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Scaling properties of fluid adsorption near the base of a cylinder

Andrew O. Parry

Carlos Rascón

  • Department of Mathematics, Imperial College London, London SW7 2BZ, United Kingdom

  • Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain

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Phys. Rev. E 85, 031606 – Published 30 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.031606

Abstract

We consider the adsorption of fluid at the foot of a cylinder that protrudes from a flat substrate made of the same material. Provided the contact angle θ is small enough, a drop of liquid condenses near the base, the size of which can be determined using simple macroscopic arguments. The adsorption in this geometry shows scaling behavior related to a number of different interfacial phase transitions and, for systems with short-ranged forces, shows a remarkable property; for small θ, the height of the drop (measured from the base) and the width (measured from the cylinder axis) are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films (at planar walls). The only difference is that the bulk correlation length is replaced by the radius of the cylinder. By taking into account the correct singular behavior of the line tension we show that this geometrical amplification of the microscopic lengths occurs for second-order, first-order, and complete wetting transitions, and is specific to three dimensions. Similar phenomena occurs for long-ranged forces, and shows crossover scaling behavior.

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Phys. Rev. E 85, 031606– Published 30 March, 2012
  • Received 17 February 2012

©2012 American Physical Society

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