DRAG OF A SPHERE IN DILUTE POLYMER-SOLUTIONS IN HIGH REYNOLDS-NUMBER RANGE

We have measured by means of four ultrasonic transducers the fall velo city of a sphere at high Reynolds number range in dilute polyacrylamid e solutions which have viscoelastic effects. The polymer solutions wer e 5, 20 and 50 ppm in the concentration. Basset-Bousinessq-Oseen equat ion for the falling sphere was analyzed numerically on Newtonian fluid s in order to compare with the fall velocity of a sphere in the polyme r solutions, and the experimental data of the fall velocity in tap wat er is in agreement with the range of no effect of the test tank wall. In polymer solutions, it was shown that the fall velocity is larger th an that in Newtonian fluids within the critical Reynolds number range such that the drag reduction occurs and is smaller than that of Newton ian fluids over the range. The experimental data for the drag reductio n ratio of polymer solutions is arranged by Weissenberg number calcula ting the experimental data of the first normal stress differences. It was shown that the maximum drag reduction ratio in the polymer solutio ns lies in the range of We = 3 similar to 10.