The Mathematics of Multilayer Microfluidics: analysis, hybrid modelling and novel simulations underpinning new technologies at the microscale

多层微流体数学：支持微尺度新技术的分析、混合建模和新颖模拟

• 批准号: EP/K041134/1
• 负责人: Demetrios Papageorgiou
• 金额: $ 58.87万
• 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%2FK041134%2F1
• 关键词: Mathematics; Multilayer; Microfluidics; analysis; hybrid

One of the widest scientific revolutions currently taking place is the quest towards miniaturization and manufacture of tiny devices that can perform tasks (such as fluid handling and processing) on the micro-scale. In many cases the manipulation can be done rapidly and accurately and the automation of such processes is expected to have a huge impact in areas such as drug development and delivery (e.g. ``lab-on-chip" technologies). Small volumes of fluid imply large surface to volume ratios, and such geometries enhance the effects of mechanisms that are absent in larger scale devices. Many applications involve processes that utilise more than one immiscible fluid - such fluids do not mix (e.g. water and oil) and more importantly they have separating interface(s) that is free to move under the action of surface tension, flow and any other imposed external effects such as electric fields or gravity. Consequently, a process can be made successful and robust if we can understand how the interface between the different fluids (or phases) evolves. Such understanding opens the way for introducing flow controls. These can be either passive, as for example by building fixed structures such as bumps or rivulets on surfaces over which the fluids flow, or, active as in the case of switching an electric field on and off in a way determined by the evolving flow characteristics. One of the main mechanisms affecting multilayer microfluidic flows is surface tension. Its presence makes the mathematical problems highly challenging both analytically and computationally due to the intrinsically nonlinear nature of the resulting boundary conditions on unknown moving interfaces. The interfacial configuration affects the flow and the flow in turn affects the interfacial position - they need to be solved together and the instability mechanisms present need to be identified and followed into the nonlinear regime where complex dynamics can emerge.Producing interfaces in multi-fluid flows and controlling their configurations and spatio-temporal dynamics is also of vast importance to state-of-the-art materials science - known as Origami engineering, a mostly experimental research field. Interfaces act as the fabric where particles can self-assemble to produce homogeneous or pre-designed inhomogeneous material membranes to be manipulated and folded for desired engineering purposes.Our goal is to identify, control and manipulate nonlinear interfacial instabilities in multifluid flows to produce desirable surfaces that could be used forthe directed self-assembly of nano- and micro-particles to create smart films with exotic elastic properties, or that can host mammalian cells for tissue engineering.To achieve an extensive theoretical knowledge of fluid-surface interactions we consider three canonical models to describe some of the "designer" substrates currently used experimentally: (i) topographical structures (bumps and indentations), (ii) stick-slip superhydrophobic surfaces, and (iii) etched electrode networks that produce non-uniform electric fields. Within channels made up of such surfaces we have multilayer flows with several fluid-fluid interfaces. The resulting instabilities are complicated and include resonance, shear-induced stability or instability, and electrohydrodynamic instability to mention some. An additional challenge addressed by the present proposal is three-dimensionality. The computational challenges are enormous and will be addressed at least partially. We will make analytical progress by deriving reduced model equations to produce coupled systems of nonlinear partial differential equations depending on time and two spatial variables. These will be studied fully, both analytically and computationally, and compared with direct numerical simulations. Emphasis will be given to new solutions and mathematical structures but also on the phenomena that they describe and the underlying mechanisms that produce complex dynamics.

目前正在发生的最广泛的科学革命之一是寻求小型化和制造可以在微尺度上执行任务（例如流体处理和处理）的微小设备。在许多情况下，操作可以快速准确地完成，预计这种过程的自动化将在药物开发和交付等领域产生巨大影响（例如“芯片实验室”技术）。小体积的流体意味着大的表面与体积比，并且这样的几何形状增强了在较大规模装置中不存在的机制的效果。许多应用涉及利用多于一种不混溶流体的过程-这些流体不混合（例如水和油），并且更重要的是，它们具有分离界面，该分离界面在表面张力、流动和任何其他施加的外部效应（例如电场或重力）的作用下自由移动。因此，如果我们能够理解不同流体（或相）之间的界面是如何演变的，那么一个过程就可以成功和稳健。这种理解为引入流量控制开辟了道路。这些可以是被动的，例如通过在流体流过的表面上建立固定结构，例如凸起或溪流，或者是主动的，如在以由演变的流动特性确定的方式打开和关闭电场的情况下。影响多层微流体流动的主要机制之一是表面张力。它的存在使得数学问题极具挑战性的分析和计算，由于固有的非线性性质的边界条件上未知的移动接口。界面结构影响流动，流动反过来又影响界面位置--它们需要一起解决，存在的不稳定机制需要被识别并遵循到非线性区域，在非线性区域中可能出现复杂的动力学。在多流体流动中产生界面并控制它们的结构和时空动力学对最先进的材料科学也非常重要。被称为折纸工程，一个主要是实验性的研究领域。界面作为一种织物，颗粒可以在其中自组装以产生均匀或预先设计的非均匀材料膜，以用于所需的工程目的。我们的目标是识别、控制和操纵多流体流动中的非线性界面不稳定性，以产生可用于纳米和微米颗粒的定向自组装的所需表面，以产生具有奇异弹性性能的智能膜，为了获得流体-表面相互作用的广泛理论知识，我们考虑三种典型模型来描述目前实验上使用的一些“设计者”基底：（i）地形结构（凸起和凹陷），（ii）粘滑超疏水表面，和（iii）产生非均匀电场的蚀刻电极网络。在由这种表面组成的通道内，我们有多个流体-流体界面的多层流动。由此产生的不稳定性是复杂的，包括共振，剪切诱导的稳定性或不稳定性，以及电流体动力学不稳定性。本提案所处理的另一个挑战是三维性。计算方面的挑战是巨大的，至少会得到部分解决。我们将通过推导简化的模型方程来产生依赖于时间和两个空间变量的非线性偏微分方程的耦合系统。这些将被充分研究，分析和计算，并与直接数值模拟。重点将给予新的解决方案和数学结构，但也对他们所描述的现象和产生复杂动态的基本机制。

项目成果

Nonlinear Dynamics and Wall Touch-Up in Unstably Stratified Multilayer Flows in Horizontal Channels under the Action of Electric Fields

电场作用下水平通道不稳定分层多层流的非线性动力学和壁修补

• DOI: 10.1137/140968070
• 发表时间: 2015
• 期刊: SIAM Journal on Applied Mathematics
• 影响因子: 1.9
• 作者: Barannyk L

The stability of capillary waves on fluid sheets

• DOI: 10.1017/jfm.2016.588
• 发表时间: 2016-09
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: M. Blyth;E. Părău

Stability of falling liquid films on flexible substrates

• DOI: 10.1017/jfm.2020.538
• 发表时间: 2020-08
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: J. Alexander;Toby L. Kirk;D. Papageorgiou

Oxygen uptake and denitrification in soil aggregates

土壤团聚体的吸氧和反硝化

• DOI: 10.1007/s00707-017-2042-x
• 发表时间: 2017
• 期刊: Acta Mechanica
• 影响因子: 2.7
• 作者: Bocking C

Ordered and disordered dynamics in inertialess stratified three-layer shear flows

无惯性分层三层剪切流中的有序和无序动力学

• DOI: 10.1103/physrevfluids.7.014804
• 发表时间: 2022
• 期刊: Physical Review Fluids
• 影响因子: 2.7
• 作者: Alexander J