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 (<i>D</i>) and lengths (<i>L</i>). 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 <i>L</i> exceeds the sum of depth <i>D</i> and channel width <i>W</i>. This transition is manifested by a change of vortical structures within the concavity. For <i>L</i> ≤ <i>D</i> + <i>W</i>, "cavity flow" is characterized by large scale recirculations spanning the concavity length. For <i>L</i> > <i>D</i> + <i>W</i>, 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 <i>L</i>-<i>D</i> at various fixed Weissenberg numbers Wi, characterizing the transitions and describing the evolution of vortical structures influenced by viscoelastic effects.