new correlations for the prediction of terminal velocity and drag coefficient of a bubble rising

the present experimental study was done aimed to investigate dynamic of a single bubble rising through wall-bounded flow at high reynolds number. thus, rhamnolipid biosurfactant was added to stagnant fluid and bubble diameter was controlled between 2.5 and 3.5mm. the resulted reynolds number was in the range of 400 to 900 depends on biosurfactant concentration. rhamnolipid has a low toxicity, a high biodegradability and good stability at a wide range of temperatures. the results showed that terminal velocity linearly depends on reynolds number. furthermore, drag coefficient is related to eötvos number and is autonomous to reynolds number. finally, to estimate terminal velocity and drag coefficient, four empirical correlations were developed. relative errors of the proposed correlations were less than of 3.35% and 1.97% for velocity and dimensionless velocity equations, respectively, and average errors of two equations proposed for drag coefficient were 4.44% and 3.26%.