{"title":"多分散硬球流体的传输特性:分布形状和质量缩放的影响","authors":"Thokchom Premkumar Meitei, Lenin S Shagolsem","doi":"10.1007/s12043-024-02755-w","DOIUrl":null,"url":null,"abstract":"<p>A model polydisperse fluid represents many real fluids, such as colloidal suspensions and polymer solutions. In this study, we consider a concentrated size-polydisperse hard-sphere fluid with size derived from two different distribution functions, namely, uniform and Gaussian, and explore the effect of polydispersity and mass scaling on the transport properties in general. A simple analytical solution based on the Boltzmann transport equation is also presented (together with the solution using Chapman–Enskog (CE) method) using which various transport coefficients are obtained. The central idea of our approach is the realisation that, in polydisperse systems, the collision scattering cross-section is proportional to a random variable <i>z</i> which is equal to the sum of two random variables <span>\\(\\sigma _i\\)</span> and <span>\\(\\sigma _j\\)</span> (representing particle diameters), and the distribution of <i>z</i> can be written as the convolution of the two distributions <span>\\(P(\\sigma _i)\\)</span> and <span>\\(P(\\sigma _j)\\)</span>. In this work, we provide expressions for transport coefficients expressed as an explicit function of polydispersity index, <span>\\(\\delta \\)</span>, and their dependence on the nature of particle size distribution and mass scaling is explored. It is observed that in the low polydispersity limit, the transport coefficients are found to be insensitive to the type of size distribution functions considered. The analytical results (for diffusion coefficients and thermal conductivity) obtained using the CE method and our simple analytical approach agree well with the simulation. However, for shear viscosity, our analytical approach agrees for <span>\\(\\delta \\le 20\\%\\)</span>, while it agrees up to <span>\\(\\delta \\approx 40\\%\\)</span> with the result obtained using the CE method (in the limit <span>\\(\\delta \\rightarrow 0\\)</span>). Interestingly, the effect of scaling mass (i.e., mass proportional to the particle size and thus a random variable) produces no significant qualitative difference.\n</p>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"98 2","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Transport properties of polydisperse hard-sphere fluid: effect of distribution shape and mass scaling\",\"authors\":\"Thokchom Premkumar Meitei, Lenin S Shagolsem\",\"doi\":\"10.1007/s12043-024-02755-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A model polydisperse fluid represents many real fluids, such as colloidal suspensions and polymer solutions. In this study, we consider a concentrated size-polydisperse hard-sphere fluid with size derived from two different distribution functions, namely, uniform and Gaussian, and explore the effect of polydispersity and mass scaling on the transport properties in general. A simple analytical solution based on the Boltzmann transport equation is also presented (together with the solution using Chapman–Enskog (CE) method) using which various transport coefficients are obtained. The central idea of our approach is the realisation that, in polydisperse systems, the collision scattering cross-section is proportional to a random variable <i>z</i> which is equal to the sum of two random variables <span>\\\\(\\\\sigma _i\\\\)</span> and <span>\\\\(\\\\sigma _j\\\\)</span> (representing particle diameters), and the distribution of <i>z</i> can be written as the convolution of the two distributions <span>\\\\(P(\\\\sigma _i)\\\\)</span> and <span>\\\\(P(\\\\sigma _j)\\\\)</span>. In this work, we provide expressions for transport coefficients expressed as an explicit function of polydispersity index, <span>\\\\(\\\\delta \\\\)</span>, and their dependence on the nature of particle size distribution and mass scaling is explored. It is observed that in the low polydispersity limit, the transport coefficients are found to be insensitive to the type of size distribution functions considered. The analytical results (for diffusion coefficients and thermal conductivity) obtained using the CE method and our simple analytical approach agree well with the simulation. However, for shear viscosity, our analytical approach agrees for <span>\\\\(\\\\delta \\\\le 20\\\\%\\\\)</span>, while it agrees up to <span>\\\\(\\\\delta \\\\approx 40\\\\%\\\\)</span> with the result obtained using the CE method (in the limit <span>\\\\(\\\\delta \\\\rightarrow 0\\\\)</span>). Interestingly, the effect of scaling mass (i.e., mass proportional to the particle size and thus a random variable) produces no significant qualitative difference.\\n</p>\",\"PeriodicalId\":743,\"journal\":{\"name\":\"Pramana\",\"volume\":\"98 2\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pramana\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12043-024-02755-w\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s12043-024-02755-w","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
摘要 多分散流体模型代表了许多实际流体,如胶体悬浮液和聚合物溶液。在本研究中,我们考虑了由两种不同的分布函数(即均匀分布函数和高斯分布函数)推导出的粒度集中的多分散硬球流体,并探讨了多分散性和质量缩放对一般输运特性的影响。我们还给出了基于玻尔兹曼输运方程的简单解析解(以及使用查普曼-恩斯科格(CE)方法的解析解),并利用这些解析解求得了各种输运系数。我们方法的核心思想是认识到,在多分散系统中,碰撞散射截面与随机变量 z 成正比,而随机变量 z 等于两个随机变量 \(\sigma _i\) 和 \(\sigma _j\) (代表粒子直径)之和,并且 z 的分布可以写成两个分布 \(P(\sigma _i)\) 和 \(P(\sigma _j)\) 的卷积。在这项工作中,我们提供了以多分散指数(\(\delta \))的明确函数表示的传输系数表达式,并探讨了它们与粒度分布和质量缩放性质的关系。研究发现,在低多分散度极限下,传输系数对所考虑的粒度分布函数类型并不敏感。使用 CE 方法和我们的简单分析方法得出的分析结果(扩散系数和热导率)与模拟结果非常吻合。然而,对于剪切粘度,我们的分析方法在(\delta \le 20\%)时与模拟结果一致,而在(\delta \approx 40\%)时与使用CE方法得到的结果一致(在(\delta \rightarrow 0\)的极限)。有趣的是,缩放质量(即与颗粒大小成比例的质量,因此是一个随机变量)的影响没有产生明显的质的差异。
Transport properties of polydisperse hard-sphere fluid: effect of distribution shape and mass scaling
A model polydisperse fluid represents many real fluids, such as colloidal suspensions and polymer solutions. In this study, we consider a concentrated size-polydisperse hard-sphere fluid with size derived from two different distribution functions, namely, uniform and Gaussian, and explore the effect of polydispersity and mass scaling on the transport properties in general. A simple analytical solution based on the Boltzmann transport equation is also presented (together with the solution using Chapman–Enskog (CE) method) using which various transport coefficients are obtained. The central idea of our approach is the realisation that, in polydisperse systems, the collision scattering cross-section is proportional to a random variable z which is equal to the sum of two random variables \(\sigma _i\) and \(\sigma _j\) (representing particle diameters), and the distribution of z can be written as the convolution of the two distributions \(P(\sigma _i)\) and \(P(\sigma _j)\). In this work, we provide expressions for transport coefficients expressed as an explicit function of polydispersity index, \(\delta \), and their dependence on the nature of particle size distribution and mass scaling is explored. It is observed that in the low polydispersity limit, the transport coefficients are found to be insensitive to the type of size distribution functions considered. The analytical results (for diffusion coefficients and thermal conductivity) obtained using the CE method and our simple analytical approach agree well with the simulation. However, for shear viscosity, our analytical approach agrees for \(\delta \le 20\%\), while it agrees up to \(\delta \approx 40\%\) with the result obtained using the CE method (in the limit \(\delta \rightarrow 0\)). Interestingly, the effect of scaling mass (i.e., mass proportional to the particle size and thus a random variable) produces no significant qualitative difference.
期刊介绍:
Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.