The stability of neutrally and non-neutrally buoyant particles immersed in a plane Poiseuille flow of a yield-stress fluid (Bingham fluid) is addressed numerically. Particles being carried by the yield-stress fluid can behave in different ways: they might (i) migrate inside the yielded regions or (ii) be transported without any relative motion inside the unyielded region if the yield stress is large enough compared to the buoyancy stress and the other stresses acting on the particles. Knowing the static stability of particles inside a bath of quiescent yield-stress fluid (Chaparian & Frigaard, J. Fluid Mech. , vol. 819, 2017, pp. 311–351), we analyse the latter behaviour when the yield-stress fluid Poiseuille flow is host to two-dimensional particles. Numerical experiments reveal that particles lose their stability (i.e. break the unyielded plug and sediment/migrate) with smaller buoyancy compared to the sedimentation inside a bath of quiescent yield-stress fluid, because of the inherent shear stress in the Poiseuille flow. The key parameter in interpreting the present results is the position of the particle relative to the position of the yield surface in the undisturbed flow (in the absence of any particle): the larger the portion of a particle located inside the undisturbed sheared regions, the more likely is the particle to be unstable. Yet, we find that the core unyielded plug can grow locally to some extent to contain the particles. This picture holds even for neutrally buoyant particles, although they are strictly stable when they are located wholly inside the undisturbed plug. We propose scalings for all cases.

中文翻译：

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屈服应力流体泊肃叶流中粒子的稳定性

浸入屈服应力流体（宾汉流体）的平面 Poiseuille 流中的中性和非中性浮力粒子的稳定性以数值方式解决。由屈服应力流体携带的粒子可以以不同的方式表现：如果屈服应力与浮力相比足够大，它们可能 (i) 在屈服区域内迁移或 (ii) 在未屈服区域内没有任何相对运动的情况下被传输应力和作用在粒子上的其他应力。知道静态屈服应力流体浴中粒子的静态稳定性（Chaparian & Frigaard, J. Fluid Mech., vol. 819, 2017, pp. 311–351），我们分析了当屈服应力流体泊肃叶流是二维粒子的宿主。数值实验表明粒子失去稳定性（即 由于泊肃叶流中的固有剪应力，与静止屈服应力流体浴内的沉降相比，以较小的浮力破坏未屈服的塞子和沉积物/迁移）。解释当前结果的关键参数是粒子相对于未受干扰流中屈服面位置的位置（在没有任何粒子的情况下）：位于未受干扰剪切区域内的粒子部分越大，更可能是粒子不稳定。然而，我们发现核心未屈服的塞子可以在一定程度上局部生长以包含颗粒。这张图片甚至适用于中性浮力粒子，尽管当它们完全位于未受干扰的塞子内时它们是严格稳定的。我们建议对所有情况进行缩放。