## Abstract

We employ time-resolved flow velocimetry and birefringence imaging methods to study the flow of a well-characterized shear-banding wormlike micellar solution around a novel glass-fabricated microfluidic circular cylinder. In contrast with typical microfluidic cylinders, our geometry is characterized by a high aspect ratio α = H/W = 5 and a low blockage ratio β = 2r/W = 0.1, where H and W are the channel height and width, and the cylinder radius r = 20 μm. The small cylinder radius allows access up to very high Weissenberg numbers 1.9 ≤ Wi = λ _{M} U/r ≤ 3750 (where λ _{M} is the Maxwell relaxation time) while inertial effects remain entirely negligible (Reynolds number, Re < 10 ^{-4} ). At low Wi values, the flow remains steady and symmetric and a birefringent region (indicating micellar alignment and tensile stress) develops downstream of the cylinder. Above a critical value Wi _{c} ≈ 60 the flow transitions to a steady asymmetric state, characterized as a supercritical pitchfork bifurcation, in which the fluid takes a preferential path around one side of the cylinder. At a second critical value Wi _{c2} ≈ 130, the flow becomes time-dependent, with a characteristic frequency f _{0} ≈ 1/λ _{M} . This initial transition to time dependence has characteristics of a subcritical Hopf bifurcation. Power spectra of the measured fluctuations become complex as Wi is increased further, showing a gradual slowing down of the dynamics and emergence of harmonics. A final transition at very high Wi _{c3} corresponds to the re-emergence of a single peak in the power spectrum but at much higher frequency. We discuss this in terms of possible flow-induced breakage of micelles into shorter species with a faster relaxation time.

Original language | English (US) |
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Pages (from-to) | 1927-1941 |

Number of pages | 15 |

Journal | Soft Matter |

Volume | 15 |

Issue number | 9 |

DOIs | |

State | Published - Feb 27 2019 |

## ASJC Scopus subject areas

- Chemistry(all)
- Condensed Matter Physics