Creeping flow around particles in a Bingham fluid

Journal of Non-Newtonian Fluid Mechanics

Volumn 165, Issue 5-6, 2010, Pages 263-280

  Putz, A ^a   Frigaard, I A ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Augmented Lagrangian method; Creeping flow; Plug regions; Visco plastic fluids

Indexed keywords

AUGMENTED LAGRANGIAN METHODS; BINGHAM FLUID; CREEPING FLOWS; ELLIPTICAL CROSS-SECTION; INFINITE CYLINDERS; PLASTIC FLUIDS; PLASTIC SOLIDS; PROPERTIES OF SOLUTIONS; SOLUTION APPROACH; STATIC STABILITY;

FLUIDS; LAGRANGE MULTIPLIERS; SAFETY FACTOR; VISCOPLASTICITY;

PLASTICS;

EID: 77049124221     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2010.01.001     Document Type: Article

References (61)

1. Andres U.T. Equilibrium and motion of spheres in a viscoplastic liquid. Sov. Phys. Dokl. (U.S.A.) 5 (1961) 723
2. du Plessis M., and Ansley R. Settling parameters in solids pipelining. J. Pipeline Div. (ASCE) 93 (1967) 1
3. Ansley R.W., and Smith T.N. Motion of spherical particles in a Bingham plastic. AIChE J. 13 (1967) 1193
4. Whitmore R. Drag forces in Bingham plastics. Proc. 5th Int. Cong. Rheol (1969) 472
5. W. Prager, On slow visco-plastic flow, in: Studies in Mathematics and Mechanics presented to Richard von Mises, Studies in Mathematics and Mechanics, Academic Press Inc., Publishers, 1954, pp. 208-216.
6. Mosolov P.P., and Miasnikov V.P. Variational methods in the theory of the fluidity of a viscous plastic medium. J. Appl. Math. Mech. 29 3 (1965) 545-577
7. Mosolov P.P., and Miasnikov V.P. On stagnant flow regions of a viscous-plastic medium in pipes. J. Appl. Math. Mech. 30 4 (1966) 841-854
8. Mosolov P.P., and Miasnikov V.P. Asymptotic theory of rigid plastic shells. J. Appl. Math. Mech. 41 3 (1977) 550-566
9. Mosolov P.P. On certain mathematical questions of the theory of incompressible viscoplastic media. J. Appl. Math. Mech. 42 4 (1978) 787-799
10. Duvaut G., and Lions J.L. Inequalities in Mechanics and Physics (1976), Springer-Verlag, New York
11. Glowinski R. Numerical Methods for Nonlinear Variational Problems (1983), Springer-Verlag, New York
12. Adachi K., and Yoshioka N. On creeping flow of a viscoplastic fluid past a circular cylinder. Chem. Eng. Sci. 28 (1973) 215-226
13. Yoshioka N., and Adachi K. On variational principles for a non-Newtonian fluid. J. Chem. Eng. Jpn. 4 (1971) 217-220
14. Yoshioka N., and Adachi K. Applications of the extremum principles for non-Newtonian fluids. J. Chem. Eng. Jpn. 4 (1971) 221-226
15. Beris A.N., Tsamopoulos J.A., Armstrong R.C., and Brown R. Creeping motion of a sphere through a Bingham plastic. J. Fluid Mech. 158 (1985) 219-244
16. Blackery J., and Mitsoulis E. Creeping motion of a sphere in tubes filled with a Bingham plastic material. J. Non-Newton. Fluid Mech. 70 (1997) 59-77
17. Beaulne M., and Mitsoulis E. Creeping motion of a sphere in tubes filled with Herschel-Bulkley fluids. J. Non-Newton. Fluid Mech. 72 1 (1997) 55-71
18. Liu B.T., Muller S.J., and Denn M.M. Convergence of a regularization method for creeping flow of a Bingham material about a rigid sphere. J. Non-Newton. Fluid Mech. 102 (2002) 179-191
19. Deglo de Besses B., Magnin A., and Jay P. Sphere drag in a viscoplastic fluid. AIChE J. 50 10 (2004) 2627-2629
