Collaborative Research: Non-equilibrium fluctuations and diffusion in 2D

扩散是最常见的输运过程之一，广泛存在于生物系统中，由于不同物种的粒子在分子长度尺度上的随机运动，扩散常被模拟为这些粒子的混合。然而，已经发现液体中的扩散与液体本身的流动有关。这可能会导致随机浓度波动，最近发现这种波动存在于分子长度范围内，最大可达数量级更大。虽然这些波动是针对三维(3D)流体测量的，但在像生物膜这样的二维(2D)流体的约束尺寸中，它们可能会更大。研究小组利用沉积在水面上的超薄自由悬浮液晶膜和分子单分子膜，旨在量化扩散过程中2D流体中的这些波动，并探索它们对分子传输的影响。与此同时，该理论小组正在为这些波动开发一个数学模型，并运行可以模拟实验的计算机模拟。这项工作有助于更好地理解扩散过程中的巨大波动，并告知它们在生物膜中的重要性。与科罗拉多博尔德大学软材料研究中心的合作为本科生研究团队提供了更多在材料科学前沿工作并开始他们的研究生生涯的机会。技术摘要：颗粒在生物膜中的扩散在生物有机体的生化过程中起着至关重要的作用。扩散的概念最近受到了新的关注，因为发现了在存在浓度梯度的三维(3D)流体扩散混合过程中产生的巨大浓度波动(空间范围接近分子长度尺度的10,000倍)。由于扩散颗粒之间流体动力相互作用的空间范围更大，二维(2D)流体中的浓度波动预计会更大。生物膜可以被模拟为准2D流体，由于存在嵌入膜的大量流体，因此具有2D和3D流体动力学特征的组合。本项目从实验和理论上研究了非平衡浓度波动的空间和时间范围，从二维行为到三维行为的交叉，以及波动对自由悬浮近晶薄膜中扩散颗粒聚集率的影响。研究小组正在使用溶解在薄膜中的染料的光漂白后荧光恢复(FRAP)，以及二元液晶混合物薄膜和掺杂染料的脂质朗缪尔单分子膜中的可混溶相变，通过从2D行为到3D行为的交叉来测量浓度关联函数。该项目的理论部分包括基于浸没边界法和随机流体力学并利用实验的初始浓度分布特征进行分析计算和运行计算机模拟，以便与观测到的浓度关联函数进行比较。该项目的教育部分整合了对本科生的培训，特别关注招募代表性不足的群体，以帮助学生在未来的工业和学术机构的职位上。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical AbstractDiffusion, one of the most common transport processes, is ubiquitous in biological systems and is often modeled as mixing of particles of different species due to the random motion of these particles at molecular length scales. However, diffusion in liquids has been found to couple with the flow of the fluid itself. This can lead to random concentration fluctuations that were recently found to exist at the molecular length scale and up to orders of magnitude larger. While these fluctuations have been measured for three-dimensional (3D) fluids, in the constrained dimensions of a two-dimensional (2D) fluid like a bio-membrane, they may be much larger still. Using ultra-thin freely-suspended liquid crystal films and molecular monolayers deposited on the surface of water, the research team aims to quantify these fluctuations within 2D fluids during diffusion and explore their effects on molecular transport. At the same time, the theory group is developing a mathematical model for these fluctuations and running computer simulations that can mimic experiments. This work contributes to an improved understanding of colossal fluctuations during diffusion and informs their importance in bio-membranes. The collaboration with the Soft Materials Research Center at the University of Colorado Boulder provides additional opportunities for the team of undergraduate research students to work at the frontiers of materials science and launch their post graduate careers.Technical Abstract:Diffusion of particles in bio-membranes plays an essential role in biochemical processes in living organisms. The concept of diffusion has recently received renewed attention with the discovery of giant concentration fluctuations (of spatial extent approaching 10,000 times molecular length scales) that develop during diffusive mixing of three-dimensional (3D) fluids in the presence of a concentration gradient. The concentration fluctuations are expected to be even larger in two-dimensional (2D) fluids due to the larger spatial extent of hydrodynamic interactions between diffusing particles. Bio-membranes can be modeled as quasi-2D fluids, having a combination of 2D and 3D hydrodynamic features due to the presence of a bulk fluid embedding the membrane. This project studies experimentally and theoretically the spatial and temporal extent of out-of-equilibrium concentration fluctuations, the crossover from 2D to 3D behavior, and the effects of fluctuations on the aggregation rate of diffusing particles in freely suspended smectic films, a model quasi-2D fluid. The research team is using Fluorescence Recovery After Photobleaching (FRAP) of dye dissolved in the film, and a miscibility phase transition in films of a binary liquid crystal mixture as well as in a dye-doped lipid Langmuir monolayer, to measure the concentration correlation function through the crossover from 2D to 3D behavior. The theory component of the project involves performing analytic calculations and running computer simulations, based on the immersed boundary method and stochastic hydrodynamics and using initial concentration distributions characteristic of the experiments, in order to generate a comparison to the observed concentration correlation functions. The education component of the project integrates training for undergraduate students, with a particular focus on recruiting under-represented groups, to help students in future positions at industrial and academic institutions.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.