Flow of wormlike micellar solutions over concavities†

Abstract

We present a comprehensive investigation combining numerical simulations with experimental validation, focusing on the creeping flow behavior of a shear-banding, viscoelastic wormlike micellar (WLM) solution over concavities with various depths (D) and lengths (L). The fluid is modeled using the diffusive Giesekus model, with model parameters set to quantitatively describe the shear rheology of a 100 : 60 mM cetylpyridinium chloride:sodium salicylate aqueous WLM solution used for the experimental validation. We observe a transition from “cavity flow” to “expansion–contraction flow” as the length L exceeds the sum of depth D and channel width W. This transition is manifested by a change of vortical structures within the concavity. For L ≤ D + W, “cavity flow” is characterized by large scale recirculations spanning the concavity length. For L > D + W, the recirculations observed in “expansion–contraction flow” are confined to the salient corners downstream of the expansion plane and upstream of the contraction plane. Using the numerical dataset, we construct phase diagrams in L–D at various fixed Weissenberg numbers Wi, characterizing the transitions and describing the evolution of vortical structures influenced by viscoelastic effects.