Many-body effects for critical Casimir forces

TL;DR

This paper uses mean-field theory to analyze critical Casimir forces in a colloid-liquid system, revealing how many-body effects significantly influence force behavior near criticality and under various geometries.

Contribution

It provides the first detailed mean-field analysis of many-body effects on critical Casimir forces in colloidal systems with different boundary conditions.

Findings

Many-body forces can reach up to 25% of total force near criticality.

Sign change in forces occurs with varying colloid positions or temperature.

Many-body effects are more pronounced at small distances and close to the critical temperature.

Abstract

Within mean-field theory we calculate the scaling functions associated with critical Casimir forces for a system consisting of two spherical colloids immersed in a binary liquid mixture near its consolute point and facing a planar, homogeneous substrate. For several geometrical arrangements and boundary conditions we analyze the normal and the lateral critical Casimir forces acting on one of the two colloids. We find interesting features such as a change of sign of these forces upon varying either the position of one of the colloids or the temperature. By subtracting the pairwise forces from the total force we are able to determine the many-body forces acting on one of the colloids. We have found that the many-body contribution to the total critical Casimir force is more pronounced for small colloid-colloid and colloid-substrate distances, as well as for temperatures close to criticality, where the many-body contribution to the total force can reach up to 25%.