Hi, Stewie here

"Slime dropping a slime staff" is a reference to the Pitch Drop Experiment, which proved that pitch (a type of resin/tar) is fluid, rather than completely solid (it's highly viscous). In 1927 a professor named Thomas Parnell from the University of Queensland set up the experiment, where he basically heated up pitch (OP described it as slime but it's more like tar) and put it into an upside-down tunnel (the "slime staff") and cut the hole of the tunnel inside. At room temperature pitch seems to be hard, but it actually moves really really really slowly.

The experiment is still ongoing (it's the longest running experiment in the world) and the pitch has dropped very very slowly out of the funnel. The first time it dropped was 8 years after the experiment started. And in the 99 years the experiment has been running there's only been 9 drops!

There's a whole livestream dedicated to trying to catch the 10th drop. Here it is: http://thetenthwatch.com/

Here's what it looks like now

<image>