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

在这项工作中，研究人员为自由表面微流体设计了创新的计算方法，以了解和控制亚微米级明渠中的吸收和蒸发过程，并了解如何有效地控制沿通道的表面张力和温度分布的影响。特别是，为了解决问题的多尺度性质和计算机资源的限制，构造了自适应网格上的有效数值格式。研究人员引入了一种新的范式，允许在高度自适应的网格上离散偏微分方程组，就好像网格是均匀的一样，同时在最大范数下达到二阶精度。数值模拟是对物理实验的补充，以优化自由表面射流装置的设计。模拟考虑了液体和周围通道壁面的温度场，温度引起的表面张力的变化，随后的表面张力驱动的主流横向流动(Marangoni效应)及其对空气悬浮颗粒从液体表面到其主体的传输的影响。此外，模拟考虑了整个空气-液体系统的结构，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年里，基于微/纳米流体的平台在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“芯片上实验室”平台只有在样品被注入微通道后才能处理样品。这种长期存在的技术和科学障碍限制了这些监测空气中物种的平台的生存能力，因为这项技术对国家安全问题的重要性已经变得明显。自由表面流体是由UCSB的研究人员的合作者首创的一项创新技术，它通过对某些微量空气中的化学制剂和病原体实现以前不可能的检测阈值来消除这一障碍。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，以及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，研究人员设计了数值方法，以优化自由表面流体装置的设计，并更好地了解其中涉及的物理现象。这些方法对其他领域也有重要影响，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、燃烧以及肿瘤生长模型等领域有关键应用。此外，研究人员还开发了一个关于计算科学和工程的免费互动网站，指导用户完成计算科学之旅，探索诸如微流体、晶体生长、单相流和多相流等有趣的主题。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，从而提供计算科学方面的教程。

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.