before you start separation acccording to the grain size you should know more about the mineralogical composition of the sludge , particular about the fractions in question. Otherwise it will be difficult to recommend an effective method to process the sludge.
First you use a sieve of 53 micron diameter to remove sand particles and then take the sludge in a 2.5 L Winchester bottle and shake for few hours with some distilled water. After shaking put the bottle on a table and let it rest for at least 5-6 hours undisturbed. By a rubber tube siphon the liquid from the first 10 cm of the bottle. Please keep on doing shaking with distilled water and removing the first 10 cm dispersed matter till you get the transparent first 10 cm liquid. It will ensure you the removal all clay sized particles from the sludge. Just try it.