The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop
type: Item
instance of: scholarly article
title: The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop
zbMATH Open document ID: 1200.76054
DOI: 10.1155/MPE.2005.703
published in: Mathematical Problems in Engineering
publication date: 2008-11-20T00:00:00Z
full work available at URL: https://eudml.org/doc/45328
review text: Summary: The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin viscous liquid drop are investigated. A second-order nonlinear partial differential equation modelling the evolution of the free surface of a thin viscous liquid drop is derived. The nonuniform surface tension is represented by a function \(\Sigma(r)\). The Lie group method is used to determine \(\Sigma(r)\) such that exact and approximate invariant solutions admitted by the free surface equation can be determined. It is shown that the nonuniform surface tension can be represented as a power law in \(r\). The effect of this nonuniformity is to reduce the surface tension at the centre of the drop and increase it at the foot of the drop. This results in a deflection away from the solution for spreading under gravity only and the formation of a capillary ridge.
Mathematics Subject Classification ID: 76D45
Mathematics Subject Classification ID: 76A20
Mathematics Subject Classification ID: 76M60
zbMATH DE Number: 5369090
author: E. Momoniat
MaRDI profile type: Publication
OpenAlex ID: W2018543839
description: scientific article; zbMATH DE number 5369090