The extensional effective viscosity, ${\eta }_{\mathrm{e}}$, of a suspension of solid cylindrical fibers in a Newtonian liquid is measured from the gravitational stretching of a quasisteady jet. We vary the length-to-diameter aspect ratio of the fibers, $a$, from $\sim 10$ to $\sim {10}^2$, and the particle volume fraction, $\varphi$, in the range $a\varphi \sim 0.1–2$. For low values of $\varphi$, the extensional viscosity is found to agree with Batchelor's model for the dilute regime, which assumes noninteracting fibers aligned with the stretching direction, but for higher concentrations, ${\eta }_{\mathrm{e}}$ is found to increase much more strongly with increasing $\varphi$ than predicted by available models assuming purely hydrodynamics interactions between the fibers. Additional experiments are performed on the breakup of an unstable capillary bridge for $a=11$. Although the variability in the bridge shape and the deviation from a viscous Newtonian dynamics in the late stage of the breakup increase significantly with increasing $\varphi$, it is found that the mean total duration of the breakup is in good agreement with a Newtonian effective dynamics limited by the extensional viscosity, ${\eta }_{\mathrm{e}}$.

中文翻译：

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拉伸粘度和纤维悬浮线的细化

拉伸有效粘度， ${\eta }_{\mathrm{Ë}}$从准稳态射流的重力拉伸测量在牛顿液体中的实心圆柱形纤维的悬浮液的α1。我们改变了纤维的长径比，$\mathrm{一种}$， 从 $〜10$ 至 $〜{10}^{\mathrm{2个}}$，以及颗粒体积分数， $\varphi$， 范围中 $\mathrm{一种}\varphi 〜0.1–\mathrm{2个}$。对于低值$\varphi$，发现稀释粘度的拉伸粘度与Batchelor模型一致，该模型假定非相互作用的纤维与拉伸方向一致，但浓度较高时， ${\eta }_{\mathrm{Ë}}$ 被发现随着增加而更加强烈地增加 $\varphi$假设纤维之间仅存在流体动力学相互作用，则比可用模型预测的结果要好。对于不稳定的毛细管桥的破裂，还进行了另外的实验，用于$\mathrm{一种}=11$。尽管在分解的后期，桥梁形状的可变性和与粘性牛顿动力学的偏差随增加而显着增加。$\varphi$，发现破裂的平均总持续时间与受拉伸粘度限制的牛顿有效动力学很好地吻合， ${\eta }_{\mathrm{Ë}}$。