Fluctuation-Induced Interactions Between Ellipsoidal Particle and Planar Substrate Immersed in Critical Medium

TL;DR

This study investigates the net force between an ellipsoidal particle and a planar substrate immersed in a near-critical fluid, considering critical Casimir and van der Waals forces, revealing conditions for force sign change.

Contribution

It introduces a numerical approach combining scaling, mean-field calculations, and surface integration to analyze fluctuation-induced forces in complex geometries.

Findings

Force sign can change with temperature or chemical potential.

Competition between coating and core effects influences net force.

Method applicable for systems with known parallel plate forces.

Abstract

In our study we investigate the behaviour of the net force (NF) emerging between an ellipsoidal particle and a thick plate (slab), when the interaction takes place in a near critical fluid medium with account for the omnipresent van der Waals forces (vdWF). Here we consider the case of complete wetting of the objects surfaces by the medium, due to strong adsorbing local surface potentials, exerted by thin solid coating films. The influence of the bulk inner regions of the particle and the slab on the constituents of the fluid results in long-ranged competing dispersion potentials. As a consequence from the critical fluctuations of the medium, the system experiences an additional effective interaction, traditionally termed critical Casimir force (CCF). The forces of interest are evaluated numerically from integral expressions obtained utilizing general scaling arguments and mean-field type calculations in combination with the so-called "surface integration approach" (SIA). Within the scenario considered here, this technique is applicable if one has knowledge of the forces between two parallel semi-infinite plates, confining in between some fluctuating fluid medium characterized by its temperature $T$ and chemical potential $\mu$. It is demonstrated that for a suitable set of particle-fluid, slab-fluid, and fluid-fluid coupling parameters the competition between the effects due to the coatings and the core regions of the objects result, when one changes $T$ or $\mu$, in {\it sign change} of the NF acting between the ellipsoid and the slab.