Controlling the order of wedge filling transitions: the role of line tension

TL;DR

This paper investigates how line tension influences the order of wedge filling transitions in 3D geometries, revealing conditions for first-order or critical transitions and providing exact results for different interaction types.

Contribution

It introduces a transfer matrix approach to analyze the role of line tension in 3D wedge filling, including exact results and comparison with other models.

Findings

Line tension determines whether filling transitions are first-order or continuous.

Critical and first-order lines meet at a tricritical point for short-ranged forces.

For dispersion forces, the lines meet at a critical end-point.

Abstract

We study filling phenomena in 3D wedge geometries paying particular attention to the role played by a line tension associated with the wedge bottom. Our study is based on transfer matrix analysis of an effective one dimensional model of 3D filling which accounts for the breather-mode excitations of the interfacial height. The transition may be first-order or continuous (critical) depending on the strength of the line tension associated with the wedge bottom. Exact results are reported for the interfacial properties near filling with both short-ranged (contact) forces and also van der Waals interactions. For sufficiently short-ranged forces we show the lines of critical and first-order filling meet at a tricritical point. This contrasts with the case of dispersion forces for which the lines meet at a critical end-point. Our transfer matrix analysis is compared with generalized random-walk arguments based on a necklace model and is shown to be a thermodynamically consistent description of fluctuation effects at filling. Connections with the predictions of conformal invariance for droplet shapes in wedges is also made.