Direct calculation of the critical Casimir force in a binary fluid

TL;DR

This paper demonstrates a method to directly compute the critical Casimir force in a binary fluid near its demixing transition using simulations in a semi grand canonical ensemble, revealing universal scaling behavior.

Contribution

It introduces a simulation approach to measure the critical Casimir force directly in a binary fluid, linking pressure anisotropy to universal scaling functions.

Findings

Critical Casimir effects can be observed via direct simulation.

Perpendicular pressure and chemical potential excesses are significantly larger than the Casimir force.

A universal scaling function relates pressure anisotropy to the Casimir force.

Abstract

We show that critical Casimir effects can be accessed through direct simulation of a model binary fluid passing through the demixing transition. We work in the semi grand canonical ensemble, in slab geometry, in which the Casimir force appears as the excess of the generalized pressure, $P_{\bot}-n\mu$. The excesses of the perpendicular pressure, $P_{\bot}$, and of $n\mu$, are individually of much larger amplitude. A critical pressure anisotropy is observed between forces parallel and perpendicular to the confinement direction, which collapses onto a universal scaling function closely related to that of the critical Casimir force.