When you work at home and more at your desk than in the field your stuff gets grimy and full of gunk. Spend about 30 mins and you can have a fresh, smooth free-flowing chair again. In this apartment therapy post they give a lot of detail on how to clean out the wheels and rolling parts of your chair.
In my case I never have a drop cloth and if the cloth and rubbing alcohol isn’t within a 10 sec hunt I don’t bother. For a faster hack I recommend the following: An old WSJ or other newspaper sitting within arms reach, a knife (keep small sharp pocket knives everywhere – a hobby) from kitchen will do preferably sharp. Now browse through and clean up the areas that you can and catch the gunk in the paper. Careful you don’t cut yourself with the sharp knife but use it to scrape the bottoms. Then use it to poke into the shaft of each wheel – probably easiest to remove them right away. This way you can saw out the hairs as needed. With those two things done you have cleaned up 90% of the problem and you’re good to go in less than 30 mins (keep it to 15 if you can).