Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer

Journal of Non-Newtonian Fluid Mechanics

Volumn 177-178, Issue , 2012, Pages 46-53

  Di Federico, Vittorio ^a   Archetti, Renata ^a   Longo, Sandro ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

Gravity current; Porous medium; Power law; Self similar solution

Indexed keywords

ANALYTICAL APPROXIMATION; CLOSED FORM SOLUTIONS; DARCY'S LAW; DIFFERENTIAL PROBLEMS; EQUATION OF MOTION; FLOW BEHAVIOR INDEX; FLOW BEHAVIORS; FLOW LAW; GRAVITY CURRENTS; IMPERMEABLE BOUNDARY; MASS BALANCE EQUATIONS; NEWTONIAN FLUIDS; NON-LINEARITY; NON-NEWTONIAN GRAVITY; NUMERICAL INTEGRATIONS; NUMERICAL SCHEME; POINT SOURCES; POROUS LAYERS; POROUS MEDIUM; POWER LAW FLUID; POWER-LAW; RHEOLOGICAL EQUATIONS; SELF-SIMILAR SOLUTION; SIMILARITY SOLUTION; TWO-DIMENSIONAL GRAVITY; VOLUME OF FLUIDS;

CONTROL NONLINEARITIES; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FLOW FIELDS; FLUID DYNAMICS; GRAVITY WAVES; NON NEWTONIAN FLOW; NONLINEAR EQUATIONS; POROUS MATERIALS; TWO DIMENSIONAL;

GRAVITATION;

EID: 84861000844     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2012.04.003     Document Type: Article

References (52)

