Research Papers: Fundamental Issues and Canonical Flows

Slipping of a Viscoplastic Fluid Flowing on a Circular Cylinder

[+] Author and Article Information
Hamdullah Ozogul

Laboratoire Rhéologie et Procédés,
UMR 5520,
Université Grenoble Alpes;
LRP, Grenoble F-38000, France

Pascal Jay

Laboratoire Rhéologie et Procédés,
UMR 5520,
Université Grenoble Alpes;
LRP, Grenoble F-38000, France
e-mail: pascal.jay@ujf-grenoble.fr

Albert Magnin

Laboratoire Rhéologie et Procédés,
UMR 5520,
Université Grenoble Alpes;
LRP, Grenoble F-38000, France

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 6, 2014; final manuscript received January 28, 2015; published online March 19, 2015. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 137(7), 071201 (Jul 01, 2015) (9 pages) Paper No: FE-14-1293; doi: 10.1115/1.4029760 History: Received June 06, 2014; Revised January 28, 2015; Online March 19, 2015

The slipping effect during creeping flow of viscoplastic fluids around a circular cylinder has been investigated via numerical simulations. For the bulk behavior of the fluid, a Herschel–Bulkley law is considered. For the parietal behavior, an original and recent slip law based on an elastohydrodynamic lubrication model defined with a physical approach has been implemented. In particular, this law represents the behavior of Carbopol gels, which are commonly used during experimental studies on yield stress fluid mechanics and in industry. This law has two parameters that control the kinematic conditions at the fluid–structure interface. Variations in the plastic drag coefficient are given as a function of these parameters. It has been shown in particular the decreasing of the drag coefficient when there is slipping at the fluid–structure interface. The kinematic field has been analyzed and the evolution of rigid zones is illustrated. Results are provided for different slipping conditions ranging from the no-slip to the perfect-slip (PS) case. The sheared zone becomes smaller so the flow is more and more confined due to the slip, which induces modifications on the rigid zones. Some of the results are compared with existing asymptotic plastic drag coefficients and experimental data.

