CAREER: Mathematical Modeling of Microfluidic Dynamics and Transport

本计画将探讨在固体表面上扩散的黏性薄膜的流体动力学中的数学问题。这种具有强表面张力效应的润滑流动的基本数学模型是四阶非线性偏微分方程。这些方程会产生某些奇异行为，使它们成为问题。在这项工作中，这些困难是克服通过使用物理动机的广义模型，包括液体膜和固体基质之间的相互作用力。这些所谓的分离压力或"去湿膜“模型将被用作研究一系列相互关联的问题的基础。该研究项目的目标是：（i）数学上建立去湿膜模型可以提供涂层流动中重要物理效应的忠实表示，以及（ii）将这一基础研究扩展到微流体装置的设计。这些目标将进行使用的非线性偏微分方程的去湿模型的计算和分析相结合的研究。通过对二维模型进行数值模拟和相似性求解，获得结构化几何形状中的流动动力学;这项工作将与薄膜流体流动及其稳定性的驱动机制研究相结合。本项目侧重于描述固体表面上液滴运动的数学模型。这项工作的影响在于它作为基础研究的作用，支持生物医学工程和微流体技术的进步。该项目的一个主要重点是利用表面张力效应进行液体的主动输送。通过仔细控制局部环境的变化，我们可以产生表面张力，以任何所需的方式操纵液滴。这种方法是用于下一代生物医学研究工具的微流体装置设计的关键要素。该项目还将研究固体表面的材料特性如何影响更复杂流体的运动。这项工作将作为理解的基础，在制定药物输送生物凝胶用于生理涂层流动和其他生物动力的流体流动问题的重要物理因素。

This project will investigate mathematical problems in the fluid dynamics of thin viscous films spreading on solid surfaces. The basic mathematical models for such lubrication flows with strong surface tension effects are fourth-order nonlinear partial differential equations. These equations yield certain singular behaviors that make them problematic. In this work, these difficulties are overcome through the use of physically-motivated generalized models that include interaction forces between the liquid film and the solid substrate. These so-called disjoining-pressure or ``dewetting-film'' models will be used as the basis for the study of an array of interconnected problems. The goals of this research project are: (i) to mathematically establish that dewetting film models can provide faithful representations of the important physical effects in coating flows, and (ii) to extend this basic research to the design of microfluidic devices. These goals will be carried out using a combined computational and analytic study of the nonlinear partial differential equations for the dewetting models. Applying numerical simulations and similarity solutions to the two-dimensional version of the models, the dynamics of flows in structured geometries will be obtained; this work will be combined with a study of mechanisms used to drive thin film fluid flows and their stability.This project focuses on mathematical models for describing the motion of drops of fluids on solid surfaces. The impact of this work lies in its role as basic research supporting advances in biomedical engineering and microfluidic technology. A major focus of this project is the use surface-tension effects for active transport of liquids. Using carefully controlled changes in the local environment, we can create surface tension forces to manipulate fluid droplets in any desired manner. This approach is a key element used in the designs of microfluidic devices for the next generation of biomedical research tools. The project will also examine how material properties of the solid surfaces influence the motion of more complicated fluids. This work will serve as the basis for understanding the important physical factors in the formulation of drug delivery bio-gels used in physiological coating flows and other biologically-motivated fluid flow problems.