
How the lungs clear themselves from dust, smoke, food particles?
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nuhcole is mostly correct.
Airborne particles first pass through the nasal passageways and/or mouth and throat and many are caught, but those that enter the lungs become trapped in mucus.
Your cilia act like a constant escalator, bringing up that mucus from your lungs 24/7. You reflexively swallow it without even realizing it. That is why when you are healthy, you might not even notice.
If you are sick (or asthma/allergies), more mucus is produced. That is when you may notice the increased quantity coming up, and may need to cough to bring more up.
If your cilia are damaged (like in smokers), then mucus does not clear well from the lungs. In this case, people must cough more in order to bring it up.
Our respiratory tract is lined with cilia, which are hair-like structure that extend from the outside of the cells. They wave back and forth and act like brushes to catch dust particles before they enter the lungs.
Some particles do get past these cilia and enter the lungs, however. The lungs will secrete mucus that collects the dust. You then cough up the mucus to get rid of the dust particles.
The mucus your lungs excrete also help against pathogens you inhale. Bacteria and viruses are also collected in the mucus, and then removed via coughing. This is why you may cough up phlegm when you're sick.