A method of separating contaminants from at least one continuous fluid stream. The method includes steps that are performed inside of a solids dissociation apparatus (SDA) and inside of a solids separation apparatus (SSA) for separating contaminants from at least one continuous fluid stream. The method includes steps of eviscerating the contaminants in the at least one continuous fluid stream inside of SDA upon pumping the at least one continuous fluid stream in SDA, generating a traveling sonic wave in SDA, and cavitating the at least one continuous fluid stream in SDA. The method also includes steps of removing the eviscerated contaminants of a first configuration from the at least one continuous fluid stream by SSA upon generating a standing sonic wave in SSA and forcing the eviscerated contaminants into at least one set of ports of at least one removal stage of a tower of SSA.