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Some generic capillary-driven flows
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-3132-7252
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-3336-1462
2006 (English)In: International Journal of Multiphase Flow, ISSN 0301-9322, E-ISSN 1879-3533, Vol. 32, no 8, 1072-1086 p.Article in journal (Refereed) Published
Abstract [en]

This paper deals with numerical simulations of some capillary-driven flows. The focus is on the wetting phenomenon in sintering-like flows and in the imbibition of liquids into a porous medium. The wetting phenomenon is modeled using the coupled Cahn-Hilliard/Navier-Stokes system. The Cahn-Hilliard equation is treated as a system where the chemical potential is solved first followed by the composition. The equations are discretised in space using piecewise linear functions. Adaptive finite element method is implemented with an ad hoc error criterion that ensures mesh resolution along the vicinity of the interface. In the 3D case we use parallel adaptive finite element method. First, a basic wetting of a liquid drop on a solid surface is shown and is established the independence of the dynamic contact angle on the interface width. In addition, the dependence of the dynamic contact angle on the Capillary number is matched with experimental data. Next, some generic sintering-like flows with a fixed matrix is presented. Different geometries in 2D and 3D are considered. We observed rapid wetting, precursor films, coalescence, breakup of melt drops as well as pore migration and elimination that are all microstructural characteristics of a liquid phase sintering. Finally, the effect of equilibrium contact angles on imbibition of liquid into a porous medium is studied.

Place, publisher, year, edition, pages
2006. Vol. 32, no 8, 1072-1086 p.
Keyword [en]
Cahn-Hilliard/Navier-Stokes system; Capillary-driven flow; Imbibition; Sintering; Wetting; Computer simulation; Finite element method; Mathematical models; Navier Stokes equations; Sintering; Wetting; Cahn-Hilliard equation; Capillary number; Capillary-driven flow; Mesh resolution; Capillary flow; Capillary flow; Computer simulation; Finite element method; Mathematical models; Navier Stokes equations; Sintering; Wetting
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-7212DOI: 10.1016/j.ijmultiphaseflow.2006.05.003ISI: 000240760900004Scopus ID: 2-s2.0-33747810056OAI: oai:DiVA.org:kth-7212DiVA: diva2:12153
Note
QC 20100823Available from: 2007-05-29 Created: 2007-05-29 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Diffuse-Interface Simulations of Capillary Phenomena
Open this publication in new window or tab >>Diffuse-Interface Simulations of Capillary Phenomena
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Fluid flows mainly driven by capillary forces are presented in this thesis. By means of modeling and simulations, interesting dynamics in capillary-driven flows are revealed such as coalescences, breakups, precursor films, flow instabilities, rapid spreading, rigid body motions, and reactive wetting.

Diffuse-interface methods model a fluid interface as having a finite thickness endowed with physical properties such as surface tension. Two diffuse-interface models that are based on the free energy of the system are presented. The binary model, more specifically the coupled Navier-Stokes/Cahn-Hilliard equations, was used to study different two-phase flows including problems related to microfluidics. Numerical issues using this model have been addressed such as the need for mesh adaptivity and time-step restrictions. Moreover, the flexibility of this model to simulate 2D, axisymmetric, and 3D flows has been demonstrated.

The factors affecting reproducibility of microdroplet depositions performed under a liquid medium are investigated. In the deposition procedure, sample solution is dispensed from the end of a capillary by the aid of a pressure pulse onto a substrate with pillar-shaped sample anchors. In both the experimental and numerical study it was shown that the deposited volume mainly depends on the capillary-substrate distance and anchor surface wettability. Furthermore, a critical equilibrium contact angle has been identified below which reproducible depositions are facilitated.

The ternary model is developed for more complicated flows such as liquid phase sintering. With the introduction of a Gibbs energy functional, the governing equations are derived, consisting of convective concentration and phase-field equations which are coupled to the Navier-Stokes equations with surface tension forces. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. Detailed analysis of the important capillary phenomena in liquid phase sintering such as reactive and nonreactive wetting and motion of two particles connected by a liquid bridge are presented. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Factors affecting the equilibrium configuration of the particles such as equilibrium contact angles and volume ratios are also investigated.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. ix, 34 p.
Series
Trita-MEK, ISSN 0348-467X ; 2007:05
Keyword
capillary-driven flows, wetting, Cahn-Hilliard/Navier-Stokes system, multicomponent and multiphase flows, parallel adaptive computing
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-4402 (URN)978-91-7178-718-7 (ISBN)
Public defence
2007-06-08, Sal F2, KTH, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20100823Available from: 2007-05-29 Created: 2007-05-29 Last updated: 2010-08-23Bibliographically approved

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Villanueva, WalterAmberg, Gustav

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