Mathematical modelling of droplet impact on soft substrates

液滴撞击软基材的数学模型

• 批准号: 2100031
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2100031
• 关键词: Mathematical; modelling; droplet; impact; soft

Splashing on soft substrates is an active research topic with a wide range of applications including rainfall, pesticide application, inkjet printing, fuel combustion, forensic science and spray coating. However, recent experiments have shown that the splashing process is more complex than previously thought, so that there are many outstanding questions still remaining regarding the fundamental physical mechanisms involved in droplet splashing and how they are promoted or prohibited by substrate deformation. Finding out how to eliminate splashing is a relatively new topic, and can be useful in situations where splashing could cause hygiene or safety concerns. Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. Recent experimental results [1] have shown that substrate stiffness also affects the splashing threshold, for example, droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. The energy losses are caused by deformations of the soft substrate during the first few microseconds of impact. There is currently no theory for the effect of substrate stiffness on the splashing threshold.The aim of the project is to derive and analyse the impact of a liquid droplet on a range of soft substrates of practical importance, guided by extensive close collaboration with the Fluid Dynamics Laboratory in the Department of Engineering, Oxford. The objectives are to (i) use the method of matched asymptotic expansions to derive systematically reduced models for the early stages of the impact that retain all of the essential physics while remaining tractable, generalising thereby classical impact theory into new regimes; (ii) develop, test and validate state-of-the-art direct numerical simulations for the early and late stages of the impact. The reduced asymptotic models will be used to extract physical insight and both initiate and validate the numerical simulations. The numerical simulations will be used to characterise the effect of the substrate on the splashing threshold. We will begin with the simplest possible model for the substrate, namely a cantilever, before moving onto more complicated substrate rheologies including elastic, highly viscous, viscoelastic substrates and vibrating soft surfaces.This project falls within the EPRSC Continuum Mechanics and Fluid Dynamics and Aerodynamics research areas. [1] Howland, CJ, Antkowiak, A, Castrejón-Pita, JR; Howison, SD, Oliver, JM, Style, RW, Castrejón-Pita, AA. It's Harder to Splash on Soft Solids. Physical Review Letters 117, 184502 (2016).Collaborators: Alfonso Castrejon-Pita, Fluid Dynamics Laboratory in the Department of Engineering, Oxford.

软基材上的溅射是一个活跃的研究课题，具有广泛的应用，包括降雨、农药应用、喷墨打印、燃料燃烧、法医科学和喷涂。然而，最近的实验表明，飞溅过程比以前认为的要复杂得多，因此，关于液滴飞溅的基本物理机制以及衬底变形如何促进或禁止液滴飞溅，仍然存在许多悬而未决的问题。找出如何消除溅水是一个相对较新的话题，在溅水可能引起卫生或安全问题的情况下可能很有用。当液滴撞击干燥、平坦的基材时，其飞溅速度超过临界速度，这取决于液滴大小、粘度和气压等参数。最近的实验结果[1]表明，基材刚度也会影响飞溅阈值，例如，液滴在最软的基材上飞溅所需的动能比在刚性基材上多70%以上。能量损失是由软基板在撞击前几微秒的变形引起的。目前还没有关于衬底刚度对溅射阈值影响的理论。该项目的目的是推导和分析液滴对一系列具有实际意义的软基材的影响，并与牛津大学工程系流体动力学实验室进行广泛的密切合作。目标是：(i)使用匹配渐近展开的方法推导出撞击早期阶段的系统简化模型，这些模型保留了所有基本物理性质，同时保持可处理性，从而将经典撞击理论推广到新的制度中；（ii）为撞击的早期和后期阶段，发展、测试和验证最先进的直接数值模拟。简化的渐近模型将用于提取物理洞察力，并启动和验证数值模拟。数值模拟将用于表征基材对溅射阈值的影响。我们将从最简单的基材模型开始，即悬臂，然后再讨论更复杂的基材流变学，包括弹性、高粘性、粘弹性基材和振动软表面。该项目属于EPRSC连续介质力学、流体动力学和空气动力学研究领域。[1] Howland， CJ, Antkowiak， A, Castrejón-Pita， JR；Howison， SD, Oliver， JM, Style， RW, Castrejón-Pita， AA。在软固体上更难飞溅。物理学报，17(2)（2016）。合作者：Alfonso Castrejon-Pita，牛津大学工程系流体动力学实验室。