Option 1: Water - Water is a polar molecule, which means it has a partial positive charge on one side and a partial negative charge on the other side. This property allows water molecules to form hydrogen bonds with other water molecules and with the surface of the glass vessel. As a result, water wets the walls of the glass vessel.

Option 2: Alcohol - Like water, alcohol is also capable of forming hydrogen bonds and is a polar molecule. Therefore, alcohol wets the walls of the glass vessel.

Option 3: Mercury - Mercury is a non-polar metal and does not form hydrogen bonds. It has a low surface tension, which means that it does not easily wet the walls of the glass vessel. Instead, it forms droplets and rolls off the surface.

Option 4: Phenol - Phenol is a polar molecule capable of forming hydrogen bonds, similar to water and alcohol. Therefore, phenol also wets the walls of the glass vessel.

In conclusion, among the given options, mercury is the one that does not wet the walls of the glass vessel due to its non-polar nature and low surface tension.