Hello artificial student,
I have not seen bowl centrifuges used for liquid-liquid separation, but have been used very successfully for liquid-solid separation in the oilfield on a daily basis.
Liquid-liquid separation will remove dispersed material, but not soluble material. For example, oil dispersed into water can be separated with a high enough force, but dissolved salt (unsaturated sodium chloride) in water will not be separated by the bowl centrifuges I am familiar with.
I hope this helps.