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

摘要扩散是生物系统中普遍存在的最常见的传递过程之一，由于粒子在分子长度尺度上的随机运动，通常被建模为不同物种粒子的混合。然而，已经发现液体中的扩散与流体本身的流动是耦合的。这可能导致随机的浓度波动，最近发现这种波动存在于分子长度尺度上，甚至更大的数量级。虽然这些波动是在三维（3D）流体中测量的，但在生物膜等二维（2D）流体的受限尺寸中，它们可能还要大得多。利用超薄自由悬浮的液晶膜和沉积在水面上的分子单层，研究小组旨在量化二维流体在扩散过程中的这些波动，并探索它们对分子运输的影响。与此同时，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。这项工作有助于提高对扩散过程中巨大波动的理解，并告知它们在生物膜中的重要性。与科罗拉多大学博尔德分校软材料研究中心的合作为本科研究生团队提供了在材料科学前沿工作的额外机会，并开始了他们的研究生生涯。技术摘要：颗粒在生物膜中的扩散在生物体的生化过程中起着至关重要的作用。随着在存在浓度梯度的三维（3D）流体扩散混合过程中出现的巨大浓度波动（空间范围接近分子长度尺度的10,000倍）的发现，扩散的概念最近再次受到关注。由于扩散颗粒之间流体动力相互作用的空间范围更大，预计二维流体中的浓度波动会更大。生物膜可以建模为准二维流体，由于存在大量嵌入膜的流体，因此具有二维和三维流体动力学特征的组合。本项目通过实验和理论研究了非平衡浓度波动的时空范围、从二维到三维的交叉行为，以及波动对自由悬浮近晶膜中扩散粒子聚集速率的影响。研究小组利用溶解在薄膜中的染料的光漂白后荧光恢复（FRAP）、二元液晶混合物薄膜中的混相相变以及染料掺杂脂质Langmuir单层中的混相相变，通过从2D到3D行为的交叉来测量浓度相关函数。该项目的理论部分包括基于浸入边界法和随机流体力学，并利用实验的初始浓度分布特征，进行分析计算和计算机模拟，以便与观测到的浓度相关函数进行比较。该项目的教育部分包括对本科生的培训，特别侧重于招募代表性不足的群体，以帮助学生未来在工业和学术机构担任职务。该奖项反映了美国国家科学基金会的法定使命，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。

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.