Computational Mechanics

, Volume 58, Issue 6, pp 937–956 | Cite as

A frictional sliding algorithm for liquid droplets

Original Paper


This work presents a new frictional sliding algorithm for liquid menisci in contact with solid substrates. In contrast to solid–solid contact, the liquid–solid contact behavior is governed by the contact line, where a contact angle forms and undergoes hysteresis. The new algorithm admits arbitrary meniscus shapes and arbitrary substrate roughness, heterogeneity and compliance. It is discussed and analyzed in the context of droplet contact, but it also applies to liquid films and solids with surface tension. The droplet is modeled as a stabilized membrane enclosing an incompressible medium. The contact formulation is considered rate-independent such that hydrostatic conditions apply. Three distinct contact algorithms are needed to describe the cases of frictionless surface contact, frictionless line contact and frictional line contact. For the latter, a predictor–corrector algorithm is proposed in order to enforce the contact conditions at the contact line and thus distinguish between the cases of advancing, pinning and receding. The algorithms are discretized within a monolithic finite element formulation. Several numerical examples are presented to illustrate the numerical and physical behavior of sliding droplets.


Computational contact mechanics Contact angle hysteresis Liquid meniscus Nonlinear finite element methods Rough surface contact Wetting 



The author thanks Dr. Tobias Luginsland and Yannick Omar for proofreading the manuscript.

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Aachen Institute for Advanced Study in Computational Engineering Science (AICES)RWTH Aachen UniversityAachenGermany

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