For example, in hydro-metallurgical processes you often perform some type of reaction with a solid-liquid mixture, for instance to extract (leach) a component from the solid. In order to then recuperate the leached compound, for example by precipitation, you then need to remove the residual solid, otherwise you will precipitate your desired compound with the residual material and end up with a mixture rather than a pure compound. Looking from the solid phase perspective, it may also be important to remove as much as possible of the liquid phase before proceeding to a next processing step, in cases when the aqueous reactants from one step are incompatible with those from the next step, or if the leached compounds can contaminate the subsequent leachate. This is just one example, that are many more solid-liquid separation of industrial importance.
If you consider that the most of pharmaceuticals are solid products, as well as several chemical products (organic acids, organic and iorganic salts, sugar, salt, etc) and they are all produced by wet processes,it is easy to see the importance og solid liquid separation in the recovery of the products in chemical processes. Depending on particle size, density difference between solid and liquid phases, as well as in other proprties (viscosity, solid hardness, process flow rate, etc), a good separation process is defined between filtration, centrifugal processes, flotation, decatntation or some kind of combination of then.
Some times the valuables need to remain/stay back with the solid only, leaving the unwanted component with the liquid portion; this is termed as reverse leaching.