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Oscillatory pipe flows of a yield-stress fluid

Published online by Cambridge University Press:  10 June 2010

YONG SUNG PARK  and
PHILIP L.-F. LIU
YONG SUNG PARK*
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
PHILIP L.-F. LIU
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taoyuan 320, Taiwan
*
†Email address for correspondence: yp54@cornell.edu
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Abstract

Oscillatory pipe flows of aqueous Carbopol solutions are investigated both experimentally and analytically. Using the PIV technique, the velocity profiles are measured and compared with the numerical solutions based on an elasto-viscoplastic rheological model, in which an elastic spring is serially connected to a regularized Bingham viscoplastic model. The rheological parameters, such as shear modulus of elasticity, yield stress and viscosity, are estimated from steady-shear measurements. Good agreement between the experiments and the model results is observed. It is apparent that the elasticity plays an important role in the unsteady flows of the soft yield-stress fluid studied herein.

JFM classification

Geophysical and Geological Flows: Coastal engineering Non-Newtonian Flows: Plastic materials Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 211 - 228
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Balmforth, N. J. & Craster, R. V. 2001 Geophysical aspects of non-Newtonian fluid mechanics. In Geomorphological Fluid Mechanics (ed. Tyvand, P. A. & Provenzale, A.), pp. 34–51. Springer.CrossRefGoogle Scholar
Balmforth, N. J., Forterre, Y. & Pouliquen, O. 2009 The viscoplastic Stokes layer. J. Non-Newton. Fluid Mech. 158, 46–53.CrossRefGoogle Scholar
Bird, R. B., Dai, G. C. & Yarusso, B. J. 1983 The rheology and flow of viscoplastic materials. Rev. Chem. Engng 1, 1–70.CrossRefGoogle Scholar
Chan, I.-C. & Liu, P. L.-F. 2009 Responses of Bingham-plastic muddy seabed to a surface solitary wave. J. Fluid Mech. 618, 155–180.CrossRefGoogle Scholar
Cheddadi, I., Saramito, P., Raufaste, C., Marmottant, P. & Graner, F. 2008 Numerical modelling of foam Couette flows. Eur. Phys. J. E 27, 123–133.CrossRefGoogle ScholarPubMed
Coussot, P., Tocquer, L., Lanos, C. & Ovarlez, G. 2009 Macroscopic vs. local rheology of yield stress fluids. J. Non-Newton. Fluid Mech. 158, 85–90.CrossRefGoogle Scholar
Dalrymple, R. A. & Liu, P. L.-F. 1978 Waves over soft muds: a two-layer model. J. Phys. Oceanogr. 8, 1121–1131.2.0.CO;2>CrossRefGoogle Scholar
Fan, Y., Phan-Thien, N. & Tanner, R. I. 2001 Tangential flow and advective mixing of viscoplastic fluids between eccentric cylinders. J. Fluid Mech. 431, 65–89.CrossRefGoogle Scholar
Foda, M. A. 1989 Sideband damping of water waves over a soft bed. J. Fluid Mech. 201, 189–201.CrossRefGoogle Scholar
Gade, H. G. 1958 Effects of a nonrigid, impermeable bottom on plane surface waves in shallow water. J. Mar. Res. 16, 61–82.Google Scholar
Jain, M. & Mehta, A. J. 2009 Role of basic rheological models in determination of wave attenuation over muddy seabeds. Cont. Shelf Res. 29, 642–651.CrossRefGoogle Scholar
Joseph, D. D. 1990 Fluid Dynamics of Viscoelastic Liquids. Springer.CrossRefGoogle Scholar
Liu, P. L.-F. & Chan, I.-C. 2007 On long wave propagation over a fluid-mud seabed. J. Fluid Mech. 579, 467–480.CrossRefGoogle Scholar
Luu, L.-H. & Forterre, Y. 2004 Drop impact of yield-stress fluids. J. Fluid Mech. 632, 301–327.CrossRefGoogle Scholar
MacPherson, H. 1980 The attenuation of water waves over a non-rigid bed. J. Fluid Mech. 97, 721–742.CrossRefGoogle Scholar
Mahaut, F., Chateau, X., Coussot, P. & Ovarlez, G. 2008 Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 52, 287–313.CrossRefGoogle Scholar
Manos, T., Marinakis, G. & Tsangaris, S. 2006 Oscillating viscoelastic flow in a curved duct: exact analytical and numerical solution. J. Non-Newton. Fluid Mech. 135, 8–15.CrossRefGoogle Scholar
McAnally, W. H., Friedrichs, C., Hamilton, D., Hayter, E., Shrestha, P., Rodriguez, H., Sheremet, A. & Teeter, A. 2007 a Management of fluid mud in estuaries, bays and lakes. Part 1. Present state of understanding on character and behavior. ASCE Task Committee on Management of Fluid Mud. J. Hydraul. Engng 133, 9–22.CrossRefGoogle Scholar
McAnally, W. H., Friedrichs, C., Hamilton, D., Hayter, E., Shrestha, P., Rodriguez, H., Sheremet, A. & Teeter, A. 2007 b Management of fluid mud in estuaries, bays and lakes. Part 2. Measurement, modeling and management. ASCE Task Committee on Management of Fluid Mud. J. Hydraul. Engng 133, 23–38.CrossRefGoogle Scholar
Mei, C. C., Krotov, M., Huang, Z & Aode, H. 2010 Short and long waves over a muddy seabed. J. Fluid Mech. 643, 33–58.CrossRefGoogle Scholar
Mei, C. C. & Liu, K.-F. 1987 A Bingham-plastic model for a muddy seabed under long waves. J. Geophys. Res. 92, 14581–14594.CrossRefGoogle Scholar
Minirani, S. & Kurup, P. G. 2007 Energy attenuation of sea surface waves through generation of interface waves on viscoelastic bottom as in the mud banks, SW coast of India. J. Indian Geophys. Union 11, 143–146.Google Scholar
Papanastasiou, T. C. 1987 Flows of materials with yield. J. Rheol. 31, 385–404.CrossRefGoogle Scholar
Park, Y. S. 2009 Seabed dynamics and breaking waves. PhD dissertation, Cornell University.Google Scholar
Park, Y. S., Liu, P. L.-F. & Clark, S. J. 2008 Viscous flows in a muddy seabed induced by a solitary wave. J. Fluid Mech. 598, 383–392.CrossRefGoogle Scholar
Piau, J. M. 2007 Carbopol gels: elastoviscoplastic and slippery glasses made of individual swollen sponges: meso- and macroscopic properties, constitutive equations and scaling laws. J. Non-Newton. Fluid Mech. 144, 1–29.CrossRefGoogle Scholar
Putz, A. M. V. & Burghelea, T. I. 2009 The solid–fluid transition in a yield stress shear thinning physical gel. Rheol. Acta 48, 673–689.CrossRefGoogle Scholar
Saramito, P. 2007 A new constitutive equation for elastoviscoplastic fluid flows. J. Non-Newton. Fluid Mech. 145, 1–14.CrossRefGoogle Scholar
Saramito, P. 2009 A new elastoviscoplastic model based on the Herschel–Bulkley viscoplastic model. J. Non-Newton. Fluid Mech. 158, 154–161.CrossRefGoogle Scholar
Tanner, R. I. & Walters, K. 1998 Rheology: An Historical Perspective. Elsevier.Google Scholar
Wen, J. & Liu, P. L.-F. 1995 Mass transport in water waves over an elastic bed. Proc. R. Soc. A 450, 371–390.Google Scholar