Mathematical Modelling of Rare Events in Nanoflows: A Feasibility Study

21世纪预示着流体技术小型化的革命，与20世纪电子技术所取得的成就相媲美，微流体长度尺度技术现已完全商业化（例如3D打印机）。自然，现在的焦点已经转向开发纳米尺度（即纳米流体）流动的巨大潜力，在纳米尺度上，巨大的表面积与体积比创造了由表面/界面效应驱动的系统，因此可以以我们在日常生活中观察到的尺度上无法想象的方式操纵微小体积的流体。我们的重点是在纳米尺度上液体体积的分解，这是应用的关键，包括纳米制造（例如薄膜太阳能电池），泪膜和眼睛的“干燥”，用于再生医学的仿生纳米设备和新型纳米颗粒药物。值得注意的是，目前还没有科学的工具来研究这些纳米流，因为：-实验技术只能提供有限的信息，因为动力学发生得太快了。-基于传统流体动力学的理论方法在纳米尺度上失败，因为热波动（“噪声”或“布朗运动”）驱动定性的新随机动力学。这项可行性研究将探索一种新的数学方法来克服这些挑战，该方法基于最初为量子力学开发的罕见事件的新方法。如果成功，这将为一个更广泛的跨学科内/跨学科研究项目提供一个平台，该项目将研究实际相关纳米系统的数学模型，这将使英国处于这一高科技新兴领域的前沿。

The 21st century has heralded a revolution in the miniaturisation of fluid-based technologies that parallels those achieved in electronics in the 20th century, with technologies on microfluidics length scales now fully commercialised (e.g. 3D printers). Naturally, focus has now turned to exploiting the tremendous potential of flows at the nanoscale (i.e. nanofluidics), where huge surface area to volume ratios create systems that are driven by surface/interfacial effects, so that tiny volumes of fluid can be manipulated in ways that are unimaginable at the scales we observe in our daily lives. Our focus here is on the breakup of liquid volumes at the nanoscale, which are key to applications including nano-manufacturing (e.g. of thin-film solar cells), tear films and 'dry out' of the eye, bionic nano-devices for regenerative medicine and novel nano-particle drugs. Remarkably, at present, no scientific tools have been developed for these nanoflows as: - Experimental techniques can only provide limited information, as the dynamics occur too fast. - Theoretical approaches based on conventional fluid dynamics fail at the nanoscale, as thermal fluctuations ('noise' or 'Brownian motion') drive qualitatively new stochastic dynamics.This feasibility study will explore a new mathematical approach to overcome these challenges based on new methods for rare events that were originally developed for quantum mechanics. If successful, this will provide a platform for a much broader programme of intra-/inter-disciplinary research into the mathematical modelling of practically relevant nano-systems that could put the UK at the forefront of this high-tech emerging area.