Elastic instabilities and bifurcations in flows of wormlike micellar solutions past single and two vertically aligned microcylinders: Effect of blockage and gap ratios

Abstract

This study presents an extensive numerical investigation on the flow characteristics of wormlike micellar (WLM) solutions past a single and vertically aligned two microcylinders placed in a microchannel in the creeping flow regime. The rheological behavior of the micellar solution is realized based on the two-species Vasquez–Cook–McKinley (VCM) constitutive model, which takes into account both the breakage and re-formation dynamics of micelles. For the case of single microcylinder, as the blockage ratio (ratio of the cylinder diameter to that of the channel height) is gradually varied, we find the existence of a flow bifurcation in the system, and also a gradual transition for a range of flow states, for instance, steady and symmetric or Newtonian like, steady and asymmetric, unsteady periodic and asymmetric, unsteady quasi-periodic and asymmetric, and, finally, unsteady quasi-periodic and symmetric. For the case of two microcylinders, we observe the presence of three distinct flow states in the system, namely diverging (D), asymmetric-diverging (AD), and converging (C) states as the intercylinder spacing in between the two cylinders is varied. Similar types of flow states are also observed in the recent experiments dealing with WLM solutions. However, we show that either this transition from one flow state to another in the case of a single microcylinder or the occurrence of any flow state in the case of two microcylinders is strongly dependent upon the values of the Weissenberg number and the nonlinear VCM model parameter ξ, which basically indicates how easy or hard it is to break a micelle. Based on the results and discussion presented herein for the single and two microcylinders, we hope this study will facilitate the understanding behind the formation of preferential paths or lanes during the flow of viscoelastic fluids through a porous media, which was seen in many prior experiments in the creeping flow regime.

Upstream wall vortices in viscoelastic flow past a cylinder

“…3(b) and (c). However, these effects are extremely weak compared with the downstream asymmetries observed for viscoelastic flow past low- B R cylinders, 20,51–58 and the flow regains symmetry beyond the distance of approximately 10 R . In the present case, by far the most significant phenomena are observed upstream of the cylinder, so we will focus on the instability that forms upstream for the remainder of this work.…”

“…Detailed experiments and numerical simulations suggest that this steady flow asymmetry arises due to a combination of extension in the wake and shear-thinning in the gaps between cylinder and walls. 20,[52][53][54][55][56][57][58] For viscoelastic flow past high-blockage-ratio microcylinders (B R Z 0.5) in low-aspect-ratio channels (a r 0.6), experiments show dynamics that are significantly different from those observed in flow past smaller blockage ratio cylinders in higher aspect ratio channels. For both constant viscosity, highly elastic polymer solutions, 59 and shear-thinning, viscoelastic wormlike micellar solutions, 60 the elastic instability results in the formation of a stagnant vortex region attached to the upstream pole of the cylinder.…”

“…Detailed experiments and numerical simulations suggest that this steady flow asymmetry arises due to a combination of extension in the wake and shear-thinning in the gaps between cylinder and walls. 20,52–58…”

Birefringent strands drive the flow of viscoelastic fluids past obstacles

“…This phenomenon is linked to the shear-thinning rheology of the fluid (Haward et and is hypothesized to stem from a positive feedback mechanism involving the strand (Haward et al 2021b). Khan & Sasmal (2021) recovered these results and showed a change of curvature sign in the convergent and divergent cases. This observation, along with the known effect of a strand in slowing down the flow in the wake of a single cylinder, suggests that strands may play a central role in controlling the relative flow through the different parts of the geometry and the transition mechanisms.…”

Flow dynamics of wormlike micellar solutions through a model porous media

“…All the simulations were run in a parallel fashion with MPI (Message Passing Interface) interface facility available in OpenFOAM wherein each simulation was distributed among 8 to 12 CPU cores, each having 2 GB RAM. A detailed validation of the present numerical setup has already been presented in our earlier studies 39,49,55 , and hence it is not again performed here.…”