I think you didn't prior your concern in your question that's why people concern more about your pc case but indoor air in your room is what matters.
With the state of your heat sink, you can come easily to conclusion that no other than you guys smoking contributes to this problem. Air purifier is known for asthma and eliminating smoke so why not? Your sister's Clair is nice (I check the site and it has the testing video for smoke as well (https://www.youtube.com/watch?v=1djBOzppZmw).
Crucial thing is air flow circulation. If you smoke in front of PC and air purifier is hidden some corners then lol, no. But if you placed your Clair somewhere that would get smoke before your case inhale it, it would work.
I share a gaming PC with my roommate. Recently it started over heating and kept freezing after every restart. When we opened it we saw a lot of yellow glue like substance caked on the underside of the CPU and heat sink. It looked like cigarette smoke build up (both of us are smokers and smoke a lot inside our room). We cleaned it out using compressed air and rubbing alcohol but had to replace the fan and a lot of time and money was spent in the process.Now we are looking for ways to prevent smoke from entering the PC and on few forums people mentioned they use room air purifiers to prevent dust and smoke build up.My sister uses this small room air purifier for asthma and I am thinking of trying out the same. Maybe keep it running all the time next to the PC.
Will this suffice ? Is there any other easy DIY method to prevent smoke and dust from entering PC?

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