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arXiv 1905.09779cond-mat.soft
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在多种几何形状下验证的稠密细颗粒悬浮液的通用本构模型

A general constitutive model for dense, fine particle suspensions validated in many geometries

Aaron Baumgarten, Ken Kamrin

摘要:

细颗粒悬浮液(如玉米淀粉与水的混合物)在剪切时表现出粘度的巨大变化,产生令人着迷的行为,吸引了儿童和流变学家。最近检查这些混合物在简单的流动几何形状表明,颗粒间的排斥是这种效果的核心-混合物在休息或剪切缓慢,排斥防止颗粒之间形成摩擦接触,而当剪切更有力,颗粒应力克服排斥,使颗粒相互作用的阻力,并形成微观结构,抵制流动。这些混合物以前的本构研究集中在特定的情况下,通常限于二维,稳定,简单的剪切流。在这项工作中,我们介绍了一个预测和一般的,三维连续模型,这种材料,使用混合物理论耦合的流体和颗粒相。在模型中扮演核心角色,我们引入了一个微观结构状态变量,其演变推导出小尺度的物理参数,并检查与现有的数据。我们的空间和时间相关模型在各种不稳定、非均匀流配置中进行了数值实现,其中显示出准确捕获各种关键行为:(i)在定常流中观察到的连续剪切增稠(CST)和不连续剪切增稠(DST)行为,(ii)“剪切干扰锋”随时间的传播,(iii)“撞击激活干扰锋”的时间依赖性传播,以及(iv)非牛顿的“运行在欧布莱克”效应,其中快速运动体保持漂浮,而慢速运动体下沉。

英文摘要:

Fine particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Recent examination of these mixtures in simple flow geometries suggests inter-granular repulsion is central to this effect --- for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas, when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to two-dimensional, steady, simple shearing flows. In this work, we introduce a predictive and general, three-dimensional continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a micro-structural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, non-uniform flow configurations where it is shown to accurately capture a variety of key behaviors: (i) the continuous shear thickening (CST) and discontinuous shear thickening (DST) behavior observed in steady flows, (ii) the time-dependent propagation of `shear jamming fronts', (iii) the time-dependent propagation of `impact activated jamming fronts', and (iv) the non-Newtonian, `running on oobleck' effect wherein fast locomotors stay afloat while slow ones sink.

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