Rheology of crosslinked assemblies of flexible fibres in viscous flow

粘性流中柔性纤维交联组件的流变学

• 批准号: 2747249
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2747249
• 关键词: Rheology; crosslinked; assemblies; flexible; fibres; Rheology; crosslinked; assemblies; flexible; fibres

Many industrial and biomedical materials consist of a fibrous solid phase immersed in a viscous fluid, e.g. the cellular cytoskeleton, tissue engineering scaffolds, medical filters, fibre reinforced materials etc. Modelling the flow of such composites provides the capability to rationally design new products and enhance our understanding of natural systems - thus, the time-dependent mechanical (viscoelastic) response of scaffolds controls stem cell differentiation, and the cytoskeleton propagates stress in moving cells. Our recent simulations demonstrated unexpected and potentially exploitable modalities in the viscoelastic response of fibre networks modelled as immersed spring networks. However, the coupling between the fluid and the fibre network in this model is not mathematically rigorous. Whilst a full numerical simulation would be prohibitively expensive, more rigorous frameworks exist (e.g. immersed boundary, slender body and regularised Stokeslet methods) for calculating the flow through immersed fibres. However, they cannot be immediately applied to networks as (a) the crosslinking of fibres has not been considered, and (b) networks can span the system. In this project, the student will develop a rigorous theoretical framework (through a combination of analytical and/or numerical approaches) for assemblies of crosslinked elastic fibres in viscous flow, generating predictions for linear viscoelasticity and more complex non-linear phenomena.The outcomes of this project will be:1. A theoretical framework for modelling hydrodynamic interactions within crosslinked elastic slender fibres in oscillatory shear flow. The crosslinking, representing chemical or physical bonding, can be implemented as constraining predefined points along each fibre's arc length to occupy the same position in space at all times. The framework may be analytical, numerical, or a combination of both, adapting existing ideas from the fluid-structure coupling literature, including slender body theory (local or non-local), and/or the immersed boundary method. Although the formulation should be fully non-linear, predictions will be generated for the linear viscoelastic response in the first instance. 2. Expand the framework to system-spanning networks, i.e. where the elastic phase is conceptually infinite, or spans a periodic system. One issue here is to achieve numerical efficiency in computing the hydrodynamic interactions between distant parts of the fibre network. One approach would be to implement fast solution methodologies for the Stokes' equations such as the Fast Multipole Method. For the immersed boundary method, IBAMR, an existing software package with adaptive meshing, could be considered.

许多工业和生物医学材料由浸入粘性液中的纤维固相组成，例如the cellular cytoskeleton, tissue engineering scaffolds, medical filters, fibre reinforced materials etc. Modelling the flow of such composites provides the capability to rationally design new products and enhance our understanding of natural systems - thus, the time-dependent mechanical (viscoelastic) response of scaffolds controls stem cell differentiation, and the cytoskeleton propagates stress in moving cells.我们最近的模拟表明，在建模为浸入春季网络的纤维网络的粘弹性响应中，出乎意料的和潜在的模式。但是，该模型中流体和光纤网络之间的耦合并不是数学上严格的。尽管完整的数值模拟将非常昂贵，但存在更严格的框架（例如，浸入边界，细长的身体和正则化的Stokeslet方法），以通过浸入式纤维来计算流动。但是，它们不能立即应用于网络，因为（a）尚未考虑纤维的交联，并且（b）网络可以跨越系统。在这个项目中，学生将开发一个严格的理论框架（通过分析和/或数值方法的组合），用于粘性流中的交联弹性纤维组装，从而产生线性粘弹性和更复杂的非线性现象的预测。该项目的现象将为：1：1。振荡性剪切流中的交联弹性纤维纤维内的流体动力相互作用的理论框架。代表化学或物理键合的交联，可以作为沿每个纤维的弧长的约束预定点来实现，以始终在空间中占据相同的位置。该框架可以是分析性的，数值的，也可以是两者的组合，从而适应流体结构耦合文献中的现有思想，包括细长的身体理论（本地或非本地）和/或沉浸式边界方法。尽管该公式应完全非线性，但首先将对线性粘弹性响应产生预测。 2。将框架扩展到系统跨系统网络，即弹性阶段在概念上是无限的，或跨越周期系统。这里的一个问题是在计算光纤网络遥远部分之间的流体动力相互作用时达到数值效率。一种方法是为Stokes方程（例如快速多极方法）实施快速解决方案方法。对于沉浸式边界方法，可以考虑使用具有自适应网格的现有软件包IBAMR。