This is the simplest of all separation equipment. You have a big box, with the inlet and outlet streams way up at the top, and as the fluid flows through, the particles fall out. If the box is long enough, then all the particles should fall out. This brings us back to the settling velocity; if the flow rate through is too fast for the size of the box you are using, then not all the particles, if any, are going to settle.
There are two types of classifiers, for the most part. One, the simple gravity settling classifier, and the other, which is known as a Spitzkasten gravity settling chamber.
Both of these work on essentially the same principle. The slower the settling velocity, the farther a particle will travel before settling. So, essentially, the big, heavy particles will fall first, and the small, light particles will fall last.
In the simple classifier, the design is similar to that of the straight gravity settling tank, except that the bottom half is divided into several equal partitions. What happens is that instead of just falling into a big mess on the bottom of the tank, the coarse particles get trapped in the first chamber, the intermediates get trapped in the middle partitions, and the fine particles, the dust, gets captured in the last section. Then, you can drain the sections from the bottom and have a segregated sediment.
The Spitzkasten chamber runs like this. A series of conical vessels of increasing size is set up in the direction of flow. As the slurry enters the first vessel, the coarse particles get trapped, and the overflow continues on to the next, where more separation takes place. This particular settling chamber is unique because you can adjust the flow rates in between each vessel in order to provide the necessary degree of separation.
Below you can see what a thickener is/does, schematically. Essentially what occurs is this. the slurry is fed into the center of the tank, several feet below the surface of the liquid. Around the top edge is a kind of overflow outlet that just takes away the top clear fluid. The bottom of the sloping tank contains a continually moving rake, which scrapes all the sludge towards the center, where it is taken away.
What occurs in a little more detail is that when the slurry is forced into the tank, the particles settle on the top of the other particles through free settling, since for most industrial things, the tanks are large and the slurry is fairly dilute. Anyway, right under this settling zone is an intermediate, transition zone, and directly below that is the compression zone, and then, finally, you have the rake and the sludge outflow.
One thing to keep in mind, when designing one of these thickeners, is that if you want to have a clear fluid on the top, you have to keep the terminal velocity of the particles that are settling greater than the force of the fluid that is being compressed out of the lower zones. Otherwise, the force of the fluid pushing up would create too much bouyancy, and force the particles back up. Which, if you want a clear top layer, is bad.
The following two pictures are just neat images of reactors used for sedimentation. It should be interesting to note that both of these reactors use a form of the thickener described above.