Diffusive spreading and mixing of fluid monolayers

Abstract

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