Abstract:
Flow past a microfluidic cylinder confined in a channel is considered as one of the benchmark problems
for the analysis of transport phenomena of complex fluids. Earlier experiments show the existence of an
elastic instability for the flow of a wormlike micellar solution in this model system after a critical value of
the Weissenberg number in the creeping flow regime (G. R. Moss and J. P. Rothstein, J. Non-Newtonian
Fluid Mech., 2010, 165, 1505–1515; Y. A. Zhao et al., Soft Matter, 2016, 12, 8666–8681; S. J. Haward
et al., Soft Matter, 2019, 15, 1927–1941). This study presents a detailed numerical investigation of this
elastic instability in this model system using the two-species VCM (Vasquez–Cook–McKinley) constitutive
model for the wormlike micellar solution. Inline with the experimental trends, we also observe the
existence of a similar elastic instability in this flow once the Weissenberg number exceeds a critical value.
However, we additionally find that the elastic instability in this model geometry is greatly influenced by
the breakage and reformation dynamics of the wormlike micelles. In particular, the onset of such an
elastic instability is delayed or even may be completely suppressed as the micelles become progressively
easier to break. Furthermore, this elastic instability is seen to be associated with the elastic wave
phenomena which has been recently observed experimentally for polymer solutions. The present study
reveals that the speed of such an elastic wave increases non-linearly with the Weissenberg number
similar to that seen in polymer solutions.