20. Zisis T.H., and Mitsoulis E. Viscoplastic flow around a cylinder kept between parallel plates. J. Non-Newton. Fluid Mech. 105 (2002) 1-20
21. Mosolov P.P., and Miasnikov V.P. Boundary layer in the problem of longitudinal motion of a cylinder in a viscoplastic medium. J. Appl. Math. Mech. 38 4 (1974) 634-644
22. Roquet N., and Saramito P. An adaptive finite element method for Bingham fluid flows around a cylinder. Comput. Methods Appl. Mech. Eng. 192 31-32 (2003) 3317-3341
23. Deglo de Besses B., Magnin A., and Jay P. Viscoplastic flow around a cylinder in an infinite medium. J. Non-Newton. Fluid Mech. 115 (2003) 27-49
24. Mitsoulis E. On creeping drag flow of a viscoplastic fluid past a circular cylinder: wall effects. Chem. Eng. Sci. 59 (2004) 789-800
25. Tokpavi D.L., Magnin A., and Jay P. Very slow flow of Bingham viscoplastic fluid around a circular cylinder. J. Non-Newton. Fluid Mech. 154 (2008) 65-76
26. Randolph M.F., and Houlsby G.T. The limiting pressure on a circular pile loaded laterally in cohesive soil. Geotechnique 34 4 (1984) 613-623
27. Liu B.T., Muller S.J., and Denn M. Interactions of two rigid spheres translating collinearly in creeping flow in a Bingham material. J. Non-Newton. Fluid Mech. 113 (2003) 49-67
28. Tokpavi D.L., Jay P., and Magnin A. Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid. J. Non-Newton. Fluid Mech. 157 3 (2009) 175-187
29. Jie P., and Zhu K.-Q. Drag force of interacting coaxial spheres in viscoplastic fluids. J. Non-Newton. Fluid Mech. 135 (2006) 83-91
30. Dean E.J., Glowinski R., and Pan T.W. A fictitious domain method for the numerical simulation of particulate flow for Bingham visco-plastic. In: Heikkola E., Kuznetzov Y., and Neittaanmaki P. (Eds). Numerical Methods for Scientific Computing: Variational Problems and Applications (2003), CIMNE, Barcelona, Spain 11-19
31. Wachs A., and Yue Z. A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J. Non-Newton. Fluid Mech. 145 2-3 (2007) 78-91
32. Atapattu D.D., Chhabra R.P., and Uhlherr P.H.T. Wall effect for spheres falling at small Reynolds number in a viscoplastic medium. J. Non-Newton. Fluid Mech. 38 1 (1990) 31-42
33. Atapattu D.D., Chhabra R.P., and Uhlherr P.H.T. Creeping sphere motion in Herschel-Bulkey fluids: Flow field and drag. J. Non-Newton. Fluid Mech. 59 (1995) 245-265
34. Hariharaputhiran M., Subramanian R.S., Campell G.A., and Chhabra R.P. Settling of spheres in a viscoplastic fluid. J. Non-Newton. Fluid Mech. 79 (1998) 87-97
35. Jossic J., and Magnin A. Drag and stability of objects in a yield stress fluid. AIChE J. 47 (2001) 2666-2672
36. Merkak O., Jossic L., and Magnin A. Spheres and interactions between spheres moving at very low velocities in a yield stress fluid. J. Non-Newton. Fluid Mech. 133 (2006) 99-108
37. Tabuteau H., Coussot P., and de Bruyn J.R. Drag force on a sphere in steady motion through a yield-stress fluid. J. Rheol. 51 1 (2007) 125-137
38. Tabuteau H., Sikorski D., and de Bruyn J.R. Shear waves and shocks in soft solids. Phys. Rev. E (3) 75 1 (2007) 012201
39. Putz A.M.V., Burghelea T.I., Frigaard I.A., and Martinez D.M. Settling of an isolated spherical particle in a yield stress shear thinning fluid. Phys. Fluids 20 3 (2008) 033102 doi:10.1063/1.2883937
