Sink to the bottom. addition of potassium nitrate past it’s dissolution capacity at a particular temperature will cause the extra to just sink to the bottom of the glass.however, if you were to raise the temperature of the solution prior to dissolving it, and then slowly decrease the temperature after the dissolution, you would create a “supersaturated” solution - a solution that has more solute dissolved into it than should be allowed. if you add any extra solute past this, the entire solution would “crystallize,” and this is how you get those cool videos on youtube.