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Balmforth, N. J., Frigaard, I. A., and Ovarlez, G., 2014, “Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics,” Annu. Rev. Fluid Mech., 46(1), pp. 121–146. [CrossRef]
Daprà, I., and Scarpi, G., 2011, “Pulsatile Poiseuille Flow of a Viscoplastic Fluid in the Gap Between Coaxial Cylinders,” ASME J. Fluids Eng., 133(8), p. 081203. [CrossRef]
Kalombo, J. J. N., Haldenwang, R., Chhabra, R. P., and Fester, V. G., 2014, “Centrifugal Pump Derating for Non-Newtonian Slurries,” ASME J. Fluids Eng., 136(3), p. 031302. [CrossRef]
Barnes, H. A., 1999, “The Yield Stress—A Review or ‘παντα ρει’—Everything Flows?,” J. Non-Newtonian Fluid Mech., 81(1–2), pp. 133–178. [CrossRef]
Barnes, H. A., 1995, “A Review of the Slip (Wall Depletion) of Polymer Solutions, Emulsions and Particle Suspensions in Viscometers: Its Cause, Character, and Cure,” J. Non-Newtonian Fluid Mech., 56(3), pp. 221–251. [CrossRef]
Sochi, T., 2011, “Slip at Fluid–Solid Interface,” Polym. Rev., 51(4), pp. 309–340. [CrossRef]
Sunarso, A., Yamamoto, T., and Mori, N., 2006, “Numerical Analysis of Wall Slip Effects on Flow of Newtonian and Non-Newtonian Fluids in Macro and Micro Contraction Channels,” ASME J. Fluids Eng., 129(1), pp. 23–30. [CrossRef]
Ahonguio, F., Jossic, L., and Magnin, A., 2014, “Influence of Surface Properties on the Flow of a Yield Stress Fluid Around Spheres,” J. Non-Newtonian Fluid Mech., 206, pp. 57–70. [CrossRef]
Darbouli, M., Métivier, C., Piau, J.-M., Magnin, A., and Abdelali, A., 2013, “Rayleigh-Bénard Convection for Viscoplastic Fluids,” Phys. Fluids (1994-present), 25(2), p. 023101. [CrossRef]
Magnin, A., and Piau, J. M., 1990, “Cone-and-Plate Rheometry of Yield Stress Fluids. Study of an Aqueous Gel,” J. Non-Newtonian Fluid Mech., 36, pp. 85–108. [CrossRef]
Wang, C. Y., 2012, “Brief Review of Exact Solutions for Slip-Flow in Ducts and Channels,” ASME J. Fluids Eng., 134(9), p. 094501. [CrossRef]
Piau, J.-M., and Piau, M., 2005, “Letter to the Editor: Comment on ‘Origin of Concentric Cylinder Viscometry’ [J. Rheol. 49, 807–818 (2005)]. The Relevance of the Early Days of Viscosity, Slip at the Wall, and Stability in Concentric Cylinder Viscometry,” J. Rheol., 49(6), pp. 1539–1550. [CrossRef]
Meeker, S. P., Bonnecaze, R. T., and Cloitre, M., 2004, “Slip and Flow in Pastes of Soft Particles: Direct Observation and Rheology,” J. Rheol., 48(6), pp. 1295–1320. [CrossRef]
Seth, J. R., Cloitre, M., and Bonnecaze, R. T., 2008, “Influence of Short-Range Forces on Wall-Slip in Microgel Pastes,” J. Rheol., 52(5), pp. 1241–1268. [CrossRef]
Piau, J.-M., 2007, “Carbopol Gels: Elastoviscoplastic and Slippery Glasses Made of Individual Swollen Sponges,” J. Non-Newtonian Fluid Mech., 144(1), pp. 1–29. [CrossRef]
Mossaz, S., Jay, P., and Magnin, A., 2012, “Experimental Study of Stationary Inertial Flows of a Yield-Stress Fluid Around a Cylinder,” J. Non-Newtonian Fluid Mech., 189–190, pp. 40–52. [CrossRef]
Seth, J. R., Locatelli-Champagne, C., Monti, F., Bonnecaze, R. T., and Cloitre, M., 2012, “How do Soft Particle Glasses Yield and Flow Near Solid Surfaces?,” Soft Matter, 8(1), pp. 140–148. [CrossRef]
Métivier, C., and Magnin, A., 2011, “The Effect of Wall Slip on the Stability of the Rayleigh–Bénard Poiseuille Flow of Viscoplastic Fluids,” J. Non-Newtonian Fluid Mech., 166(14–15), pp. 839–846. [CrossRef]
Métivier, C., Rharbi, Y., Magnin, A., and Bou Abboud, A., 2012, “Stick-Slip Control of the Carbopol Microgels on Polymethyl Methacrylate Transparent Smooth Walls,” Soft Matter, 8(28), pp. 7365–7367. [CrossRef]
Navier, C. L. M. H., 1823, Mémoire sur les Lois du Mouvement des Fluides, Memoires de l'Academie Royale des Sciences de l'Institut de France, Paris, pp. 389–440.
Damianou, Y., Philippou, M., Kaoullas, G., and Georgiou, G. C., 2014, “Cessation of Viscoplastic Poiseuille Flow With Wall Slip,” J. Non-Newtonian Fluid Mech., 203, pp. 24–37. [CrossRef]
Lawal, A., and Kalyon, D. M., 1997, “Viscous Heating in Nonisothermal Die Flows of Viscoplastic Fluids With Wall Slip,” Chem. Eng. Sci., 52(8), pp. 1323–1337. [CrossRef]
Lawal, A., and Kalyon, D. M., 1997, “Nonisothermal Extrusion Flow of Viscoplastic Fluids With Wall Slip,” Int. J. Heat Mass Transfer, 40(16), pp. 3883–3897. [CrossRef]
Tang, H. S., and Kalyon, D. M., 2004, “Estimation of the Parameters of Herschel–Bulkley Fluid Under Wall Slip Using a Combination of Capillary and Squeeze Flow Viscometers,” Rheol. Acta, 43(1), pp. 80–88. [CrossRef]
