Effect of micelle breaking rate and wall slip on unsteady motion past a sphere translating steadily in wormlike micellar solutions

Abstract

Many prior experimental studies have found the existence of an unsteady or fluctuating flow field around a solid sphere when falling in wormlike micellar solutions. Based on the two-species Vasquez–Cook–McKinley constitutive model for micelles, a recent numerical study shows that the breakage of long micelles downstream of the translating sphere causes this unsteady motion [C. Sasmal, “Unsteady motion past a sphere translating steadily in wormlike micellar solutions: A numerical analysis,” J. Fluid Mech. 912, A52, (2021)]. This numerical study further shows that the micelle breakage rate and wall slip can strongly influence this phenomenon. In particular, we find that the onset of this unsteady motion is delayed to higher values of the Weissenberg number as the micelle breakage rate decreases, or in other words, micelles become hard to break. Additionally, we observe that at some values of the micelle breakage rate, again, a transition in the flow field from unsteady to steady occurs at high Weissenberg numbers. Therefore, there is a window of the Weissenberg number present to observe this unsteady motion past the translating sphere. On the other hand, we show that the presence of wall slip on the sphere surface suppresses this unsteady motion past the translating sphere, and a probable explanation is also provided for the same.