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Unsteady sedimentation of a sphere in wormlike micellar fluids

Yiran Zhang and Susan J. Muller*

  • Department of Chemical & Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, USA

  • *muller2@berkeley.edu
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Phys. Rev. Fluids 3, 043301 – Published 9 April, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.043301

Abstract

The unsteady sedimentation of a sphere in wormlike micellar fluids is studied experimentally through shear and extensional rheometry, sphere trajectory tracking, and particle image velocimetry. Unsteady sphere sedimentation characterized by fluctuations in the sphere settling velocity was observed for a range of sphere size and density in two non-shear-banding wormlike micellar solutions, a cetylpyridinium chloride (CpCl)-sodium salicylate (NaSal) solution and a cetyltrimethylammonium p-toluenesulfonate (CTAT)-NaCl solution. The onset of the transition from steady to unsteady sphere motion is characterized by an extensional Deborah number, Deext, defined locally in the negative wake of the falling sphere. This instability criterion is in agreement with previous findings by Mohammadigoushki and Muller [J. Rheol. 60, 587 (2016)] in the wormlike micelle system of cetyltrimethylammonium bromide (CTAB) and NaSal, and appears to be universally valid independent of micelle chemistry or solution rheology (e.g., shear banding or not). Moreover, the frequency at which the sphere velocity fluctuates is found to be linearly correlated with an average shear Deborah number Des, which is a measure of the overall flow strength. This suggests that a constant critical strain is accumulated before the flow instability takes place in each velocity oscillation. The velocity fluctuations are found to become increasingly disordered with increasing elastic Mach number, Mae, indicating that the interactions between the flow instability and elastic wave propagation result in more chaotic velocity fluctuations.

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Phys. Rev. Fluids 3, 043301– Published 9 April, 2018
  • Received 22 December 2017
Article part of CHORUS
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