We study the inertial settling of suspensions of flexible and rigid fibers using an immersed boundary method. The fibers considered are inextensible and slender, with an aspect ratio of 20. For a single Galileo number of $\text{Ga}=160$, we examine a range of dimensionless bending rigidities $0.1<\gamma <20$ and fiber concentrations $0.5<n{L}^3<25$, with $n$ being the fiber number density and $L$ the fiber length, that spans dilute and semidilute regimes. The settling fibers form streamers, regions where the fibers are packed and settle faster than the average settling velocity of the suspension, for $n{L}^3>10$. In the low-concentration regions outside the streamers, the fibers either go upward or have low settling velocities. Flexible fibers exhibit higher packing inside the streamers and smaller streamers compared to the streamers formed by the rigid fibers. Due to this higher packing, the flexible fibers settle faster compared to the rigid fibers. The formation of the streamers counterbalances the hindering of the settling velocity at higher concentrations. At higher $n{L}^3$, however, the maximum local concentration of fibers relative to a uniform distribution diminishes for both flexible and rigid fibers as the mobility of the fibers becomes limited due to the presence of other fibers in their vicinity. Due to this limited mobility, the deformation of the fibers and their settling orientation become insensitive to $n{L}^3$ for $n{L}^3>7$. In both the dilute and semidilute regimes, flexible fibers are more aligned with the direction perpendicular to gravity compared to rigid fibers.

中文翻译：

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柔性纤维悬浮液的惯性沉降

我们使用沉浸边界方法研究柔性和刚性纤维悬浮液的惯性沉降。所考虑的纤维不可伸长且细长，长径比为20。对于单个伽利略数，$\text{嘎}=160$，我们研究了无量纲的弯曲刚度范围 $0.1<\gamma <20$ 和纤维浓度 $0.5<ñ{\mathrm{大号}}^3<25$，带有 $ñ$ 是纤维数密度和 $\mathrm{大号}$纤维长度，跨越稀薄和半稀薄状态。沉降纤维形成流光，这些区域的纤维堆积和沉降速度比悬浮液的平均沉降速度快，对于$ñ{\mathrm{大号}}^3>10$。在拖缆外的低浓度区域中，纤维要么向上运动，要么沉降速度低。与由刚性纤维形成的拖缆相比，柔性纤维在拖缆内部表现出更高的堆积，而拖缆则更小。由于这种较高的堆积率，所以与刚性纤维相比，柔性纤维沉降得更快。拖缆的形成抵消了较高浓度下沉降速度的阻碍。在更高$ñ{\mathrm{大号}}^3$然而，由于柔性纤维和刚性纤维的移动性由于附近存在其他纤维而受到限制，因此相对于均匀分布的纤维的最大局部浓度减小。由于这种受限的流动性，纤维的变形及其沉降方向变得不敏感$ñ{\mathrm{大号}}^3$ 对于 $ñ{\mathrm{大号}}^3>7$。在稀释和半稀释状态下，与刚性纤维相比，柔性纤维在垂直于重力的方向上更加对齐。