Bifurcation of cylinders for wetting and dewetting models with striped geometry

TL;DR

This paper investigates the bifurcation of cylindrical interfaces with constant mean curvature in striped geometries, providing a mathematical proof for experimentally observed abrupt shape changes in liquids on structured substrates.

Contribution

It introduces a bifurcation analysis of cylinders in wetting models, revealing new periodic non-rotational interfaces with constant mean curvature.

Findings

Identification of bifurcating periodic surfaces

Mathematical proof of interface stability and bifurcation

Connection between theoretical results and experimental observations

Abstract

We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial interfaces in a problem of microscale range modeling the morphologies that adopt a liquid deposited in a chemically structured substrate with striped geometry or a liquid contained in a right wedge with Dirichlet and capillary boundary condition on the edges of the wedge. Experiments show that starting from these cylinders and once reached a certain stage, the shape of the liquid changes drastically in an abrupt manner. Studying the stability of such cylinders, the paper provides a mathematical proof of the existence of these new interfaces obtained in experiments. The analysis is based on the theory of bifurcation by simple eigenvalues of Crandall-Rabinowitz.