40. Chafe N.P., and de Bruyn J.R. Drag and relaxation in a Bentonite clay suspension. J. Non-Newton. Fluid Mech. 131 (2005) 44-52
41. B. Gueslin, L. Talini, B. Herzhaft, Y. Peysson, C. Allain, Flow induced by a sphere settling in an aging yield-stress fluid, Phys. Fluids 18 (2006).
42. B. Gueslin, L. Talini, B. Herzhaft, Y. Peysson, C. Allain, Aggregation behavior of two spheres falling through an aging fluid, Phys. Rev. E (3) 74 (2006).
43. Oldroyd J.G. A rational formulation of the equations of plastic flow for a Bingham solid. Proc. Cambridge Philos. Soc. 43 1 (1947) 100-105
44. Oldroyd J.G. Two-dimensional plastic flow of a Bingham solid. A plastic boundary-layer theory for slow motion. Proc. Cambridge Philos. Soc. 43 3 (1947) 383-395
45. Aris R. Vectors, Tensors And The Basic Equations Of Fluid Mechanics (1962), Dover
46. I. Ekeland, R. Temam, Convex Analysis and Variational Problems, no. 28 in Classics in Applied Mathematics, SIAM, 1999.
47. Dubash N., and Frigaard I.A. Conditions for static bubbles in viscoplastic fluids. Phys. Fluids 16 12 (2004) 4319-4330
48. Dubash N., and Frigaard I.A. Propagation and stopping of air bubbles in Carbopol solutions. J. Non-Newton. Fluid Mech. 142 1-3 (2007) 123-134
49. Hill R. The Mathematical Theory of Plasticity, Oxford Classic Texts (1950), Oxford University Press
50. Temam R., and Strang G. Functions of bounded deformation. Arch. Rational Mech. Anal. (1980) 7-21
51. Tsamopoulos J., Dimakopoulos Y., Chatzidai N., Karapetsas G., and Pavlidis M. Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for bubble entrapment. J. Fluid Mech. 601 (2008) 123-164
52. Glowinski R., Pan T.W., Hesla T.I., Joseph D.D., and Periaux J. A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: Application to particulate flow. Comput. Methods Appl. Mech. Eng. 184 (2000) 241-267
53. Hu H.H., Patankar N.A., and Zhu M.Y. Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. (2001) 427-462
54. Glowinski R., and Le Tallec P. Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics, Studies in Applied Mathematics (1989), SIAM
55. R. Glowinski, J.L. Lions, R. Tremolieres, Analyse Numérique des inéquations variationelles, vol. 2, Dunod, Paris, 1976.
56. Roquet N., and Saramito P. Stick-slip transition capturing by using an adaptive finite element method. M2AN Math. Model. Numer. Anal. 38 2 (2004) 249-260
57. A.M.V. Putz, I.A. Frigaard, D.M. Martinez, On the lubrication paradox and the use of regularisation methods for lubrication flows, J. Non-Newton. Fluid Mech. (available online 8 July 2009).
58. Saramito P., and Roquet N. An adaptive finite element method for viscoplastic fluid flow in pipes. Comput. Methods Appl. Mech. Eng. 190 40-41 (2001) 5391-5412
59. H. Borouchaki, L. George, P.F. Hecht, P. Laug, E. Saltel, Delaunay mesh generation governed by metric specifications. I. Algorithms, Finite Elem. Anal. Des. 25 (1-2) (1997) 61-83 (adaptive meshing, Part 1).
60. Castro-Díaz M.J., Hecht F., Mohammadi B., and Pironneau O. Anisotropic unstructured mesh adaption for flow simulations. Int. J. Numer. Methods Fluids 25 4 (1997) 475-491
61. Faxen O.H. Forces exerted on a rigid cylinder in a viscous fluid between two parallel fixed planes. Proc. R. Swed. Acad. Eng. Sci. 187 (1946) 1-13