scholarly journals Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids

Polymers ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 465 ◽  
Author(s):  
Soroush Moghadam ◽  
Indranil Saha Dalal ◽  
Ronald Larson
Keyword(s):  
Unit Length ◽  
Extensional Flow ◽  
Computational Cost ◽  
Weissenberg Number ◽  
Dynamics Simulation ◽  
Contour Length ◽  
Spring Model ◽  
Single Chain ◽  
Hencky Strain ◽  
Affine Motion

We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number W i R ≫ 1 ) of long ( M w > 1   Mkg / mol for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of ζ ′ ϵ ˙ L 2 / 8 where ζ ′ , ϵ ˙ and L are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight ( M w > 1   Mkg / mol ) polymers in fast flows ( W i R ≫ 1 ), where conventional simulation techniques are less applicable due to computational cost.

Bayesian active learning of interatomic force field for molecular dynamics simulation of Pt/Ag(111)

2021 ◽  
Author(s):  
Kai Xu ◽  
Lei Yan ◽  
Bingran You
Keyword(s):  
Molecular Dynamics ◽  
Active Learning ◽  
Force Field ◽  
Density Functional ◽  
Process Model ◽  
Large Scale ◽  
Computational Cost ◽  
Dynamics Simulation ◽  
Potential Energy Landscape ◽  
Three Body

Force field is a central requirement in molecular dynamics (MD) simulation for accurate description of the potential energy landscape and the time evolution of individual atomic motions. Most energy models are limited by a fundamental tradeoff between accuracy and speed. Although ab initio MD based on density functional theory (DFT) has high accuracy, its high computational cost prevents its use for large-scale and long-timescale simulations. Here, we use Bayesian active learning to construct a Gaussian process model of interatomic forces to describe Pt deposited on Ag(111). An accurate model is obtained within one day of wall time after selecting only 126 atomic environments based on two- and three-body interactions, providing mean absolute errors of 52 and 142 meV/Å for Ag and Pt, respectively. Our work highlights automated and minimalistic training of machine-learning force fields with high fidelity to DFT, which would enable large-scale and long-timescale simulations of alloy surfaces at first-principles accuracy.

scholarly journals Turbulent drag reduction by polymer additives in parallel-shear flows

2017 ◽  
Vol 827 ◽  
Author(s):  
Bayode E. Owolabi ◽  
David J. C. Dennis ◽  
Robert J. Poole
Keyword(s):  
Drag Reduction ◽  
Cross Sections ◽  
Shear Flows ◽  
Extensional Flow ◽  
Relaxation Times ◽  
Weissenberg Number ◽  
Mechanical Degradation ◽  
Turbulent Drag Reduction ◽  
Time Resolved ◽  
Turbulent Drag

In this study, we experimentally investigate the turbulent drag-reduction (DR) mechanism in flow through ducts of circular, rectangular and square cross-sections using two grades of polyacrylamide in aqueous solution having different molecular weights and various semidilute concentrations. Specifically, we explore the relationship between drag reduction and fluid elasticity, purposely exploiting the mechanical degradation of polymer molecules to vary their rheological properties. We also obtain time-resolved velocity data for various DR levels using particle image velocimetry and laser Doppler velocimetry. Elasticity is quantified via relaxation times determined from uniaxial extensional flow using a capillary breakup apparatus. A plot of DR against Weissenberg number ($Wi$) is found to approximately collapse the data, with the onset of DR occurring at $Wi\approx 0.5$ and the maximum drag-reduction asymptote being approached for $Wi\gtrsim 5$. Thus quantitative predictions of DR in a range of shear flows can be made from a single measurable material property of a polymer solution, at least for this particular flexible linear polymer.

scholarly journals Contraction of Entangled Polymers After Large Step Shear Deformations in Slip-Link Simulations

Polymers ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 370 ◽  
Author(s):  
Yuichi Masubuchi
Keyword(s):  
Dynamics Simulation ◽  
Uniaxial Deformation ◽  
Single Chain ◽  
Orientational Relaxation ◽  
Entangled Polymers ◽  
Constraint Release ◽  
Large Step ◽  
Entangled Polymer ◽  
Convective Constraint Release ◽  
Chain Contraction

Although the tube framework has achieved remarkable success to describe entangled polymer dynamics, the chain motion assumed in tube theories is still a matter of discussion. Recently, Xu et al. [ACS Macro Lett. 2018, 7, 190–195] performed a molecular dynamics simulation for entangled bead-spring chains under a step uniaxial deformation and reported that the relaxation of gyration radii cannot be reproduced by the elaborated single-chain tube model called GLaMM. On the basis of this result, they criticized the tube framework, in which it is assumed that the chain contraction occurs after the deformation before the orientational relaxation. In the present study, as a test of their argument, two different slip-link simulations developed by Doi and Takimoto and by Masubuchi et al. were performed and compared to the results of Xu et al. In spite of the modeling being based on the tube framework, the slip-link simulations excellently reproduced the bead-spring simulation result. Besides, the chain contraction was observed in the simulations as with the tube picture. The obtained results imply that the bead-spring results are within the scope of the tube framework whereas the failure of the GLaMM model is possibly due to the homogeneous assumption along the chain for the fluctuations induced by convective constraint release.

