Critical adsorption and critical Casimir forces for geometrically structured confinements

TL;DR

This paper investigates how fluids near their critical point behave when confined by geometrically structured surfaces, analyzing order parameter profiles, adsorption, and Casimir forces using mean field theory.

Contribution

It introduces universal scaling functions for order parameter profiles and critical Casimir forces in fluids confined by structured substrates, extending understanding beyond flat surfaces.

Findings

Universal scaling functions for order parameter profiles near structured substrates.

Comparison of excess adsorption on corrugated versus planar walls.

Calculation of critical Casimir forces between structured and flat surfaces.

Abstract

We study the behavior of fluids, confined by geometrically structured substrates, upon approaching a critical point at T = Tc in their bulk phase diagram. As generic substrate structures periodic arrays of wedges and ridges are considered. Based on general renormalization group arguments we calculate, within mean field approximation, the universal scaling functions for order parameter profiles of a fluid close to a single structured substrate and discuss the decay of its spatial variation into the bulk. We compare the excess adsorption at corrugated substrates with the one at planar walls. The confinement of a critical fluid by two walls generates effective critical Casimir forces between them. We calculate corresponding universal scaling functions for the normal critical Casimir force between a flat and a geometrically structured substrate as well as the lateral critical Casimir force between two identically patterned substrates.