Candid Engineer in Academia wrote about using a separation funnel to part organic and aqueous phases in solvent extration.
I remember doing this in lab. The instructions were to shake vigorously, remembering to release the vapour pressure build up but not too hard. Shaking too hard may form an emulsion.
This technique takes practice. A friend ended up with corrosive mixture splattered all over her. I was glad that she did the lab before me and warned me about it!
I hope this video clip demonstrating liquid-liquid extraction helps.