The process of separating a liquid/solid mixture by slowly pouring the liquid component into a new vessel as the solid settles to the bottom of the original vessel is known as

The process you're referring to is known as "decantation." Here are the steps:

1. Allow the mixture to stand undisturbed. This lets the solid particles settle at the bottom of the container due to gravity. This process is called sedimentation.

2. Once the solid particles have settled, slowly and carefully pour the liquid into a new container. The aim is to leave the solid particles in the bottom of the original container.

3. Continue pouring the liquid until only the solid particles remain in the original container.

4. The liquid in the new container is now separated from the solid particles. This process is called decantation.

5. If necessary, the liquid can be further purified through filtration or distillation.