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Diffuse-Interface Simulations of Capillary Phenomena
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-3132-7252
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 [en]
capillary-driven flows, wetting, Cahn-Hilliard/Navier-Stokes system, multicomponent and multiphase flows, parallel adaptive computing
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-4402ISBN: 978-91-7178-718-7 (print)OAI: oai:DiVA.org:kth-4402DiVA: diva2:12158
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
List of papers
1. Some generic capillary-driven flows
Open this publication in new window or tab >>Some generic capillary-driven flows
2006 (English)In: International Journal of Multiphase Flow, ISSN 0301-9322, 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.

Keyword
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:nbn:se:kth:diva-7212 (URN)10.1016/j.ijmultiphaseflow.2006.05.003 (DOI)000240760900004 ()2-s2.0-33747810056 (Scopus ID)
Note
QC 20100823Available from: 2007-05-29 Created: 2007-05-29 Last updated: 2010-08-23Bibliographically approved
2. Microdroplet deposition under a liquid medium
Open this publication in new window or tab >>Microdroplet deposition under a liquid medium
Show others...
2007 (English)In: Langmuir, ISSN 0743-7463, E-ISSN 1520-5827, Vol. 23, no 3, 1171-1177 p.Article in journal (Refereed) Published
Abstract [en]

An experimental and numerical study of the factors affecting the reproducibility of microdroplet depositions performed under a liquid medium is presented. 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. The deposition was modeled using the convective Cahn-Hilliard equation coupled with the Navier-Stokes equations with added surface tension and gravity forces. To avoid a severe time-step restriction imposed by the fourth-order Cahn-Hilliard equation, a semi-implicit scheme was developed. An axisymmetric model was used, and an adaptive finite element method was implemented. In both the experimental and numerical study it was shown that the deposited volume mainly depends on the capillary-substrate distance and the anchor surface wettability. A critical equilibrium contact angle has been identified below which reproducible depositions are facilitated.

Keyword
Contact angle; Deposition; Finite element method; Gravitational effects; Mathematical models; Navier Stokes equations; Surface tension; Cahn Hilliard equations; Liquid mediums; Microdroplet deposition; Pressure pulses; Fluid dynamics; article; mathematical computing; particle size; reproducibility; solution and solubility; surface tension; technique; wettability; Methods; Numerical Analysis, Computer-Assisted; Particle Size; Reproducibility of Results; Solutions; Surface Tension; Wettability
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-7213 (URN)10.1021/la0626712 (DOI)000243684100035 ()17241029 (PubMedID)2-s2.0-33847175859 (Scopus ID)
Note
QC 20100823Available from: 2007-05-29 Created: 2007-05-29 Last updated: 2010-08-23Bibliographically approved
3. Parallel adaptive computation of some time-dependent materials-related microstructural problems
Open this publication in new window or tab >>Parallel adaptive computation of some time-dependent materials-related microstructural problems
2007 (English)In: Bulletin of the Polish Academy of Sciences: Technical Sciences, ISSN 0239-7528, Vol. 55, no 2, 229-237 p.Article in journal (Refereed) Published
Abstract [en]

Some materials-related microstructural problems calculated using the phase-field method are presented. It is well known that the phase field method requires mesh resolution of a diffuse interface. This makes the use of mesh adaptivity essential especially for fast evolving interfaces and other transient problems. Complex problems in 3D are also computationally challenging so that parallel computations are considered necessary. In this paper, a parallel adaptive finite element scheme is proposed. The scheme keeps the level of node and edge for 2D and level of node and face for 3D instead of the complete history of refinements to facilitate derefinement. The information is local and exchange of information is minimized and also less memory is used. The parallel adaptive algorithms that run on distributed memory machines are implemented in the numerical simulation of dendritic growth and capillary-driven flows.

Keyword
Adaptive finite element method; Dendritic growth; Parallel computing; Wetting; Computational complexity; Finite element method; Interfaces (materials); Parallel processing systems; Wetting; Adaptive finite element method; Dendritic growth; Microstructure
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-7214 (URN)000255242300012 ()2-s2.0-34547291979 (Scopus ID)
Note
QC 20100823. Uppdaterad från In press till Published 20100823.Available from: 2007-05-29 Created: 2007-05-29 Last updated: 2012-03-21Bibliographically approved
4. Multicomponent and multiphase modeling and simulation of reactive wetting
Open this publication in new window or tab >>Multicomponent and multiphase modeling and simulation of reactive wetting
2008 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 77, no 5, 056313- p.Article in journal (Refereed) Published
Abstract [en]

A multicomponent and multiphase model with fluid motion is developed. The model is used to study reactive wetting in the case where concentration change of the spreading liquid and the substrate occurs. 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. The solid substrate is modeled hydrodynamically with a very high viscosity. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. An axisymmetric model with an adaptive finite element method is utilized. Numerical simulations were done revealing two stages in the wetting process. First, the convection-dominated stage where rapid spreading occurs. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Second, the diffusion-dominated stage where we observed depression of the substrate-liquid interface and elevation of the contact line region.

Keyword
Finite element method; Flow patterns; Flow simulation; Gibbs free energy; Multiphase flow; Navier Stokes equations; Governing equations; Multiphase modeling; Phase-field equations; Reactive wetting; Fluid dynamics
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-11085 (URN)10.1103/PhysRevE.77.056313 (DOI)000256885500050 ()2-s2.0-44649192678 (Scopus ID)
Note

QC 20100622

Available from: 2009-09-16 Created: 2009-09-16 Last updated: 2016-04-20Bibliographically approved
5. Multicomponent and multiphase simulation of liquid-phase sintering
Open this publication in new window or tab >>Multicomponent and multiphase simulation of liquid-phase sintering
2009 (English)In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 47, no 2, 512-520 p.Article in journal (Refereed) Published
Abstract [en]

Numerical simulation of liquid-phase sintering using a multicomponent and multiphase model is presented. The model consists of convective concentration and phase-field equations coupled with the Navier-Stokes equations with surface tension forces. The governing equations are nondimensionalized and an adaptive finite element method is utilized. An idealized phase diagram, surface energies, and typical dimensionless parameters are some input into the model. Important dynamics in liquid-phase sintering such as rapid wetting and motion of particles due to capillary forces are studied. Some factors that are known to significantly affect the dynamics of the sintering process such as contact angles and volume ratios are also investigated. In addition, numerical results on the motion of particles due to capillary forces were compared with an existing analytical model. Good agreement between numerical and analytical results is obtained within the validity of the analytical model.

Keyword
Liquid-phase sintering, Multicomponent and multiphase model, Navier-Stokes flow, Wetting, Capillary-driven flow, REARRANGEMENT PROCESSES, WETTING BEHAVIOR, FIELD APPROACH, SIC CERAMICS, MODEL
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-13650 (URN)10.1016/j.commatsci.2009.09.018 (DOI)000273115500029 ()2-s2.0-70449622731 (Scopus ID)
Note

QC 20100622

Available from: 2010-06-22 Created: 2010-06-22 Last updated: 2016-04-20Bibliographically approved

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