We explore theoretically the interplay between shear banding and edge fracture in complex fluids, by performing a detailed simulation study within two constitutive models: the Johnson-Segalman model and the Giesekus model. We consider separately parameter regimes in which the underlying constitutive curve is monotonic and non-monotonic, such that the bulk flow (in the absence of any edge effects) is respectively homogeneous and shear banded. Phase diagrams of the levels of edge disturbance and of bulk (or quasi-bulk) shear banding are mapped as a function of the surface tension of the fluid-air interface, the wetting angle where this interface meets the walls of the flow cell, and the imposed shear rate. In particular, we explore in more detail the basic result recently announced in Hemingway et al. (2018): that precursors to edge fracture can induce quasi-bulk shear banding. We also appraise analytical predictions that shear banding can induce edge fracture, Skorski and Olmsted (2011). Although a study of remarkable early insight, that study made some strong assumptions about the nature of the "base state", which we examine using direct numerical simulation. The basic prediction that shear banding can cause edge fracture remains valid, but with qualitatively modified phase boundaries.

中文翻译：

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复杂流体中边缘断裂和剪切带的相互作用

我们通过在两个本构模型（Johnson-Segalman 模型和 Giesekus 模型）中进行详细的模拟研究，从理论上探索复杂流体中剪切带和边缘裂缝之间的相互作用。我们分别考虑基本本构曲线是单调和非单调的参数制度，使得体流（在没有任何边缘效应的情况下）分别是均匀的和剪切带。边缘扰动和体积（或准体积）剪切带水平的相图被映射为流体 - 空气界面的表面张力，该界面与流动池壁相遇的润湿角，以及施加的剪切速率。特别是，我们更详细地探讨了 Hemingway 等人最近宣布的基本结果。(2018): 边缘断裂的前兆会引起准整体剪切带。我们还评估了剪切带会导致边缘断裂的分析预测，Skorski 和 Olmsted (2011)。尽管这项研究是对早期洞察力的研究，但该研究对“基态”的性质做了一些强有力的假设，我们使用直接数值模拟对其进行了检查。剪切带会导致边缘断裂的基本预测仍然有效，但具有定性修改的相边界。