Contact Analysis Between a Moving Solid and the Boundary of Its Swept Volume

2008 ◽  
Author(s):  
Hu¨seyin Erdim ◽  
Horea T. Ilies¸
Keyword(s):  
Moving Objects ◽  
Tool Path ◽  
Computational Cost ◽  
Moving Object ◽  
Reconstruction Algorithms ◽  
Functional Changes ◽  
Affine Motion ◽  
The Family ◽  
Data Output ◽  
Swept Volume

The modeling of many practical problems in design and manufacturing involving moving objects relies on sweeps and their boundaries, which are mathematically described by the envelopes to the family of shapes generated by the moving object. In many problems, such as the design and analysis of higher pairs or tool path planning, contact changes between the moving object and the boundary of its swept volume become critical because they often translate into functional changes of the system under consideration. However, the difficulty of this task quickly escalates beyond the reach of existing approaches as the complexity of the shape and motion increases. We recently proposed a sweep boundary evaluator for general sweeps in conjunction with efficient point sampling and surface reconstruction algorithms that relies on our novel point membership classification (PMC) test for general solid sweeps. In this paper we describe a new approach that automates the prediction of changes in the state of contact between a shape of arbitrary complexity moving according to an affine motion, and the boundary of its swept set. We show that we can predict when and where such contact changes occur with only minimal additional computational cost by exploiting the data output by our sweep boundary evaluator. We discuss the problem and the associated computational issues in a 2D framework, and we conclude by discussing the extension of our approach to 3D moving objects.

Calculation of Stall Margin Enhancement With Micro-Tip Injection in an Axial Compressor

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Xiaohua Liu ◽  
Jinfang Teng ◽  
Jun Yang ◽  
Xiaofeng Sun ◽  
Dakun Sun ◽  
...  
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Radial Profile ◽  
Computational Cost ◽  
Tip Clearance ◽  
Dynamics Simulation ◽  
Qualitative Assessment ◽  
Force Model ◽  
Tip Leakage Flow ◽  
Stall Margin

Although steady micro-injection is experimentally validated as an attractive method in improving the stall margin of axial compressors, up to now a fast prediction of stall boundary remains some way off. This investigation is to propose such a prediction model. A flow stability model is developed to further consider the effect of high-speed micro-injection. After the base flow field is calculated by steady computational fluid dynamics simulation, a body force model is applied to reproduce the effect of blade on the flow turning and loss. A group of homogeneous equations are obtained based on linearized Navier–Stokes equations and harmonic decomposition of small flow disturbance. The stall onset point can be judged by the imaginary part of the resultant eigenvalue. After the existing experimental results are summarized, an unsteady numerical simulation reveals that the computed characteristics and radial profile of pressure rise coefficient are almost unchanged. The unsteady response of compressor to the micro-injection is preliminarily verified based on the observation of the disturbed spillage of tip leakage flow. It is verified that this approach can provide a qualitative assessment of stall point with acceptable computational cost. Both high injection velocity and short axial gap between injector and rotor leading edge are beneficial for the stall margin extension. These theoretical findings agree well with experimental measurements. It is inferred that the spillage of tip clearance flow, which is inward pushed by higher speed injection with shortened distance away from rotor, could lead to further stable flow field.

scholarly journals Hierarchical Stochastic Model in Bayesian Inference for Engineering Applications: Theoretical Implications and Efficient Approximation

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Stephen Wu ◽  
Panagiotis Angelikopoulos ◽  
James L. Beck ◽  
Petros Koumoutsakos
Keyword(s):  
Stochastic Model ◽  
Interpolation Method ◽  
Computational Cost ◽  
Dynamics Simulation ◽  
Cancer Drug ◽  
Engineering Applications ◽  
Pkpd Model ◽  
Selection Framework ◽  
Model Class Selection ◽  
Efficient Approximation

Hierarchical Bayesian models (HBMs) have been increasingly used for various engineering applications. We classify two types of HBM found in the literature as hierarchical prior model (HPM) and hierarchical stochastic model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on importance sampling (IS) and empirical interpolation method (EIM). We illustrate our method using two engineering examples—a molecular dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamics (PKPD) model for cancer drug.

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