GOALI: Multiscale Modeling of Electro- and Magnetorheological Fluids

摘要-0424087电流变液和磁流变液是一种颗粒悬浮液，其流变性分别受到电场和磁场的影响。外加电场还改变了悬浮液的微观结构，使静止悬浮液中形成向场方向的颗粒柱，而在剪切悬浮液中形成沿流动方向的浓密颗粒条纹。这些结构变化与流变现象密切相关。众所周知，颗粒柱的形成会引起剧烈的流变性变化。条纹的出现与瞬时流变反应的开始有关，其中剪切应力随着条纹的合并、粗化和致密而缓慢增加。电流变液和磁流变液正被用于减震器、离合器和刹车等应用的开发，磁流变液的应用最近达到了商业化。对于电流变和磁流变流体和装置的设计、优化和控制，了解和模拟其结构和流变行为是至关重要的。粒子级模拟对于理解粒子特性、相互作用和宏观行为之间的关系很有价值。然而，这些方法计算成本很高，因此不适合对整个设备的行为进行建模。必须开发其他建模策略来补充粒子级别的模拟，并克服其固有的限制。我们发展了电流变悬浮液结构演化的连续统描述，其特征是颗粒体积分数_(x；t)随时间和位置的变化。颗粒通量通过动量平衡与颗粒对应力的贡献有关。使用这种双流体方法，人们可以预测实验中观察到的模式--静止悬浮液中的柱状形成和剪切悬浮中的条纹形成--而不需要跟踪单个颗粒的运动的计算费用。虽然这种连续介质模型可以成功地再现结构演化的某些特征，但对本构行为所采用的假设限制了它的预测能力。最值得注意的是，假设适用于各向同性悬浮液的静电应力的形式排除了对场诱导剪切应力的估计，从而排除了相关的流变瞬变；忽略非局部极化几乎不能洞察长时间的瞬变。所提出的工作的主要目标是结合两种建模方法的优点，以获得对ER/MR流体和器件的多尺度描述，克服我们先前连续介质建模工作的局限性。我们将使用粒子级模拟(即，斯托克斯动力学模拟)来确定用于连续介质模型的颗粒应力和颗粒通量的适当本构行为。采用这种本构行为将使我们能够从连续介质的角度来探索结构的演化和剪切流变学。我们还将扩展电流变流体的自洽场模型来模拟连续介质模型中的非局域极化贡献，以便描述长时间的瞬变现象。所提出的工作将产生一个完整的连续描述电流变和磁流变流体中的质量传输，可用于电流变和磁流变流体和装置的设计、优化和控制。模拟研究将由克林根伯格、莫里斯和学生进行，并继续与通用汽车的乌利克尼进行咨询。验证实验将在威斯康星州大学和通用汽车进行。通用汽车还将在通用汽车的离合器试验台上提供离合器性能的实验结果。所提出的工作将特别有益于剪切电流变和磁流变装置的设计、优化和控制，因为它为流变学和质量传输提供了一个模型。这些信息是必要的，因为在剪切的ER和MR流体中，颗粒传输似乎无处不在，并影响表观流变学。更广泛地说，随着我们进一步发展描述悬浮液流动的连续介质方法，所提出的工作将有利于悬浮力学研究。这项工作的更广泛影响包括通过培训本科生和研究生在这项工作的技术建模方面以及实验技术方面的教育部分。这项工作的成果将通过向参考期刊提交手稿和在科学会议上介绍的方式向科学界提供。

ABSTRACT - 0424087Electro- and magnetorheological (ER and MR) fluids are particulate suspensions whose rheological properties are dramatically altered by electric and magnetic fields, respectively. The applied fields also alter the suspension microstructure, causing the formation of particulate columns oriented in the field direction in quiescent suspensions, and the formation of concentrated particulate stripes oriented in the flow direction in sheared suspensions. These structural changes are intimately connected to the rheological phenomena. The formation of particulate columns is known to cause the dramatic rheological changes. The appearance of stripes is associated with the onset of a transient rheological response, where the shear stress slowly increases as the stripes coalesce, coarsen, and densify. ER and MR fluids are being exploited in the development of such applications as shock absorbers, clutches, and brakes, with MR applications recently reaching commercialization. Understanding and modeling the transient structural and rheological behavior is crucial for the design, optimization and control of ER and MR fluids and devices. Particle-level simulations have been valuable for understanding the relationships between particle properties, interactions, and macroscopic behavior. However, these approaches are computationally expensive, and thus ill-suited for modeling the behavior of an entire device. Other modeling strategies must be developed to complement particle-level simulations and overcome their inherent limitations. We have developed a continuum description of the structure evolution in ER suspensions, as characterized by the time and position-dependent particle volume fraction _(x; t). The particle flux is related to the particle contribution to the stress via a momentum balance. Using this two-fluid approach, one predicts the patterns observed experimentally-column formation in quiescent suspensions, and stripe formation in sheared suspensions- without the computational expense of following the motion of individual particles. Although this continuum model can successfully reproduce certain features of structure evolution, assumptions employed for the constitutive behavior limit its predictive power. Most notably, assuming a form for the electrostatic stress appropriate for an isotropic suspension precludes an estimate for the field-induced shear stress and thus the associated rheological transients; and the neglect of nonlocal polarization gives little insight into the long-time transients. The main goal of the proposed work is to combine the strengths of the two modeling approaches to obtain a multiscale description of ER/MR fluids and devices, overcoming the limitations of our prior continuum modeling effort. We will employ particle-level simulations (i.e., Stokesian dynamics simulations) to determine the appropriate constitutive behavior for particle stress and particle flux for use in the continuum model. Employing this constitutive behavior will allow us to probe both the evolution of structure and shear rheology from a continuum perspective. We will also extend a selfconsistent field model of ER fluids to model nonlocal polarization contributions in the continuum model, in order to describe the long-time transient phenomena. The proposed work will yield a complete continuum description of the rheology and mass transport in ER and MR fluids that can be used in the design, optimization and control of ER and MR fluids and devices. Simulation studies will be performed by Klingenberg, Morris, and students, with continuing consultation with Ulicny at General Motors. Experiments for verification will be performed at both UW and GM. GM will also provide experimental results for clutch performance from measurements on a clutch test rig at GM.Intellectual Merit and Broader Impact. The proposed work will specifically benefit the design, optimization and control of sheared ER and MR devices by providing a models for both the rheology and mass transport. Such information is necessary as particle transport appears to be ubiquitous in sheared ER and MR fluids, and impacts the apparent rheology. More generally, the proposed work will benefit suspension mechanics research as we further develop continuum methods for describing the flow of suspensions. The broader impact of this work includes an educational component through the training of undergraduate and graduate students in the technical modeling aspects of this work, as well as the experimental techniques. Results from this work will be available to the scientific community through submission of manuscripts to refereed journals, and presentations at scientific meetings.