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

Non-technical Abstract

Diffusion, 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.