{"title":"Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution","authors":"A. Menzel, P. Daivis, B. D. Todd","doi":"10.12921/CMST.2017.0000016","DOIUrl":null,"url":null,"abstract":"The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier's Law and Fick's Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux. We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 104 reduced time units for relaxation to the steady state and averaging over very long runs of order 105 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"1 1","pages":"219-231"},"PeriodicalIF":0.0000,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"computational methods in science and technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12921/CMST.2017.0000016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier's Law and Fick's Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux. We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 104 reduced time units for relaxation to the steady state and averaging over very long runs of order 105 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.
聚合物溶液在高度受限几何中的行为仍然是流变学和流体动力学中感兴趣的主题。在本文中,我们研究了基于Navier-Stokes方程、傅里叶定律和菲克定律的经典流体力学描述如何很好地描述高受限聚合物溶液的流动。特别地,我们研究了在壁-流体界面处聚合物浓度的损耗和应变速率耦合对热流的影响。我们展示了一种模型聚合物溶液在显式溶剂中进行平面泊泽维尔流动的分子动力学模拟数据,通道宽度从大约10个溶剂原子直径到大约80个溶剂原子直径不等。我们发现经典的连续介质方法对于超过20个溶剂原子直径的通道非常有效。对于较窄的通道,我们观察到由于壁附近的密度振荡、聚合物耗损效应和可能的弱应变速率耦合而导致的速度、温度和浓度分布的偏差。对于最窄的通道,壁效应延伸到通道的中心,但是底层的剖面可以用经典的连续谱图很好地描述。通过允许很长时间的104阶简化时间单位松弛到稳定状态,并在很长时间内平均105阶简化时间单位和16个独立的集合成员,我们能够得出这样的结论:先前报道的与经典连续统预测的偏差(I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20,404211(2008))可能是平衡时间不足的结果。我们的结果也足够精确,足以验证经典流体力学理论预测的四次温度分布,只有很小的偏差,我们可以将其归因于热流矢量与应变率的非线性耦合。