Brader J M, Voigtmann Th, Cates M E, Fuchs M
Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany.
Phys Rev Lett. 2007 Feb 2;98(5):058301. doi: 10.1103/PhysRevLett.98.058301. Epub 2007 Jan 31.
We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity), we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear stress as an example, we derive exactly a generalized Green-Kubo relation and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step strain.
我们考虑了在随时间变化的简单剪切流作用下致密胶体悬浮液的非线性流变学。从描述受剪切作用的相互作用布朗粒子的斯莫卢霍夫斯基方程出发（忽略流体速度的涨落），我们发展了一种形式体系，该体系能够计算随时间变化的、远离平衡的平均值。以剪切应力为例，我们精确推导了一个广义格林 - 库博关系以及瞬态密度关联函数的运动方程，其中涉及一个三次记忆函数。模式耦合近似给出了一个封闭的本构方程，可得出任意剪切速率历史下随时间变化的应力。对于硬球玻璃在阶跃应变作用下的特殊情况，我们对该方程进行了数值求解。
