General terms:
* Solid-liquid separation
* Filtration (a broad term encompassing many different methods)
* Clarification (removing suspended solids, making the liquid clearer)
* Dehydration (removing water from a solid)
* Purification (removing impurities, including solids)
More specific terms:
* Sedimentation (allowing solids to settle to the bottom)
* Decantation (carefully pouring off the liquid, leaving the solids behind)
* Centrifugation (using centrifugal force to separate solids from the liquid)
* Filtration (passing the liquid through a porous medium that traps the solids)
* Membrane filtration (using a semi-permeable membrane to separate solids and liquids)
* Flocculation (using chemicals to clump together small particles into larger ones, making them easier to remove)
* Coagulation (using chemicals to neutralize charges on particles, causing them to clump together)
The best term depends on the specific context. For example, if you're removing large particles from a liquid using a filter, "filtration" would be the most appropriate term. If you're removing dissolved solids, "purification" might be more accurate.
It's important to consider the nature of the solids, the desired purity of the liquid, and the scale of the operation when choosing a term.