Effective Hamiltonian for a liquid-gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

TL;DR

This paper derives effective Hamiltonians for liquid-gas interfaces on curved substrates with van der Waals interactions, revealing non-universal curvature-dependent rigidity coefficients that differ across interfaces.

Contribution

It introduces a mean-field density functional approach to derive curvature-dependent Hamiltonians for liquid interfaces on complex substrates, extending the Helfrich model.

Findings

Rigidity coefficients are non-universal functions of curvature.

The structure of the Hamiltonian varies with substrate geometry.

Implications for understanding liquid interface fluctuations on curved surfaces.

Abstract

We investigate liquid layers adsorbed at spherical and corrugated cylindrical substrates. The effective Hamiltonians for the liquid-gas interfaces fluctuating in the presence of such curved substrates are derived via the mean-field density functional theory. Their structure is compared with the Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity coefficients. For long-ranged interparticle interactions of van der Waals type these coefficients turn out to be non-universal functions of interfacial curvatures; their form varies from one interface to another. We discuss implications of the structure of these functions on the effective Hamiltonian.