A mathematical formulation of the boundary integral equations for a compressible stokes flow

Computational and Applied Mathematics

Volumn 22, Issue 1, 2003, Pages 53-73

  Cunha, Francisco Ricardo ^a   De Sousa, Aldo João ^a   Loewenberg, Michael ^b  

^a UNIVERSITY OF BRASILIA   (Brazil)

^b Yale University   (United States)

Author keywords

Boundary integral; Compressible drops; Densification; Emulsion

Indexed keywords

BOUNDARY INTEGRAL EQUATIONS; CLASSIFICATION (OF INFORMATION); DROPS; EMULSIFICATION;

BOUNDARY INTEGRAL FORMULATIONS; BOUNDARY INTEGRAL METHODS; BOUNDARY INTEGRALS; COMPRESSIBLE DROP; DENSIFICATIONS; DISCRETIZATIONS; FLUID VELOCITIES; HYDRODYNAMIC POTENTIALS; MATHEMATICAL FORMULATION; STOKES FLOWS;

VISCOUS FLOW;

EID: 33846150955     PISSN: 22383603     EISSN: 18070302     Source Type: Journal    
DOI: 10.1590/s1807-03022003000100004     Document Type: Article

References (18)

1. G.K. Youngren and A. Acrivos, Stokes flow past a particle of arbitrary shape: A numerical method of solution, J. Fluid Mech., 69 (1975), pp. 377–403.
2. C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, Cambridge, (1992).
3. O.A. Ladyzheskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach, NewYork, (1969).
4. J.M. Rallison and A. Acrivos, A numerical study of the deformation and burst of a viscous drop in an extensional flow, J. Fluid Mech., 89 (1978), pp. 191–200.
5. J.M. Rallison, The deformation of small viscous drops and bubbles in shear flows, Ann. Rev. Fluid Mech., 16 (1984), pp. 45–66.
6. H.A. Stone, Dynamics of drop deformation and breakup in viscous fluids, Ann. Rev. Fluid Mech., 26 (1994), pp. 65–102.
7. M. Loewenberg and E.J. Hinch, Numerical simulations of a concentrated emulsion in shear flow, J. Fluid Mech., 321 (1996), pp. 395-419.
8. F.R. Cunha, M. Neimer, J. Blawzdziewicz and M. Loewenberg, Rheology of an Emulsion in Shear Flow, In: Proceedings of American Institute of Chemical Engineers, Annual Meeting, Fundamental Research in Fluid Mechanics: Particulate & Multiphase Flow II., paper 124j., October (1999).
9. F.R. Cunha and M. Loewenberg, Emulsion Drops in Oscillatory Shear Flow In: 52ndAmerican Physical Society, Annual Meeting of the Division of Fluid Dynamics, paper GK. 08, session: suspension I, November (1999).
10. V. Cristini, J. Blawzdziewicz and M. Loewenberg, Drop breakup in three-dimensional viscous flows, Phys. Fluids, 10 (1998), pp. 1781–1783.
11. G.L. Leal, Laminar flow and convective transport processes, Butterworth-Heinemann, Boston, (1992).
12. L.E. Scriven, Dynamics of fluid interface, Chem. Eng. Science, 12 (1960), pp. 98-108.
13. J. Happel and H. Brenner, Low Reynolds number hydrodynamics, Prentice Hall, (1965).
14. G.K. Batchelor, An introduction to Fluid Dynamics, Cambridge University Press, Cambridge, (1967).
15. T.G. Mason, M.D. Lacasse, S.G. Grest, D. Levine, J. Bibette and D.A. Weitz, Osmotic pressure and viscoelasticity shear moduli of concentrated emulsions, Physical Review E, 56 (1997), pp. 3150.
16. C.W.J. Beenakker, Ewald sum of Rotne-Prager tensor, J. Chem. Phys., 85 (1986), pp. 1581–1582.
17. M.P. Almeida and F.R. Cunha, Numerical simulation of non-colloidal deformable particles at low Reynolds numbers, In: Proceedings, 7th Brazilian Congress of Engineering and Thermal Sciences, 1 (1998), pp. 963–970.
18. A.Z. Zinchenko, M.A. Rother and R.H. Davis, A novel boundary-integral algorithm for viscous interaction of deformable drops, Phys. Fluids, 9 (1997), pp. 1493–1511.