Effect of chain scission on flow characteristics of wormlike micellar solutions past a confined microfluidic cylinder: a numerical analysis†

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.