Sorry. Jug of Water.
Here is the skinny. Mineral particles that we find in water pretty much divide up into Sand Silt and Clay. Sands average size is 0.05 mm to 2.0 mm. Silt is 0.002 mm to 0.05. Clay is <0.002 mm. A mm is about the width of a fine pencil lead as a reference. All three being minerals that have essentially the same specific gravity, but they settle at different rates in water. Shake up a jug of water and then set it down and the sand will settle out in less than 40 seconds. That is followed by silt with the smaller silt particles settling out in 2 hours. Much of the clay will not settle out and stay in supension. So in short, the smaller the particle the longer it takes for that particle to settle out of suspension.
So your water treatment plant, if its source of water is surface, will bring the water into the plant and slow down the flow. The larger particles will settle out. To speed up the settling of the small silt and largely the clay particles a chemical is added so that the particles cling together (coagulation) and form a structure (floc). Now the particles readily settle out. There is a lot of colloidal and ionic chemistry behind this, but the above information is enough. So the primary coagulant used by plans is aluminum sulfate AKA alum. They add alum to the resource water, mixed it hard and fast then allow the coagulation/flocculaton take place followed by settlig.
So if you are having to purify water that is cloudy, you add alum. Alum is expensive when purchased as a spice, but again in the Asian stores it is cheap.