  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.
