Implementing surfactant mass balance in 2D FEM-ALE models

Engineering with Computers

Volumn 27, Issue 2, 2011, Pages 165-175

  Pohjoranta, Antti ^a   Tenno, Robert ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

ALE method; Curvature computation; Surface deformation; Surfactant modeling

Indexed keywords

ALE METHODS; ALTERNATIVE APPROACH; BOUNDARY CURVATURE; CARTESIAN COORDINATE; CURVATURE COMPUTATION; FINITE ELEMENT; GOVERNING EQUATIONS; LOCAL SURFACES; MASS BALANCE; MASS CONSERVATION; MODEL GEOMETRY; NUMERICAL OSCILLATION; RATE OF CHANGE; SHAPE CHANGE; SURFACE CURVATURES; SURFACE DEFORMATION; SURFACE DIFFERENTIALS; SURFACTANT MODELING; TANGENTIAL VELOCITIES;

NUMERICAL METHODS;

SURFACE ACTIVE AGENTS;

EID: 79960037905     PISSN: 01770667     EISSN: 14355663     Source Type: Journal    
DOI: 10.1007/s00366-010-0186-6     Document Type: Article

References (26)

1. Aris R (1962) Vectors, tensors, and the basic equations of fluid mechanics. Prentice-Hall, Englewood Cliffs
2. Askes H, Kuhl E, Steinman P (2004) An ALE formulation based on spatial and material settings on continuum mechanics. Part 2: classification and applications. Comput Methods Appl Mech Eng 193: 4223-4245 (Pubitemid 39182521)
3. Bonet J, Wood R (1997) Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, London. ISBN 0-521-57272-X
4. COMSOL AB (2008) COMSOL multiphysics user guide and model library, version 3.5a, 3.5.0.606. COMSOL AB, Sweden
5. Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New York. ISBN 0-417-49666-9
6. Dziuk G, Elliot C (2007) Finite elements on evolving surfaces. IMA J Numer Anal 27: 262-292
7. Eggleton C, Stebe K (1998) An adsorption-desorption-controlled surfactant on a deforming droplet. J Colloid Interface Sci 208: 68-80 (Pubitemid 28563532)
8. Feigl K, Megias-Alguacil D, Fischer P, Windhab E (2007) Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants. Chem Eng Sci 62: 3242-3258 (Pubitemid 46726266)
9. Gadala M, Wang J (1998) A practical procedure for mesh motion in arbitrary Lagrangian-Eulerian method. Eng Comput 14: 223-234 (Pubitemid 128482860)
10. James J, Lowengrub J (2004) A surfactant-conserving volume-offluid method for interfacial flows with insoluble surfactant. J Comput Phys 201: 685-722 (Pubitemid 39518803)
11. Kardestuncer H (1987) Finite element handbook. McGraw-Hill, New York. ISBN 0-07-033305-X
12. Knobbe E (2004) A FEM-ALE approach for continuous domains with arbitrary moving boundaries. In: ECCOMAS 2004. JyvSskylS, Finland, pp 1-20
13. Knupp P (1999) Winslow smoothing on unstructured twodimensional meshes. Eng Comput 15: 263-268
14. Kuhl E, Askes H, Steinman P (2004) An ale formulation based on spatial and material settings on continuum mechanics. Part 1: generic hyperelastic formulation. Comput Methods Appl Mech Eng 193: 4207-4222 (Pubitemid 39182520)
15. Milliken W, Stone H, Leal L (1993) The effect of surfactant on the transient motion of newtonian drops. Phys Fluids A 5(1): 69-79
16. Schlesinger M, Paunovic M (2000) Modern electroplating, 4th edn. Wiley, New York. ISBN 0-471-16824-6
17. Stoker C (1999) Developments of the arbitrary lagrangian-eulerian method in non-linear solid mechanics. applications to forming processes. Ph.D. thesis, Doctoral thesis. ISBN 90-36512646
18. Stone H (1990) A simple derivation of the time-dependent convective- diffusion equation for surfactant transport along a deforming interface. Phys Fluids A 2(1): 111-112
19. Tenno R, Pohjoranta A (2008) An ale model for prediction and control of the microvia fill process with two additives. J Electrochem Soc 155(5): D383-D388 (Pubitemid 351502381)
20. Tenno R, Pohjoranta A (2009) Microvia fill process control. Int J Control 82(5): 883-893
21. Waxman A (1984) Dynamics of couple-stress fluid membrane. Stud Appl Math/Mass Inst Technol 70(1): 63-86
22. Wills B, Napier-Munn T (2006) Wills' mineral processing technology, 7th edn. Elsevier, Butterworth-Heinemann. ISBN 978-0- 750-64450-1
23. Winslow A (1997) Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh. J Comput Phys 135: 128-138 (reprinted, original version published 1966) (Pubitemid 127175583)
24. Wong H, Rumschitzki D, Maldarelli C (1996) On the surfactant mass balance at a deforming fluid interface. Phys Fluids A 8(11): 3203-3204
25. Yang X, James A (2007) An arbitrary Lagrange-Eulerian (ALE) method for interfacial flows with insoluble surfactants. Fluid Dyn Mater Process 3(1): 65-95 (Pubitemid 46844610)
26. Yin J, Theodosiu C (2008) Constrained mesh optimization on boundary. Eng Comput 24: 231-240