Explain the scientific principle for Reverse Osmosis separation for salts - liquid mixture?

What you said all of you is fine 

But there is an important point to be clarified 

Reverse osmosis is not a filtration process i.e. it does not separate salts from water by particle size difference across a semi-permeable membrane 

Actually RO membrane is treated chemically to make the flow rate of water molecules very high compared to the flow rate of salts molecules (very low) across the membrane. As a result, water molecules pass though the membrane and salt molecules are rejected (minor amount of salts passes) because the sudden reduction in the flow rate of salts

So that salt rejection across the membrane can't be "one hundred%" it is usually "ninety nine point nine%" and in the desalination engineering they say the quality of thermal desalination processes has efficiency better than the membrane processes 

Reverse Osmosis works by using a high pressure pump to increase the pressure on the salt side of the RO and force the water across the semi-permeable RO membrane, leaving almost all (around% to%) of dissolved salts behind in the reject stream. The amount of pressure required depends on the salt concentration of the feed water. The more concentrated the feed water, the more pressure is required to overcome the osmotic pressure.

The desalinated water that is demineralized or deionized, is called permeate (or product) water. The water stream that carries the concentrated contaminants that did not pass through the RO membrane is called the reject (or concentrate) stream.