Boundary-integral equation for an immersed uid sheet

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Table of contents

Acknowledgements
Abstract
Resume
1 Introduction
1.1 Free subduction
1.2 Buckling instabilities in microchannels
2 Thin Newtonian sheets: The discrete approach
2.1 Thin-sheet theory: essential concepts
2.2 Lagrangian description of a thin sheet
2.3 Boundary-integral equation for an immerseduid sheet .
2.4 The discrete viscous thin sheet model
3 Subduction of a Newtonian sheet
3.1 Bending and stretching dissipation potentials of a Newtonian sheet
3.2 Numerical implementation
3.3 The Green’s function for sheet subduction
3.4 Numerical solutions and analysis
3.4.1 Vertical sheet
3.4.2 Horizontal sheet
3.4.3 Subduction of a bent sheet
4 Parallel code for three dimensional multi phaseow
4.1 Mathematical formulation
4.2 Numerical method
4.2.1 Interface treatment
4.2.2 Extended interface for parallel processing
4.2.3 Solution procedure in parallel computing
5 Simulation of viscous folding in diverging microchannels
5.1 Thread formation
5.2 Folding instability
6 Conclusion
6.1 Summary of results obtained
6.2 Future perspectives
Bibliography