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arXiv 0903.4319cond-mat.softcond-mat.dis-nn
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均匀定常剪切流中布朗粒子的模耦合理论

A mode coupling theory for Brownian particles in homogeneous steady shear flow

Matthias Fuchs, Michael E. Cates

摘要:

提出了一种计算定常剪切下相互作用布朗粒子一般性质的微观方法。我们从精确表达式剪切相关的稳态平均值,如相关性和结构函数,广义格林-久保关系的形式。对于这些,我们应用近似的启发模式耦合理论(MCT)的静态系统,访问稳态性能的整合后,通过启动稳态剪切的瞬态动力学。精确的运动方程,与记忆效应,所需的瞬态密度关联函数推导出接下来,这些也可以近似内的MCT类方法。这导致在封闭的方程的非平衡静态剪切致密胶体分散体,与平衡结构因子的非剪切系统作为唯一的输入。在三维中,这些方程目前需要在数值解之前进一步近似。然而,一些普遍的方面可以准确地分析,包括不连续的屈服应力在理想的玻璃化转变预测的MCT。使用这些方法,我们还讨论了扭曲的微观结构的剪切硬球胶体附近的玻璃化转变,并考虑这与剪切应力。然后近似的定态周围的随时间变化的波动,并从实验和模拟的数据进行比较,产生玻璃态的反射器服从“时间剪切叠加”的原则。这里介绍的工作充分发展了一种方法,首先概述了以前(M。Fuchs和M. E. Cates,Phys. Rev. Lett. 89,248304,(2002)),同时在所使用的模式耦合近似的选择中结合了来自该工作的显著技术变化,讨论了其优点。

英文摘要:

A microscopic approach is presented for calculating general properties of interacting Brownian particles under steady shearing. We start from exact expressions for shear-dependent steady-state averages, such as correlation and structure functions, in the form of generalized Green-Kubo relations. To these we apply approximations inspired by the mode coupling theory (MCT) for the quiescent system, accessing steady-state properties by integration through the transient dynamics after startup of steady shear. Exact equations of motion, with memory effects, for the required transient density correlation functions are derived next; these can also be approximated within an MCT-like approach. This results in closed equations for the non-equilibrium stationary state of sheared dense colloidal dispersions, with the equilibrium structure factor of the unsheared system as the only input. In three dimensions, these equations currently require further approximation prior to numerical solution. However, some universal aspects can be analyzed exactly, including the discontinuous onset of a yield stress at the ideal glass transition predicted by MCT. Using these methods we additionally discuss the distorted microstructure of a sheared hard-sphere colloid near the glass transition, and consider how this relates to the shear stress. Time-dependent fluctuations around the stationary state are then approximated, and compared to data from experiment and simulation; the correlators for yielding glassy states obey a `time-shear-superposition' principle. The work presented here fully develops an approach first outlined previously (M. Fuchs and M. E. Cates, Phys. Rev. Lett. 89, 248304, (2002)), while incorporating a significant technical change from that work in the choice of mode coupling approximation used, whose advantages are discussed.

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