Analysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfaces

Handle URI:
http://hdl.handle.net/10754/597567
Title:
Analysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfaces
Authors:
Xu, Xianmin; Wang, Xiaoping
Abstract:
Wetting and contact angle hysteresis on chemically patterned surfaces in two dimensionsare analyzed from a stationary phase-field model for immiscible two phase fluids. We first study the sharp-interface limit of the model by the method of matched asymptotic expansions. We then justify the results rigorously by the γ-convergence theory for the related variational problem and study the properties of the limiting minimizers. The results also provide a clear geometric picture of the equilibrium configuration of the interface. This enables us to explicitly calculate the total surface energy for the two phase systems on chemically patterned surfaces with simple geometries, namely the two phase flow in a channel and the drop spreading. By considering the quasi-staticmotion of the interface described by the change of volume (or volume fraction), we can follow the change-of-energy landscape which also reveals the mechanism for the stick-slip motion of the interface and contact angle hysteresis on the chemically patterned surfaces. As the interface passes throughpatterned surfaces, we observe not only stick-slip of the interface and switching of the contact angles but also the hysteresis of contact point and contact angle. Furthermore, as the size of the patternde creases to zero, the stick-slip becomes weaker but the hysteresis becomes stronger in the sense that one observes either the advancing contact angle or the receding contact angle (when the interface ismoving in the opposite direction) without the switching in between. © 2011 Society for Industrial and Applied Mathematics.
Citation:
Xu X, Wang X (2011) Analysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfaces. SIAM Journal on Applied Mathematics 71: 1753–1779. Available: http://dx.doi.org/10.1137/110829593.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
SA-C0040/UK-C0016
Issue Date:
Jan-2011
DOI:
10.1137/110829593
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
This work was supported in part by award SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST), by Hong Kong RGC-GRF grants 603107 and 604209, and by the National Basic Research Program of China under project 2009CB623200.This author's work was supported by NSFC project 11001260 and by the State Key Laboratory of Scientific and Engineering Computing of China.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Xianminen
dc.contributor.authorWang, Xiaopingen
dc.date.accessioned2016-02-25T12:42:12Zen
dc.date.available2016-02-25T12:42:12Zen
dc.date.issued2011-01en
dc.identifier.citationXu X, Wang X (2011) Analysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfaces. SIAM Journal on Applied Mathematics 71: 1753–1779. Available: http://dx.doi.org/10.1137/110829593.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/110829593en
dc.identifier.urihttp://hdl.handle.net/10754/597567en
dc.description.abstractWetting and contact angle hysteresis on chemically patterned surfaces in two dimensionsare analyzed from a stationary phase-field model for immiscible two phase fluids. We first study the sharp-interface limit of the model by the method of matched asymptotic expansions. We then justify the results rigorously by the γ-convergence theory for the related variational problem and study the properties of the limiting minimizers. The results also provide a clear geometric picture of the equilibrium configuration of the interface. This enables us to explicitly calculate the total surface energy for the two phase systems on chemically patterned surfaces with simple geometries, namely the two phase flow in a channel and the drop spreading. By considering the quasi-staticmotion of the interface described by the change of volume (or volume fraction), we can follow the change-of-energy landscape which also reveals the mechanism for the stick-slip motion of the interface and contact angle hysteresis on the chemically patterned surfaces. As the interface passes throughpatterned surfaces, we observe not only stick-slip of the interface and switching of the contact angles but also the hysteresis of contact point and contact angle. Furthermore, as the size of the patternde creases to zero, the stick-slip becomes weaker but the hysteresis becomes stronger in the sense that one observes either the advancing contact angle or the receding contact angle (when the interface ismoving in the opposite direction) without the switching in between. © 2011 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was supported in part by award SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST), by Hong Kong RGC-GRF grants 603107 and 604209, and by the National Basic Research Program of China under project 2009CB623200.This author's work was supported by NSFC project 11001260 and by the State Key Laboratory of Scientific and Engineering Computing of China.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectγ-convergenceen
dc.subjectContact angle hysteresisen
dc.subjectPhase-field modelen
dc.titleAnalysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfacesen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionInstitute of Computational Mathematics and Scientific-Engineering Computing, Chinese Academy of Sciences, Beijing, Chinaen
dc.contributor.institutionHong Kong University of Science and Technology, Hong Kong, Chinaen
kaust.grant.numberSA-C0040/UK-C0016en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.