Confined flow of suspensions modelled by a frictional rheology
Confined flow of suspensions modelled by a frictional rheology
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DOI：
10.1017/jfm.2014.557
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发表时间：
2014-09
影响因子：
3.7
通讯作者：
B. Lecampion;D. Garagash
中科院分区：
文献类型：
--
作者：
B. Lecampion;D. Garagash
摘要本文根据Boyer等人最近提出的摩擦流变学理论（Phys. Rev. Lett.，第107（18）卷，2011，188301）。摩擦系数（剪切应力超过颗粒法向应力）和固体体积分数被视为无量纲粘性数$I$的函数，定义为流体剪切应力和颗粒法向应力之间的比率。我们澄清的贡献的接触和流体动力学相互作用之间的摩擦系数的演变稀和密制度减少唯象本构描述的三个物理参数。我们还提出了一个扩展的本构框架的流动制度（有界的最大流动固体体积分数）的完全堵塞的状态（随机密堆积限制）。给出了槽道和管道中充分发展流动的摩擦悬浮流变学解析解。在适当重新定义无因次数$I$后，结果可以转置为干颗粒流。的预测是在良好的协议与中性浮力悬浮液的实验结果，当使用的本构参数的值独立获得的应力控制流变测量。特别是，摩擦流变学正确地预测了从Poilluille到活塞流的转变以及伴随的颗粒迁移与入口固体体积分数的增加。我们还数值求解了从通道/管道的入口到完全发展状态的流动的轴向发展。可用的实验数据与我们的数值预测吻合得很好，当使用一个公认的现象学描述的相对相位滑移获得独立的批处理沉降实验。当连续介质假设成立时，流动的轴向发展的解决方案明显地提供了管道中悬浮液入口长度效应的定量估计。实际上，后者要求中心（堵塞）塞的预测宽度比一个颗粒直径宽。一个简单的解析表达式的发展长度，成反比的间隙平均扩散系数的摩擦悬浮液，封装的数值解在整个范围内的流动条件从稀到密。
Abstract We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al. (Phys. Rev. Lett., vol. 107 (18), 2011, 188301). The friction coefficient (shear stress over particle normal stress) and solid volume fraction are taken as functions of the dimensionless viscous number $I$ defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive framework from the flowing regime (bounded by the maximum flowing solid volume fraction) to the fully jammed state (the random close packing limit). We obtain an analytical solution of the fully developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number $I$ . The predictions are in excellent agreement with available experimental results for neutrally buoyant suspensions, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We also numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully developed state. The available experimental data are in good agreement with our numerical predictions, when using an accepted phenomenological description of the relative phase slip obtained independently from batch-settlement experiments. The solution of the axial development of the flow notably provides a quantitative estimation of the entrance length effect in a pipe for suspensions when the continuum assumption is valid. Practically, the latter requires that the predicted width of the central (jammed) plug is wider than one particle diameter. A simple analytical expression for development length, inversely proportional to the gap-averaged diffusivity of a frictional suspension, is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.