Drops with non-circular footprints

TL;DR

This paper investigates the shape and formation of non-circular drops on substrates caused by anisotropic contact line motion and hysteresis effects, combining experimental observations, theoretical modeling, and numerical simulations.

Contribution

It introduces a steady state solution for non-circular drops within lubrication theory and compares it with experimental data, highlighting the effects of contact angle hysteresis.

Findings

Derived a non-trivial steady state drop shape model

Validated the model with experimental measurements

Simulated drop dynamics using Navier-Stokes equations

Abstract

In this paper we study the morphology of drops formed on partially wetting substrates, whose footprint is not circular. This type of drops is a consequence of the breakup processes occurring in thin films when anisotropic contact line motions take place. The anisotropy is basically due to hysteresis effects of the contact angle since some parts of the contact line are wetting, while others are dewetting. Here, we obtain a peculiar drop shape from the rupture of a long liquid filament sitting on a solid substrate, and analyze its shape and contact angles by means of goniometric and refractive techniques. We also find a non--trivial steady state solution for the drop shape within the long wave approximation (lubrication theory), and compare most of its features with experimental data. This solution is presented both in Cartesian and polar coordinates, whose constants must be determined by a certain group of measured parameters. Besides, we obtain the dynamics of the drop generation from numerical simulations of the full Navier--Stokes equation, where we emulate the hysteretic effects with an appropriate spatial distribution of the static contact angle over the substrate.