We analyze a suspension of deformable particles in a pressure-driven flow. The suspension is composed of neutrally buoyant initially spherical particles and a Newtonian carrier fluid, and the flow is solved by means of direct numerical simulations, using a fully Eulerian method based on a one-continuum formulation. The solid phase is modeled with an incompressible viscous hyperelastic constitutive relation, and the flow is characterized by three main dimensionless parameters, namely the solid volume fraction, the Reynolds and capillary numbers. The dependency of the effective viscosity on these three quantities is investigated to study the inertial effects on a suspension of deformable particles. It can be observed that the suspension has a shear-thinning behavior, and the reduction in effective viscosity for high shear rates is emphasized in denser configurations. The separate analysis of the Reynolds and capillary numbers reveal that the effective viscosity depends more on the capillary than on the Reynolds number. In addition, our simulations exhibit a consistent tendency for deformable particles to move towards the center of the channel, where the shear rate is low. This phenomenon is particularly marked for very dilute suspensions, where a whole region near the wall is empty of particles. Furthermore, when the volume fraction is increased this near-wall region is gradually occupied, because of higher mutual particle interactions. Deformability also plays an important role in the process. Indeed, at high capillary numbers, particles are more sensitive to shear rate variations and can modify their shape more easily to accommodate a greater number of particles in the central region of the channel.

中文翻译：

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泊肃叶中可变形粒子的悬浮在有限惯性下流动

我们分析了压力驱动流中可变形颗粒的悬浮液。悬浮液由中性浮力的初始球形颗粒和牛顿载体流体组成，流动通过直接数值模拟求解，使用基于单连续体公式的全欧拉方法。固相用不可压缩的粘性超弹性本构关系建模，流动的特征是三个主要的无量纲参数，即固体体积分数、雷诺数和毛细管数。研究了有效粘度对这三个量的依赖性，以研究对可变形颗粒悬浮液的惯性影响。可以观察到悬浮液具有剪切稀化行为，在更密的配置中强调了高剪切速率下有效粘度的降低。雷诺数和毛细管数的单独分析表明，有效粘度更多地取决于毛细管而不是雷诺数。此外，我们的模拟显示出可变形颗粒向通道中心移动的一致趋势，此处剪切速率较低。这种现象在非常稀的悬浮液中尤为明显，其中靠近壁的整个区域都没有颗粒。此外，当体积分数增加时，由于更高的粒子相互作用，该近壁区域逐渐被占据。可变形性在该过程中也起着重要作用。事实上，在高毛细管数下，