Abstract The effect of the slip-shear as well as the rotation on the inertial migration of finite-size spheres with blockage ratio (ratio of the sphere diameter to the channel gap) 0.2 are investigated in a plane Poiseuille flow at Re = 100 – 500 using dissipative particle dynamics simulations, by means of changing the driving force, the sphere density, and the fluid-sphere boundary slip condition, respectively. Neutrally buoyant spheres with equal density with the fluid and with no-slip boundary condition are observed to equilibrated at lateral positions around midway between the channel centerline and the wall, and the positions move closer to the channel centerline with increasing Re. The spheres always lag behind the surrounding fluid. A correction to the slip is proposed by considering the effect of the distance between the sphere and the wall. A forward driving force or a larger density facilitates the forward motion of the spheres and leads to their leading relative to the surrounding fluid, which drives the spheres to lateral equilibrium positions close to the wall; and vice versa. All spheres rotate with angular velocities approximate to but a bit less than the half of the local fluid shear rate at the sphere centroid, no mater the spheres are neutrally or non-neutrally buoyant, expect the spheres much close to the wall. The lift induced by rotation is found one to two orders of magnitude less than the lift induced by slip-shear due to the small angular slip velocity between the sphere and the surrounding fluid; while the slip-shear-induced lift is found critical to determine the lateral equilibrium positions of finite-size spheres cooperating with the wall-induced lift and the shear-gradient-induced lift as Re varies. An empirical theory considering the last three lifts above mentioned is built, which interprets the relation between the slip-shear and the equilibrium positions of the spheres. Above relation holds for spheres with no-slip boundary condition, whilst for neutrally buoyant spheres with full-slip boundary condition, though they always lag behind the surrounding fluid, they migrate towards the wall as Re increases, as their hydrodynamic interactions with the fluid are changed.

中文翻译：

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平面 Poiseuille 流中有限尺寸球体的滑剪和惯性迁移

摘要 在 Re = 100 – 500 的平面 Poiseuille 流中研究了滑剪和旋转对阻塞比（球体直径与通道间隙之比）为 0.2 的有限尺寸球体惯性迁移的影响使用耗散粒子动力学模拟，分别通过改变驱动力、球体密度和流体-球体边界滑移条件。观察到与流体密度相等且具有无滑移边界条件的中性浮球在通道中心线和壁之间的中间附近的横向位置处平衡，并且这些位置随着 Re 的增加而靠近通道中心线。球体总是落后于周围的流体。通过考虑球体和壁之间距离的影响，提出了对滑移的修正。向前的驱动力或较大的密度有利于球体向前运动并导致其相对于周围流体的领先，从而将球体驱动到靠近壁的横向平衡位置；反之亦然。所有球体都以接近但略小于球体质心处局部流体剪切速率的一半的角速度旋转，无论球体是中性还是非中性浮力，都希望球体非常靠近壁。由于球体与周围流体之间的角滑移速度小，旋转引起的升力比滑移引起的升力小一到两个数量级；而滑动剪切引起的升力对于确定与壁引起的升力和剪切梯度引起的升力协同作用的有限尺寸球体的横向平衡位置至关重要，因为 Re 变化。建立了考虑上述最后三个升力的经验理论，解释了滑移剪切与球体平衡位置之间的关系。上述关系适用于具有无滑移边界条件的球体，而对于具有全滑移边界条件的中性浮力球体，尽管它们总是落后于周围的流体，但随着 Re 的增加，它们向壁迁移，因为它们与流体的流体动力学相互作用为改变了。建立了考虑上述最后三个升力的经验理论，解释了滑移剪切与球体平衡位置之间的关系。上述关系适用于具有无滑移边界条件的球体，而对于具有全滑移边界条件的中性浮力球体，尽管它们总是落后于周围的流体，但随着 Re 的增加，它们向壁迁移，因为它们与流体的流体动力学相互作用为改变了。建立了考虑上述最后三个升力的经验理论，解释了滑移剪切与球体平衡位置之间的关系。上述关系适用于具有无滑移边界条件的球体，而对于具有全滑移边界条件的中性浮力球体，尽管它们总是落后于周围的流体，但随着 Re 的增加，它们向壁迁移，因为它们与流体的流体动力学相互作用为改变了。