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Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 386, p. 218-247Article in journal (Refereed) Published
Abstract [en]

Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method for computing the evolution of surfactant-covered droplets in 2D Stokes flow. The method has spectral accuracy in space and the adaptive time-stepping scheme allows for control of the temporal errors. Previously available semi-analytical solutions (based on conformal-mapping techniques) are extended to include surfactants, and a set of algorithms is introduced to detail their evaluation. These semi-analytical solutions are used to validate and assess the accuracy of the boundary integral method, and it is demonstrated that the presented method maintains its high accuracy even when droplets are in close proximity. 

Place, publisher, year, edition, pages
Academic Press, 2019. Vol. 386, p. 218-247
Keywords [en]
Insoluble surfactants, Stokes flow, Validation, Integral equations, Two-phase flow, Drop deformation, Special quadrature
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-251466DOI: 10.1016/j.jcp.2018.12.044ISI: 000464675600011Scopus ID: 2-s2.0-85062883114OAI: oai:DiVA.org:kth-251466DiVA, id: diva2:1316037
Note

QC 20190515

Available from: 2019-05-15 Created: 2019-05-15 Last updated: 2019-11-26Bibliographically approved
In thesis
1. Boundary integral methods for fast and accurate simulation of droplets in two-dimensional Stokes flow
Open this publication in new window or tab >>Boundary integral methods for fast and accurate simulation of droplets in two-dimensional Stokes flow
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Accurate simulation of viscous fluid flows with deforming droplets creates a number of challenges. This thesis identifies these principal challenges and develops a numerical methodology to overcome them. Two-dimensional viscosity-dominated fluid flows are exclusively considered in this work. Such flows find many applications, for example, within the large and growing field of microfluidics; accurate numerical simulation is of paramount importance for understanding and exploiting them.

A boundary integral method is presented which enables the simulation of droplets and solids with a very high fidelity. The novelty of this method is in its ability to accurately handle close interactions of drops, and of drops and solid boundaries, including boundaries with sharp corners. The boundary integral method is coupled with a spectral method to solve a PDE for the time-dependent concentration of surfactants on each of the droplet interfaces. Surfactants are molecules that change the surface tension and are therefore highly influential in the types of flow problems which are considered herein.

A method’s usefulness is not dictated by accuracy alone. It is also necessary that the proposed method is computationally efficient. To this end, the spectral Ewald method has been adapted and applied. This yields solutions with computational cost O(N log N ), instead of O(N^2), for N source and target points.

Together, these innovations form a highly accurate, computationally efficient means of dealing with complex flow problems. A theoretical validation procedure has been developed which confirms the accuracy of the method.

Abstract [sv]

Att noggrant simulera viskösa flöden med deformerande droppar medför flera utmaningar. Denna avhandling identifierar de viktigaste utmaningarna och utvecklar numeriska metoder för att övervinna dem. Visköst dominerade tvådimensionella flöden studeras. Sådana flöden har många tillämpningar till exempel inom mikrofluidik och noggrann beräkning är av största vikt för att förstå och utnyttja dem.

En randintegralsmetod som möjliggör simulering av droppar och fasta ränder med en mycket hög noggrannhet presenteras. Metoden särskiljer sig från andra genom dess förmåga att hantera nära samspel mellan droppar och förekomst av hörn på de fasta ränderna. Randin- tegralsmetoden är kopplad till en spektral metod som möjliggör inkluderandet av surfaktanter i flödesproblemet. Surfaktanter är molekyler som förändrar ytspänningen och de är därför betydelsefulla för de typer av flödesproblem som beaktas här.

En metods användbarhet bestäms inte endast av dess noggrannhet. Det är också nödvändigt att den föreslagna metoden är effektiv. För detta ändamål har metoden spektral Ewald anpassats och tillämpats. Detta ger lösningar med beräkningskostnaden O(N log N ) istället för O(N^2), där N är antalet diskreta punkter i systemet.

Tillsammans utgör dessa innovationer ett mycket noggrant, be- räkningseffektivt sätt att hantera komplexa flödesproblem. Ett teoretiskt valideringsförfarande har utvecklats som bekräftar metodens noggrannhet.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2019. p. 49
Series
TRITA-SCI-FOU ; 2019;50
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics, Numerical Analysis
Identifiers
urn:nbn:se:kth:diva-264369 (URN)978-91-7873-355-2 (ISBN)
Public defence
2019-12-18, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Göran Gustafsson Foundation for Research in Natural Sciences and Medicine
Available from: 2019-11-27 Created: 2019-11-26 Last updated: 2019-11-27Bibliographically approved

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Pålsson, SaraTornberg, Anna-Karin

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