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

TL;DR

This paper investigates how micelle breakage rate and wall slip influence unsteady motion around a sphere in wormlike micellar solutions, revealing conditions that delay, induce, or suppress such motion based on the Weissenberg number.

Contribution

It demonstrates how micelle breakage rate and wall slip affect the onset and suppression of unsteady motion in wormlike micellar solutions, extending previous numerical analyses.

Findings

Lower micelle breakage rates delay unsteady motion onset.

Wall slip suppresses unsteady motion around the sphere.

Unsteady motion occurs within a specific Weissenberg number window.

Abstract

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.