Abstract:
This study numerically investigates the flow characteristics past a solid and smooth sphere
translating steadily along the axis of a cylindrical tube filled with wormlike micellar
solutions in the creeping flow regime. The two-species Vasquez–Cook–McKinley and
single-species Giesekus constitutive models are used to characterize the rheological
behaviour of the micellar solutions. Once the Weissenberg number exceeds a critical value,
an unsteady motion downstream of the sphere is observed in the case of the two-species
model. We provide evidence that this unsteady motion downstream of the sphere is caused
by the sudden rupture of long and stretched micelles in this region, resulting from an
increase in the extensional flow strength. The corresponding single-species Giesekus
model for the wormlike micellar solution, with no breakage and reformation, predicts
a steady flow field under otherwise identical conditions. Therefore, it further provides
evidence presented herein for the onset of this unsteady motion. Furthermore, we find
that the onset of this unsteady motion downstream of the sphere is delayed as the ratio
of sphere to tube diameter decreases. A similar kind of unsteady motion has also been
observed in several earlier experiments for the problem of a sphere sedimenting in a tube
filled with wormlike micellar solutions. We find a remarkable qualitative similarity in the
flow characteristics between the present numerical results for a steadily translating sphere
and prior experimental results for a falling sphere.
