Studies in Small Scale Fluid Dynamics

这个项目致力于理解液体中的小尺度物理现象。一个主要的挑战是通过渐近和变分技术的新应用来表征接触线的动力学。将探讨表面活性剂、表面缺陷和静电控制的作用。不稳定驱动的图案形成和粗化行为将是另一个研究重点。最后，将开发基于边界积分和有限元技术的数值方法，用于实验和技术应用。流体在小尺度上的行为提出了一系列具有挑战性的科学问题，应用于各种学科，如工业涂料、微观机械设备和集体细菌运动。拟议的项目不仅是为了扩展基本的理论知识，而且是为了开发具有预测能力的模型和算法。这些将是当今工程和尖端微流控应用的关键。

This project is devoted to understanding physical phenomena in liquids at small length scales. One main challenge is to characterize the dynamics of contact lines through novel applications of asymptotic and variational techniques. The role of surfactants, surface defects, and electrostatic control will be explored. Instability-driven pattern formation and coarsening behavior will be another focus of study. Finally, numerical methods based on boundary integral and finite element techniques will be developed both for experimentation and technological applications.The behavior of fluids at small scales poses a set of challenging scientific problems, with applications to subjects as diverse as industrial coatings, microscopic mechanical devices, and collective bacterial motion. The proposed projects are intended to not only extend fundamental theoretical knowledge, but to develop models and algorithms that have predictive capabilities. These will be crucial for engineering present day and cutting edge microfluidic applications.