A New Paradigm for Finite Difference Schemes on Adaptive Grids - Application to Free Surface Microfluidics

在这项工作中，研究者设计了自由表面微流体的创新计算方法，以了解和控制亚微米尺度开放通道中的吸收和蒸发过程，以及了解如何有效地控制通道表面张力和温度分布的影响。特别地，为了解决问题的多尺度性质和计算机资源的限制，构建了有效的自适应网格数值格式。研究者引入了一种新的范例，允许在高度自适应网格上离散偏微分方程，就好像网格是均匀的一样，同时在最大范数中获得二阶精度。为了优化自由表面流体装置的设计，采用数值模拟作为物理实验的补充。模拟考虑了液体和周围通道壁的温度场、温度引起的表面张力变化、随后的表面张力驱动的主流横向流动（马兰戈尼效应）以及它们对空气中颗粒从液体表面到其体的运输的影响。此外，模拟考虑了整个气液系统的结构，并确定了自由表面的形状，以便找到一种设计，使空气和液体表面之间的接触最大化，从而有效地捕获空气中的物种。在过去的15年中，在使用微/纳米流体为基础的平台检测化学和生物制剂方面取得了重大进展。然而，文献中报道的所有“芯片实验室”平台都只能在将样品注入微通道后处理样品。这种长期存在的技术和科学障碍限制了这些平台监测空气传播物种的可行性，而这项技术对国家安全问题的重要性已经变得非常明显。自由表面流体是由UCSB研究者的合作者开创的一项创新技术，通过实现以前不可能的某些痕量空气传播化学剂和病原体的检测阈值，消除了这一障碍。空气中的分子可以通过自由表面直接被吸收，在那里它们可以与金或银胶体颗粒相互作用，并使用表面增强拉曼光谱进行检测。例如，该平台可用于各种场所的公共安全，以检测爆炸物和有毒化学品，并用于持续监测空气通风系统中的生物或化学战剂。在这项工作中，研究者设计了数值方法，以优化自由表面流体装置的设计，并更好地理解所涉及的物理现象。这些方法对其他领域也有重要的影响，因为它们在半导体加工和能源工业、生物纳米技术和组织工程、燃烧以及肿瘤生长建模等领域都有重要的应用。此外，研究者开发了一个免费的计算科学与工程互动网站，引导用户通过计算科学之旅，探索有趣的话题，如微流体，晶体生长，单相和多相流。用户可以通过改变参数来观察对模拟的影响，从而进一步进行交互式探索，从而提供计算科学的教程。

In this work, the investigator devises innovative computational methods for free surface microfluidics in order to understand and control absorption and evaporation processes in the sub-micron scale open channels, as well as to understand how to efficiently control the effect of surface tension and temperature profiles along the channels. In particular, efficient numerical schemes on adaptive meshes are constructed in order to address the multiscale nature of the problem and the limitations of computer resources. The investigator introduces a new paradigm that allows the discretization of PDEs on highly adaptive meshes as if the mesh was uniform, while attaining second-order accuracy in the maximum norm. The numerical simulations are used to supplement physical experiments in order to optimize the design of free surface fluidics devices. The simulations take into account the temperature field in the liquid and the surrounding channel walls, the temperature-induced variations in surface tension, the subsequent surface tension driven flows in the transversal direction of the main flow (Marangoni effect) and their effects on the transport of airborne particles from the surface of the liquid to its bulk. Furthermore, the simulations take the configuration of the whole air-liquid system into account and determine the shape of the free surface in order to find a design that maximizes contact between the air and the liquid surface for efficient capture of airborne species.In the past 15 years, significant advances have been made in using micro/nanofluidic-based platforms for detecting chemical and biological agents. However, all the `lab-on-a-chip' platforms reported in the literature can process samples only after the samples are injected into a microchannel. This longstanding technological and scientific barrier limits the viability of these platforms for monitoring airborne species at time when the great importance of this technology to national security issues has become clear. Free-surface fluidics is an innovative technology pioneered by the investigator's collaborators at UCSB which removes this barrier by enabling previously impossible detection thresholds for certain trace airborne chemical agents and pathogens. Airborne molecules can be directly absorbed through the free surface, where they can interact with gold or silver colloidal particles and be detected using Surface-Enhanced Raman Spectroscopy. This platform could be used, for example, for public safety in a variety of venues to detect explosives and toxic chemicals, and for continuous monitoring of biological or chemical warfare agents in air ventilation systems. In this work, the investigator devises numerical methods in order to optimize the design of free-surface fluidic devices and to better understand the physical phenomena involved. These methods have an important impact on other fields as well, as they have key applications in the fields of semi-conductor processing and in the energy industry, in bio-nanotechnology and tissue engineering, in combustion as well as in the modeling of tumor growth to name a few. In addition, the investigator develops a freely available interactive web site on computational science and engineering which guides the users through a computational science journey, exploring intriguing topics such as microfluidics, crystal growth, single and multiphase flows. The users have the possibility of further interactive exploration by altering parameters to observe the effect on simulations, hence providing a tutorial on computational science.