Precipitation consists of two distinct events: nucleation, the initial formation of smaller stable particles of precipitate, and particle growth. Larger particles form when the rate of particle growth exceeds the rate of nucleation.
We define a solute’s relative supersaturation, RSS, as
RSS = (Q − S) %S
where Q is the solute’s actual concentration
and S is the solute’s concentration at equilibrium.
The numerator of equation Q – S, is a measure of the solute’s supersaturation. A solution with a large, positive value of RSS has a high rate of nucleation, producing a precipitate with many small particles. When the RSS is small, precipitation is more likely to occur by particle growth than by nucleation.
from this we can say that in the first sample the concentration of BaSO4 is high so gelatinous precipitate forms immediately as RSS value is high for this solution.
In the second sample the concentration of BaSO4 less than 1st sample since RSS value is also decreased from first sample so it forms cloudy precipitation.
In the third sample the concentration is decreased very low so the time taken for ppt also takes place slowly as particle sizes decreases to form a practical growth it takes time.