In a recent numerical study, we have shown that the unsteady motion past a sphere translating steadily in a wormlike micellar solution is caused due to the breakage of long micelles downstream of the sphere once the Weissenberg number exceeds a critical value based on the two-species Vasquez-Cook-McKinley (VCM) constitutive model for wormlike micelles (C. Sasmal, Unsteady motion past a sphere translating steadily in wormlike micellar solutions: a numerical analysis, Journal of Fluid Mechanics, 912, A52, 2021). This study further shows that this unsteady motion is strongly influenced by the micelle breakage rate and wall slip present on the sphere surface. 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, as the micelles become hard to break. Additionally, we observe that at some values of the micelle breakage rate, a transition in the flow field from steady to unsteady occurs as the Weissenberg number increases, and then again, a transition from unsteady to steady occurs as the Weissenberg number further increases. Therefore, there is a window of the Weissenberg number present in which one can see 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 for the same is provided in this study.
Oscillations of a solid sphere falling through a wormlike micellar fluid
我们提出了一个实验研究的运动的固体球通过蠕虫状胶束流体下降。当较小或较轻的球体迅速达到终极速度时，较大或较重的球体会在其下落运动的方向上振荡。这种不稳定性的开始与速度梯度尺度$Γ_{c}\sim 1$ s $^{-1}$的临界值相关。我们将这种情况与已知的蠕虫状胶束流体的复杂流变学，并建议该球的不稳定运动是由流动诱导结构的形成和破裂引起的。
Elastic instabilities and bifurcations in flows of wormlike micellar solutions past single and two vertically aligned microcylinders: Effect of blockage and gap ratios
