At room temperature....
How long will the sugar stay suspended once dissolved ?
What governs the rate of settling ?
What part does Brownian motion play ?
Sugar might be a bad example...please substitute as needed.
Anything dissolved is kept "suspended" by brownian motion. Theoreticly there will be a small gradient of concentration due to gravity, but this is unmeasurable for sugar. (Barometric formula). For much bigger particles (ãbout µm) , this gradient can be determined.
The sugar will stay dissolved until the water evaporates, then the sugar will form a solid residue. (if You are lucky, as crystals) Settling does not occur with molecules.