Computational Chemical Physics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Physical Chemistry and Soft Matter, Wageningen University, Building 124, Stippeneng 4, 6708 WE, Wageningen, The Netherlands.
J Chem Phys. 2018 Jan 21;148(3):034902. doi: 10.1063/1.5006627.
We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.
我们提出了一种新颖的基于粗粒粒子的模拟技术，用于模拟稀溶液和半稀溶液中聚合物的自发展流动。本文的核心思想是介观聚合物模型和唯象流体模型之间的双向耦合。作为我们的聚合物模型，我们选择了响应粒子动力学（RaPiD），这是一种布朗动力学方法，它通过所谓的“保守”和“瞬态”对势能来构建，聚合物通过这些对势能与随机力相互作用，同时根据涨落耗散定理经历随机力。除了这些相互作用之外，我们的聚合物团块还受到背景溶剂速度场的影响，我们通过求解在移动流体团块网格上离散的纳维-斯托克斯方程并用平滑粒子流体动力学（SPH）技术来计算速度场。当聚合物经历与背景流场相对的摩擦力时，我们的流体团块也通过相互作用项受到聚合物运动的影响。这使得我们的技术成为一种双向耦合算法。我们以一种使局部动量守恒的方式构建了这种相互作用项，从而保留了长程流体力学。此外，我们使用福克-普朗克方程为流体团块的速度推导了成对的涨落项，这些涨落项也可以使用平滑耗散粒子动力学（SDPD）文献中的通用非平衡可逆-不可逆耦合（GENERIC）方法替代推导。这些流体的速度涨落可以纳入我们的流体团块的速度更新中，以获得热力学一致的速度分布。然而，在这些涨落不显著的情况下，这些额外的项可以像在标准 SPH 模拟中一样被省略。我们将我们的技术应用于研究两种不同浓度的线性聚合物溶液的流变学。结果表明，聚合物和流体之间相互耦合得非常好，它们的速度之间没有滞后。此外，我们的结果显示了非牛顿剪切稀化和聚合物溶液中通常观察到的泊肃叶流型的特征扁平化。
