Statistical mechanics of soft matter: Derivation, analysis and implementation of dynamic density functional theories

软物质统计力学：动态密度泛函理论的推导、分析与实现

基本信息

批准号：
EP/L025159/1
负责人：
Serafim Kalliadasis
金额：
$ 48.3万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FL025159%2F1
关键词：
Statistical mechanics soft matter Derivation

项目摘要

The term "soft matter" is used to describe materials which at room temperature can easily deform under external forces like gravity or pressure while their properties are governed by slow internal dynamics. Soft matter often plays a central role in engineering and biomedical science and has numerous practical applications. The proposed research focuses on a large class of soft matter systems, that of classical fluids, i.e. systems of particles which retain a definite volume and are at sufficiently high temperatures that quantum effects can be neglected. Of particular interest are colloidal fluids whose particles are of micrometer size, suspended in a bath of many more, much smaller and lighter particles, which cannot be described by continuum macroscopic formalisms such as the Navier-Stokes equation.Modelling the dynamics of the full colloidal fluids is prohibitively expensive and in fact computationally intractable due to both the large number of particles and the wide range of length- and time-scales which must be considered. As a consequence, one must employ statistical mechanics approaches, with the most widely used method being dynamic density-functional theory (DDFT). However, previous DDFTs often involve approximations whose accuracy and validity cannot be ascertained a priori. As a consequence, the results obtained from such formulations are questionable and often inaccurate.This proposal seeks funding for a comprehensive three-year research programme into a two-pronged novel theoretical and numerical investigation aimed at rationally understanding and systematically predicting the complex physical behaviour and properties of colloidal systems. The primary aim is the development of a generic DDFT formalism that would allow for the accurate, systematic and predictive modelling of physically relevant systems where all the neglected effects in previous idealised studies now come to the fore. This in turn will allow for step improvements to the performance and efficiency of a host of technologies and applications that rely crucially on particulate systems. The analytical work will be complemented by detailed numerical simulations that will act so as to verify the efficacy of the developed models, as well as aiding the development of a toolkit for practical applications. The research will be undertaken by a team from the School of Mathematics of the University of Edinburgh and the Chemical Engineering and Mathematics Departments at Imperial College London with complementary skills and strengths: Goddard (Complex Multiscale Systems, Statistical Mechanics, Analysis and Computations), Kalliadasis (Multiscale Fluid Dynamics, Theory and Computations) and Pavliotis (Stochastic Processes, Multiscale Analysis, Statistical Mechanics).

“软物质”一词用于描述在室温下在重力或压力等外力下很容易变形的材料，而其性质受内部动力缓慢的影响。软物质通常在工程和生物医学科学中起着核心作用，并且具有许多实际应用。拟议的研究集中于大量的软物质系统，即经典流体的研究，即保留一定体积的颗粒系统，并且在足够高的温度下可以忽略量子效应。特别令人感兴趣的是胶体流体的颗粒，其颗粒具有微米大小，悬浮在许多，较小，更轻的颗粒的浴中，无法通过连续宏观形式主义（例如Navier-Stokes方程）来描述。由于必须考虑的大量颗粒和较宽的长度和时间尺度，因此流体非常昂贵，实际上在计算上棘手。因此，必须采用统计力学方法，其中最广泛使用的方法是动态密度功能理论（DDFT）。但是，以前的DDFT通常涉及近似值，其准确性和有效性无法先验确定。结果，从这种配方中获得的结果值得怀疑，而且常常不准确。该提案为一项综合的三年研究计划寻求资金，用于一项两种统治的小说理论和数值研究，旨在合理理解和系统地预测复杂的身体行为和复杂的身体行为和胶体系统的性质。主要目的是开发通用的DDFT形式主义，该形式允许对物理相关系统进行准确，系统和预测的建模，在先前理想化的研究中，所有被忽视的效果现在都浮出水面。反过来，这将允许对依赖颗粒系统至关重要的许多技术和应用的性能和效率进行逐步改进。分析工作将通过详细的数值模拟进行补充，这些模拟将起作用，以验证开发模型的功效，并有助于工具包的开发用于实际应用。这项研究将由爱丁堡大学数学学院以及伦敦帝国学院的化学工程与数学系的团队进行，具有互补的技能和优势：戈达德（复杂的多尺度系统，统计机制，分析和计算），Kalliadasisis （多尺度流体动力学，理论和计算）和Pavliotis（随机过程，多尺度分析，统计力学）。