Diffusive spreading and mixing of fluid monolayers

TL;DR

This paper models the spreading and mixing behaviors of fluid monolayers in nano-fluidic systems using lattice-gas models and nonlinear diffusion equations, focusing on obstacle interactions and species mixing.

Contribution

It introduces a continuum limit approach to lattice-gas models for analyzing monolayer dynamics, including obstacle effects and multi-species mixing.

Findings

Density relaxation after obstacle encounter studied

Mixing dynamics of different species analyzed

Model provides insights into nano-fluidic control mechanisms

Abstract

The use of ultra-thin, i.e., monolayer films plays an important role for the emerging field of nano-fluidics. Since the dynamics of such films is governed by the interplay between substrate-fluid and fluid-fluid interactions, the transport of matter in nanoscale devices may be eventually efficiently controlled by substrate engineering. For such films, the dynamics is expected to be captured by two-dimensional lattice-gas models with interacting particles. Using a lattice gas model and the non-linear diffusion equation derived from the microscopic dynamics in the continuum limit, we study two problems of relevance in the context of nano-fluidics. The first one is the case in which along the spreading direction of a monolayer a mesoscopic-sized obstacle is present, with a particular focus on the relaxation of the fluid density profile upon encountering and passing the obstacle. The second one is the mixing of two monolayers of different particle species which spread side by side following the merger of two chemical lanes, here defined as domains of high affinity for fluid adsorption surrounded by domains of low affinity for fluid adsorption.