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Computational methods for microfluidics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-7425-8029
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is concerned with computational methods for fluid flows on the microscale, also known as microfluidics. This is motivated by current research in biological physics and miniaturization technology, where there is a need to understand complex flows involving microscale structures. Numerical simulations are an important tool for doing this.

The first paper of the thesis presents a numerical method for simulating multiphase flows involving insoluble surfactants and moving contact lines. The method is based on an explicit interface tracking method, wherein the interface between two fluids is decomposed into segments, which are represented locally on an Eulerian grid. The framework of this method provides a natural setting for solving the advection-diffusion equation governing the surfactant concentration on the interface. Open interfaces and moving contact lines are also incorporated into the method in a natural way, though we show that care must be taken when regularizing interface forces to the grid near the boundary of the computational domain.

In the second paper we present a boundary integral formulation for sedimenting particles in periodic Stokes flow, using the completed double layer boundary integral formulation. The long-range nature of the particle-particle interactions lead to the formulation containing sums which are not absolutely convergent if computed directly. This is solved by applying the method of Ewald summation, which in turn is computed in a fast manner by using the FFT-based spectral Ewald method. The complexity of the resulting method is O(N log N), as the system size is scaled up with the number of discretization points N. We apply the method to systems of sedimenting spheroids, which are discretized using the Nyström method and a basic quadrature rule.

The Ewald summation method used in the boundary integral method of the second paper requires a decomposition of the potential being summed. In the introductory chapters of the thesis we present an overview of the available methods for creating Ewald decompositions, and show how the methods and decompositions can be related to each other.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , viii, 39 p.
Series
Trita-NA, ISSN 0348-2952 ; 2013:01
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-116384ISBN: 978-91-7501-625-2 (print)OAI: oai:DiVA.org:kth-116384DiVA: diva2:600178
Presentation
2013-02-19, F3, Lindstedtsvägen 26, Kungliga Tekniska Högskolan, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20130124

Available from: 2013-01-24 Created: 2013-01-17 Last updated: 2013-01-24Bibliographically approved
List of papers
1. An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant
Open this publication in new window or tab >>An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant
2014 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 101, 50-63 p.Article in journal (Refereed) Published
Abstract [en]

The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the immersed boundary method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops.

Keyword
Multiphase flow, Insoluble surfactant, Marangoni force, Moving contact line, Immersed boundary method
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-48763 (URN)10.1016/j.compfluid.2014.05.029 (DOI)000340851500005 ()2-s2.0-84903152815 (Scopus ID)
Funder
Swedish Research Council, 621-2007-6375
Note

QC 20140919. Updated from accepted to published.

Available from: 2011-11-23 Created: 2011-11-23 Last updated: 2017-12-08Bibliographically approved
2. Fast Ewald summation for Stokesian particle suspensions
Open this publication in new window or tab >>Fast Ewald summation for Stokesian particle suspensions
2014 (English)In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 76, no 10, 669-698 p.Article in journal (Refereed) Published
Abstract [en]

We present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using generalized minimal residual accelerated by the spectral Ewald method, which reduces the computational complexity to O(N log N), where N is the number of points used to discretize the particle surfaces. We develop predictive error estimates, which can be used to optimize the choice of parameters in the Ewald summation. Numerical tests show that the method is well conditioned and provides good accuracy when validated against reference solutions. 

Place, publisher, year, edition, pages
John Wiley & Sons, 2014
Keyword
viscous flows, integral equations, error estimation, microfluidics, multibody dynamics, spectral, double layer, boundary integral, ewald summation
National Category
Fluid Mechanics and Acoustics Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-116383 (URN)10.1002/fld.3953 (DOI)000344349000004 ()
Funder
Swedish Research Council, 2011-3178
Note

QC 20141119

Available from: 2013-01-17 Created: 2013-01-17 Last updated: 2017-12-06Bibliographically approved

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