An exact solution of coarse-grained polymer models with fluctuating internal friction and hydrodynamic interactions has not been proposed so far due to a one-to-all coupling between the connector vector velocities that precludes the formulation of the governing stochastic differential equations. A methodology for the removal of this coupling is presented, and the governing stochastic differential equations, obtained by attaching a kinetic interpretation to the Fokker–Planck equation for the system, are integrated numerically using Brownian dynamics simulations. The proposed computational route eliminates the calculation of the divergence of the diffusion tensor, which appears in models with internal friction, and is about an order of magnitude faster than the recursion-based algorithm for the decoupling of connector-vector velocities previously developed [Kailasham et al., J. Rheol. 65, 903 (2021)] for the solution of freely draining models with internal friction. The effects of the interplay of various combinations of finite extensibility, internal friction, and hydrodynamic interactions on the steady-shear-viscosity are examined. While finite extensibility leads solely to shear-thinning, both internal friction and hydrodynamic interactions result in shear-thinning followed by shear-thickening. The shear-thickening induced by internal friction effects is more pronounced than that due to hydrodynamic interactions.

中文翻译：

---

具有波动内摩擦和流体动力相互作用的有限可延伸链的剪切粘度

到目前为止，由于连接器矢量速度之间的一对一耦合排除了控制随机微分方程的公式，因此尚未提出具有波动内摩擦和流体动力相互作用的粗粒度聚合物模型的精确解。提出了一种消除这种耦合的方法，并使用布朗动力学模拟对通过对系统的福克-普朗克方程进行动力学解释而获得的控制随机微分方程进行了数值积分。所提出的计算路线消除了扩散张量散度的计算，该散度出现在具有内摩擦的模型中，等。, J. Rheol. 65 , 903 (2021)] 用于解决具有内摩擦的自由排水模型。研究了有限延展性、内摩擦和流体动力相互作用的各种组合的相互作用对稳态剪切粘度的影响。虽然有限的延展性只会导致剪切稀化，但内摩擦和流体动力学相互作用都会导致剪切稀化，然后是剪切增稠。由内摩擦效应引起的剪切增稠比由流体动力相互作用引起的剪切增稠更为明显。