Pearson, J. R. A., and Petrie, C. J. S., 1965, Proceedings of the Fourth International Congress on Rheology, Wiley, New York.
Fortin, A., Côté, D., and Tanguy, P. A., 1991, “On the Imposition of Friction Boundary Conditions for the Numerical Simulation of Bingham Fluid Flows,” Comput. Methods Appl. Mech. Eng., 88(1), pp. 97–109. [CrossRef]
Roquet, N., 2000, “Résolution Numérique d’écoulement à Effets de Seuil Par Éléments Finis Mixtes et Adaptation de Maillage,” Ph.D. thesis, Université de Grenoble, Grenoble.
Roquet, N., and Saramito, P., 2008, “An Adaptive Finite Element Method for Viscoplastic Flows in a Square Pipe With Stick–Slip at the Wall,” J. Non-Newtonian Fluid Mech., 155(3), pp. 101–115. [CrossRef]
Tokpavi, D. L., Magnin, A., and Jay, P., 2008, “Very Slow Flow of Bingham Viscoplastic Fluid Around a Circular Cylinder,” J. Non-Newtonian Fluid Mech., 154(1), pp. 65–76. [CrossRef]
Mitsoulis, E., 2004, “On Creeping Drag Flow of a Viscoplastic Fluid Past a Circular Cylinder: Wall Effects,” Chem. Eng. Sci., 59(4), pp. 789–800. [CrossRef]
Deglo De Besses, B., Magnin, A., and Jay, P., 2003, “Viscoplastic Flow Around a Cylinder in an Infinite Medium,” J. Non-Newtonian Fluid Mech., 115(1), pp. 27–49. [CrossRef]
Papanastasiou, T. C., 1987, “Flows of Materials With Yield,” J. Rheol., 31(5), pp. 385–404. [CrossRef]
Mossaz, S., Jay, P., and Magnin, A., 2010, “Criteria for the Appearance of Recirculating and Non-Stationary Regimes Behind a Cylinder in a Viscoplastic Fluid,” J. Non-Newtonian Fluid Mech., 165(21–22), pp. 1525–1535. [CrossRef]
Burgos, G. R., Alexandrou, A. N., and Entov, V., 1999, “On the Determination of Yield Surfaces in Herschel–Bulkley Fluids,” J. Rheol., 43(3), pp. 463–483. [CrossRef]
Jossic, L., and Magnin, A., 2009, “Drag of an Isolated Cylinder and Interactions Between Two Cylinders in Yield Stress Fluids,” J. Non-Newtonian Fluid Mech., 164(1–3), pp. 9–16. [CrossRef]
Randolph, M. F., and Houlsby, G. T., 1984, “The Limiting Pressure on a Circular Pile Loaded Laterally in Cohesive Soil,” Géotechnique, 34(4), pp. 613–623. [CrossRef]
Aubeny, C., Shi, H., and Murff, J., 2005, “Collapse Loads for a Cylinder Embedded in Trench in Cohesive Soil,” Int. J. Geomech., 5(4), pp. 320–325. [CrossRef]
Murff, J. D., 1989, “Pipe Penetration in Cohesive Soil,” Géotechnique, 39(2), pp. 213–229. [CrossRef]
Zollo, R. F., 1997, “Fiber-Reinforced Concrete: An Overview After 30 Years of Development,” Cem. Concr. Compos., 19(2), pp. 107–122. [CrossRef]
Shah, S. P., and Rangan, B. V., 1971, “Fiber Reinforced Concrete Properties,” ACI J. Proc., 68(2), pp. 126–137. [CrossRef]
Chhabra, R. P., 1993, Bubbles, Drops, and Particles in Non-Newtonian Fluids, CRC Press, Boca Raton.


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Fig. 1

Flow chart of a yield stress fluid (Carbopol gel) under different surface conditions [16]

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Fig. 2

Variation of the slip law for α = 0.5

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Fig. 3

Overview of the problem

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Fig. 4

Different rigid zones around a cylinder for steady creeping flow

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Fig. 5

Change in Cd* relative to V* for different S' values, for Od = 0.01; 1; 100

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Fig. 6

Change in Cd* as a function of Od for limiting cases

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Fig. 7

Velocity on the cylinder as a function of θ when varying S' for Od = 100: S′ = 0(—), S′ = 0.3 (– -), S′ = 0.7 (- -), S′ = 1 (······), PS (), and ADH ()

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Fig. 8

Velocity from the equator when varying V* for Od = 100: ADH (), V* = 0.1 (– ·), V* = 0.5 (- -), V* = 1 (—), V* = 10 (– -), V* = 103 (- · -), V = 105 (·······), and PS ()

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Fig. 9

Velocity from the pole when varying S′ for Od = 100: S' = 0 (—), S′ = 0.3 (– -), S' = 0.7 (- -), S' = 1 (······), PS (), and ADH ()

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Fig. 10

Changes of rigid zones according to the slip parameters for Od = 100. The flow direction occurs from the left to the right.



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