Chaotic mixing in liquid microdroplets

这个项目探索了在纳升规模的间歇反应器的流体动力学模型中引入混沌平流来增强混合的基本机制。将使用分析、数值和实验相结合的方法，它结合了两个新的特点：(1)利用温度诱导的表面张力梯度精确移动、合并和混合纳升尺寸的液滴的非接触式实验方法；(2)基于流体的Stokes方程和溶质浓度的平流方程的方便的理论模型，该模型适用于对实验中观察到的混合行为进行定量预测。这项研究的中心焦点是对含时流动中非微扰效应的基本理解，这些效应最有可能在实际应用中导致有效的混合。我们方法的主要思想是基于使用不变量，即沿着流线保留的函数，这些不变量是由于微滴中典型流动的高度对称性而产生的。由于流线不能穿过不变曲面，破坏所有不变量是实现良好混合的关键。因此，从任何实验实现的非理想方面自然产生的非微扰修正是混合过程中的基本成分，因为它们改变了流动的对称性，从而影响不变量的存在和数量。所获得的结果将被用来设计一种有效的混合控制程序，该程序应该适用于涉及离散流体混合的广泛类型的流动。微型化在化学和生物传感器、药物发现和临床试验等新应用方面具有巨大的前景，带来了速度、吞吐量和灵敏度的根本改进。该项目专注于流体混合的基本问题，该问题在大多数微流控技术中起着至关重要的作用，但在小范围内变得越来越困难。对液体微滴中混沌混合的研究是光学微流体研究的一个重要组成部分，光学微流体是一种利用光学方法在微尺度上处理液体的新方法。这种方法将允许构建新一代微流控设备，而不会出现传统基于微通道的技术的许多缺陷。这种高度集成、动态可重复编程的可重复使用的设备可以用来设计完整的“芯片实验室”，有可能彻底改变化学和生物分析的方式。

This project explores basic mechanisms of introducing chaotic advection to enhance mixing in a hydrodynamic model of a nanoliter-scale batch reactor. A combined analytical, numerical and experimental approach will be used, which brings together two novel features: (1) a non-contact experimental method of precisely moving, merging, and mixing nanoliter-sized droplets using temperature-induced surface tension gradients, and (2) a convenient theoretical model based on the Stokes equation for the fluid coupled with the advection equation for the solute concentration that is suitable for making quantitative predictions of mixing behaviors observed in the experiments. The central focus of this research is on fundamental understanding of nonperturbative effects in time-dependent flow, which are most likely to lead to effective mixing in practical applications. The main idea of our approach is based on using the invariants, or functions preserved along the streamlines of the flow, which arise due to a high symmetry of typical flows in microdroplets. As streamlines cannot cross the invariant surfaces, destruction of all invariants is the key to achieving good mixing. The nonperturbative corrections that arise naturally from non-ideal aspects of any experimental implementation are therefore essential ingredients in the mixing process as they change the symmetry of the flow and thus affect the existence and number of invariants. The obtained results will be used to design an effective procedure for controlling mixing that should be applicable to a broad class of flows involving the mixing of discrete quantities of fluid.Miniaturization holds great promise for novel applications, such as chemical and biological sensors, drug discovery, and clinical tests, bringing radical improvements in speed, throughput, and sensitivity. This project focuses on the fundamental problem of fluid mixing, which plays a crucial role in most microfluidic technologies, yet becomes increasingly difficult at small scales. The study of chaotic mixing in liquid microdroplets is an integral part of a broader study of opto-microfluidics, a novel approach for handling liquids at the microscale using optical methods. This approach will allow construction of a new generation of microfluidic devices free of many drawbacks of conventional microchannel-based technology. Such highly integrated dynamically reprogrammable reusable devices could be used to design complete "labs-on-a-chip" with a potential to revolutionize the way chemical and biological assays are done.