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表面张力和温度分布的影响沿着通道。特别是，高效的数值方案的自适应网格构造，以解决问题的多尺度性质和计算机资源的限制。研究人员介绍了一种新的范例，允许离散化的偏微分方程高度自适应网格，如果网格是均匀的，同时达到二阶精度的最大范数。数值模拟是用来补充物理实验，以优化设计的自由表面射流装置。模拟考虑到温度场的液体和周围的通道壁，温度引起的表面张力的变化，随后的表面张力驱动的主流（马兰戈尼效应）的横向流动和它们的影响上的空气中的颗粒从液体的表面运输到其散装。此外，模拟考虑到整个空气-液体系统的配置，并确定自由表面的形状，以找到一种设计，最大限度地提高空气和液体表面之间的接触，以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，用于检测化学和生物制剂取得了重大进展。然而，文献中报道的所有“芯片实验室”平台只能在样品注入微通道后才能处理样品。这一长期存在的技术和科学障碍限制了这些平台在监测空气传播物种方面的可行性，而这一技术对国家安全问题的重要性已经变得显而易见。自由表面射流技术是由UCSB的研究人员合作者开创的一项创新技术，它通过对某些痕量空气传播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，在自由表面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，并用于连续监测空气通风系统中的生物或化学战剂。在这项工作中，研究人员设计数值方法，以优化自由表面射流装置的设计，并更好地了解所涉及的物理现象。这些方法也对其他领域产生重要影响，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、燃烧以及肿瘤生长建模等领域中具有关键应用。此外，研究人员还开发了一个免费的计算科学和工程交互式网站，引导用户通过计算科学之旅，探索有趣的主题，如微流体，晶体生长，单相和多相流。用户有可能通过改变参数来观察对模拟的影响，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.