Droplet shapes on structured substrates and conformal invariance

Details Droplet shapes on structured substrates and conformal invariance Droplet shapes on structured substrates and conformal invariance

2000-08-02

arxiv.org/abs/cond-mat/0008036v1

Physics

Condensed Matter

20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.)

Scientific paper

10.1088/0953-8984/13/3/303

We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $\Lambda_{A}$ of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and the height-height correlations can be understood from the conformal invariance of an appropriate operator. This allows us to predict the explicit scaling form of the droplet height for a number of different domain shapes. For systems with long-ranged forces, conformal invariance is not obeyed but the droplet shape is still shown to exhibit strong scaling behaviour. We argue that droplet formation in heterogeneous wedge geometries also shows a number of different scaling regimes depending on the range of the forces. The conformal invariance of the wedge droplet shape for short-ranged forces is shown explicitly.

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