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

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.

arXiv commentRevised version with two added figures, accepted for publication in New Journal of Physics

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