Dynamics of Evaporating Fluids Films

该研究项目解决了对可以预测蒸发流体层行为的模型的更全面理解的需求。挥发性液体在许多环境中发挥着重要作用，从自然和生物物理系统到工程和工业过程，如印刷和绘画。 蒸发和冷凝模型对于许多应用至关重要，在这些应用中，这种缓慢的过程可以将系统转换为不同的操作条件，例如干眼综合征患者眼睛上的泪膜蒸发。 动力学是否将液体保持为均匀的层或驱动分裂成许多液滴可能会产生重大影响。挥发性液体膜可用于高功率电气或机械设备的冷却系统。已知通过均匀流体层的热传递比通过可比较的液滴阵列的热传递效率低。因此，优化这种系统的性能涉及可靠地控制流体膜的行为。 虽然已经有大量的研究蒸发导致简单的模型干燥的均匀的液体层和收缩的单个液滴在许多情况下，有差距，在应用模型统一到更广泛的设置。 这项工作的目的是建立一个系统的了解，可以从相互作用的蒸发与润湿作用的流体在固体表面上竞争的动态。 除了在面向流体动力学和工程领域更广泛受众的期刊上展示该项目的成果外，PI还将利用该项目将新技术纳入应用数学培训。 该项目的一部分将用于PI的数学建模和流体动力学课程。该项目还将作为PI在培养研究生和为本科生提供研究经验方面的持续记录的重点。该研究将使用应用数学的数值模拟和分析方法来更好地理解粘性液体蒸发层的长期动力学。 一个具有蒸发通量的润滑模型将被用来描述粘性流体薄膜的高度分布的演变。控制方程是一个四阶非线性抛物型偏微分方程，描述了润湿效应，在液滴和薄层之间产生相分离（有时称为去湿不稳定性），同时由于周围汽相的相变，流体质量损失或增加。最近的研究结果表明，有一个临界范围的参数，其中基板性能的影响可以显着改变的两个长期吸引行为之间的动态过程：蒸发液滴下降到最小的吸附膜或冷凝产生越来越厚的层。利用偏微分方程、非线性动力学和材料科学中的相关模型，对质量守恒不稳定薄膜模型研究的许多方面进行了数学分析。 然而，将蒸发引入问题从根本上改变了模型解的关键特性，并需要开发以前方法的新扩展或其他新方法。 该项目的长期目标是为相互作用的挥发性液滴阵列的演变开发渐近模型。获得这种粗化模型将面临新的挑战，因为支持质量守恒模型的准稳态框架不再直接适用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project addresses the needs to develop more comprehensive understanding of models that can predict the behaviors of layers of evaporating fluids. Volatile liquids play fundamental roles in numerous settings spanning natural and biophysical systems to engineering and industrial processes such as printing and painting. Models for evaporation and condensation are crucial for many applications where such slow processes can shift systems into different operating conditions, as in evaporation of the tear film on the human eye for people with dry-eye syndrome. Whether the dynamics maintain the liquid as a uniform layer or drive break-up into many droplets can have major consequences. Volatile liquid films can be used in cooling systems for high-power electrical or mechanical equipment. Heat transfer through uniform fluid layers is known to be less efficient than transfer through comparable arrays of droplets. Hence, optimizing the performance of such systems involves reliably controlling the behavior of the fluid film. While there have been extensive studies of evaporation leading to simple models for the drying of uniform liquid layers and shrinking of individual droplets in many contexts, there are gaps in applying the models uniformly to broader settings. This work seeks to build a systematic understanding of the dynamics that can result from the interaction of evaporation competing with wetting effects for fluids on solid surfaces. In addition to presenting results from this project in journals targeting broader audiences in fluid dynamics and engineering, the PI will use the project to incorporate new techniques into training in applied mathematics. Parts of the project will be used in the PI's courses on mathematical modeling and fluid dynamics. The project will also serve as the focus for the PI's continuing track record in the training of graduate students and providing research experiences for undergraduates.This research will use numerical simulations and analytical approaches from applied mathematics to develop a better understanding of the long-time dynamics of evaporating layers of viscous liquids. A lubrication model with an evaporative flux will be used to describe the evolution of the height profile of thin films of viscous fluids. The governing equation is a fourth-order nonlinear parabolic partial differential equation describing wetting effects generating phase separation (sometimes called de-wetting instabilities) between droplets and thin layers while fluid mass is lost or gained due to phase change from the surrounding vapor phase. Recent results have shown that there is a critical range of parameters where the influence of substrate properties can dramatically change the course of the dynamics between the two long-time attracting behaviors: evaporation of droplets down to a minimal adsorbed film or condensation yielding growing thicker layers. Mathematical analyses for many aspects of the study of mass-conserving unstable thin film models have been well-developed using techniques from partial differential equations, nonlinear dynamics, and related models in materials science. However, introducing evaporation into the problem fundamentally changes key properties of the solutions of the model and necessitates the development of new extensions of previous methods or other novel approaches. The long-term goal of the project is to develop asymptotic models for the evolution of arrays of interacting volatile droplets. Obtaining this kind of coarsening model will involve new challenges as the quasi-steady framework underpinning the mass-conserving model no longer directly applies.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.