Volkov V S, Leonov A I
Department of Polymer Engineering, The University of Akron, Akron, Ohio 44325-0301, USA
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 1):051113. doi: 10.1103/PhysRevE.64.051113. Epub 2001 Oct 24.
A theory of non-Markovian rotational Brownian motion is developed for axisymmetric particles moving in a Maxwell fluid in the presence of an external field. Both the inertial and viscoelastic effects are taken into account. A kinetic equation for the joint probability distribution of orientation, angular velocity, and acceleration of a particle without spin is derived starting from the rotational Langevin equation with relaxed hydrodynamic and random torques. A third-order stochastic differential equation for the particle orientation vector is also derived. Directly from this equation, the set of nonlinear evolution equations for one-time moments is derived in a noninertial approximation. The expressions for a linear response to a time-dependent external field and dynamic susceptibility of particle are obtained by direct averaging of particle orientation equation. Appendices derive the rotational mobility of axisymmetric particles in a general linear viscoelastic fluid, and the evolution equations for one-time moments of the orientation vector for axisymmetric particles moving in a Maxwell fluid in the presence of an external field.
针对在外部场存在下于麦克斯韦流体中运动的轴对称粒子，发展了一种非马尔可夫旋转布朗运动理论。同时考虑了惯性和粘弹性效应。从带有松弛流体动力学和随机扭矩的旋转朗之万方程出发，推导了无自旋粒子的取向、角速度和加速度联合概率分布的动力学方程。还推导了粒子取向矢量的三阶随机微分方程。直接从该方程出发，在非惯性近似下推导了一次性矩的非线性演化方程组。通过对粒子取向方程直接求平均，得到了对随时间变化的外部场的线性响应表达式以及粒子的动态磁化率。附录推导了轴对称粒子在一般线性粘弹性流体中的旋转迁移率，以及在外部场存在下于麦克斯韦流体中运动的轴对称粒子取向矢量一次性矩的演化方程。