1. Woods A.W. Liquid and vapor flow in superheated rock. Ann. Rev. Fl. Mech. 1999, 31:171-199.
2. King S.E., Woods A.W. Dipole solutions for viscous gravity currents: theory and experiments. J. Fluid Mech. 2003, 483:91-109.
3. Anderson D.M., McLaughlin R.M., Miller C.T. The averaging of gravity currents in porous media. Phys. Fluids 2003, 15(10):2810-2829.
4. Bickle M., Chadwick A., Huppert H.E., Hallworth M., Lyle S. Modelling carbon dioxide accumulation at Sleipner: implications for underground carbon storage. Earth Planet. Sci. Lett. 2007, 255(1-2):164-176.
5. Hesse M.A., Orr F.M., Tchelepi H.A. Gravity currents with residual trapping. J. Fluid Mech. 2008, 611:35-60.
6. Huppert H.E., Woods A.W. Gravity-driven flows in porous layers. J. Fluid Mech. 1995, 292:55-69.
7. Lyle S., Huppert H.E., Hallworth M., Bickle M., Chadwick A. Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 2005, 543:293-302.
8. Vella D., Huppert H.E. Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 2006, 555:353-362.
9. Takagi D., Huppert H.E. Viscous gravity currents inside confining channels and fractures. Phys. Fluids 2008, 20:023104.
10. Golding M., Huppert H.E. The effect of confining impermeable boundaries on gravity currents in a porous medium. J. Fluid Mech. 2010, 649:1-17.
11. Huppert H.E. The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 1982, 121:43-58.
12. Huppert H.E. The intrusion of fluid mechanics into geology. J. Fluid Mech. 1986, 173:557-594.
13. Simpson J.E. Gravity currents in the laboratory, atmosphere, and ocean. Ann. Rev. Fl. Mech. 1982, 14:213-234.
14. Simpson J.E. Gravity Currents: In the Environment and the Laboratory 1997, Cambridge University Press. second ed.
15. Ungarish M. An Introduction to Gravity Currents and Intrusions 2010, CRC Press.
16. Wu Y.-S., Pruess K. Flow of non-Newtonian fluids in porous media. Adv. Por. Med. 1996, 3:87-184.
17. Chhabra R.P., Richardson J.F. Non-Newtonian Flow in the Process Industries: Fundamentals and Engineering Applications 1999, Butterworth, Heinemann.
18. Sochi T. Flow of non-Newtonian fluids in porous media. J. Polym. Sci.: Part B: Polym. Phys. 2010, 48:2437-2767.
19. Wang S., Huang Y., Civan F. Experimental and theoretical investigation of the Zaoyuan field heavy oil flow through porous media. J. Pet. Sci. Eng. 2006, 50:83-101.
20. Babadagli T. Development of mature oil fields - a review. J. Pet. Sci. Eng. 2007, 57(3-4):221-246.
21. Nazar M.F., Shah S.S., Khosa M.A. Microemulsions in enhanced oil recovery: a review. Pet. Sci.Technol. 2011, 29(13):1353-1365.
22. Vallero D.A., Peirce J. Engineering the Risks of Hazardous Wastes 2003, Butterworth, Heinemann.
23. Yan Y.L., Deng Q., He F., Zhang X.Q., Liu Y.-P. Remediation of DNAPL-contaminated aquifers using density modification method with colloidal liquid aphrons. Colloids Surfaces A: Physicochem. Eng. Aspects 2011, 385(1-3):219-228.
24. Tosco T., Sethi R. Transport of non-Newtonian suspensions of highly concentrated micro- and nanoscale iron particles in porous media: a modeling approach. Environ. Sci. Technol. 2010, 44:9062-9068.
25. Bataller R.C. On unsteady gravity flows of a power-law fluid through a porous medium. Appl. Math. Comput. 2008, 196:356-362.
26. Pascal J.P., Pascal H. Similarity solutions to gravity flows of non-Newtonian fluids through porous media. Int. J. Non-Linear Mech. 1993, 28(2):157-167.
27. Saffman P.G., Taylor G.I. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. Roy. Soc. London Set. A 1958, 245:312-329.
28. Homsy G.M. Viscous fingering in porous media. Ann. Rev. Fluid Mech. 1987, 19:271-311.
29. Lindner A., Bonn D., Corvera Poiré E., Ben Amar M., Meunier J. Viscous fingering in non-Newtonian fluids. J. Fluid Mech. 2002, 469:237-256.
30. Mora S., Manna M. Saffman-Taylor instability for generalized Newtonian fluids. Phys. Rev. E 2010, 80:016308.
31. Bird R.B., Stewart W.E., Lightfoot E.N. Transport Phenomena 1960, Wiley.
32. Cristopher R.H., Middleman S. Power-law flow through a packed tube. Ind. Eng. Chem. Fundam. 1965, 4(4):422-427.
33. Savins J.G. Non-Newtonian flow through porous media. Ind. Eng. Chem. Fundam. 1969, 6(10):18-47.
34. D. Teeuw, F.T. Hesselink, Power-law flow and hydrodynamic behavior of biopolymer solutions in porous media, Soc. Pet. Eng. Paper Number SPE 8982, Fifth International Symposium on Oilfield and Geothermal Chemistry, Stanford, California, 1980, pp. 73-86.
35. Pascal H. Nonsteady flow of non-Newtonian fluids through porous media. Int. J. Eng. Sci. 1983, 21(3):199-210.
36. Velten K., Lutz A., Friedrich K. Quantitative characterization of porous materials in polymer processing. Compos. Sci. Technol. 1999, 59:495-504.
37. Kim G.B., Hyun J.M. Buoyant convection of a power-law fluid in an enclosure filled with heat-generating porous media. Numer. Heat Transfer, Part A: Appl. 2004, 45(6):569-582.
38. Vajravelu K., Sreenadh S., Viswanatha Reddy G. Helical flow of a power-law fluid in a thin annulus with permeable walls. Int. J. Non-Linear Mech. 2006, 41:761-765.
39. Degan G., Akowanou K., Awanou N.C. Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium. Int. J. Heat Mass Transfer 2007, 50:4629-4639.
40. Larsson R.G. Derivation of generalized Darcy equations for creeping flow in porous media. Ind. Eng. Chem. Fundam. 1981, 20:132-138.
41. Shenoy A.V. Non-Newtonian fluid heat transfer in porous media. Adv. Heat Transfer 1995, 24:102-190.
42. Nield D.A., Bejan A. Convection in Porous Media 2006, Springer. third ed.
43. Lundstrom T.S., Sundlof H., Holmberg J.A. Modeling of power-law fluid flow through fiber beds. J. Compos. Mater. 2006, 40(3):283-296.
44. Sadiq I.M.R., Usha R. Effect of permeability on the instability of a non-Newtonian film down a porous inclined plane. J. Non-Newton. Fluid Mech. 2010, 165:1171-1188.
45. Barletta A., Nield D.A. Linear instability of the horizontal throughflow in a plane porous layer saturated by a power-law fluid. Phys. Fluids 2011, 23:013102.
46. Vakilha M., Manzari M.T. Modelling of power-law fluid flow through porous media using smoothed particle hydrodynamics. Transp. Por. Med. 2008, 74:331-346.
47. Balhoff M.T., Thompson K.E. A macroscopic model for shear-thinning flow in packed beds based on network modeling. Chem. Eng. Sci. 2006, 61:698-719.
48. Fadili A., Tardy P.M.J., Pearson A. A 3D filtration law for power-law fluids in heterogeneous porous media. J. Non-Newton. Fluid Mech. 2002, 106:121-146.
49. Di Federico V., Pinelli M., Ugarelli R. Estimates of effective permeability for non-Newtonian fluid flow in randomly heterogeneous porous media. Stoch. Environ. Res. Risk Assess. 2010, 24:55-69.
50. Di Federico V., Cintoli S., Malavasi S. Viscous spreading of non-Newtonian gravity currents on a plane. Meccanica 2006, 41(2):207-217.
51. Li L., Lockington D.A., Parlange M.B., Stagnitti F., Jeng D.S., Selker J.S., Telyakovskiy A.S., Barry D.A., Parlange J.Y. Similarity solution of axisymmetric flow in porous media. Adv. Water Resour. 2005, 28(10):1076-1082.
52. Bender C.M., Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers 2008, McGraw-Hill.