Abstract: This is a method and apparatus for combined gravity separation-filtration for conducting physical, physical-chemical, chemical, and biological processes in solid-liquid systems; including but not limited to separation of dispersed solids from liquids, separation of alkalinity from the liquid stream, chemical acid-base interactions, chemical oxidation-reduction, chemical dissolution-precipitation, physical chemical adsorption, ion exchange, mass transfer in any combinations of multiple liquid-solid-gas phases, biological oxidation-reductions, biological growth, and combinations of these processes; gravity separation steps can be conducted in rectangular horizontal unidirectional flow clarifiers, rectangular or circular radial flow clarifiers, rectangular or circular vertical flow clarifiers, lamella clarifiers, suspended sludge blanket clarifiers, fluidized bed separators, and combinations thereof, wherein the filtration step is disposed in the upper portion of the combined process or side-by-side with clarifi