Abstract
Liquid-phase migration in highly concentrated suspensions undergoing constant-force squeeze flow is modeled numerically by taking into account the time and position dependence of the rheological properties due to changes in the volume fraction of solids. This is done by coupling the equation of motion for a non-Newtonian material that behaves approximately as a Bingham plastic with a continuity equation that includes diffusive flux. The developed model was first tested with experimental data and then used to study the effect of various parameters on liquid-phase migration.
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References
Ayadi A (2011) Exact analytic solutions of the lubrication equations for squeeze-flow of a biviscous fluid between two parallel disks. J Non-Newtonian Fluid Mech 166:1253–1261
Barnes HA (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 56:221–251
Barnes HA (1999) The yield stress—a review or ‘παντα ρει’—everything flows? J Non-Newtonian Fluid Mech 81:133–178
Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, New York, p. 110
Chaari F, Racineux G, Poitou A, Chaouche M (2003) Rheological behavior of sewage sludge and strain-induced dewatering. Rheol Acta 42:273–279
Delhaye N, Poitou A, Chaouche M (2000) Squeeze flow of highly concentrated suspensions of spheres. J Non-Newtonian Fluid Mech 94:67–74
Ellwood KRJ, Georgiou GC, Papanastasiou TC, Wilkes JO (1990) Laminar jets of Bingham-plastic liquids. J Rheol 34:787–812
Engmann J, Servais C, Burbidge AS (2005) Squeeze flow theory and applications to rheometry: a review. J Non-Newtonian Fluid Mech 132:1–27
Estellé P, Lanos C, Perrot A, Servais C (2006) Slipping zone location in squeeze flow. Rheol Acta 45:444–448
Gulmus SA, Yilmazer U (2005) Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions. J Appl Polym Sci 98:439–448
Kaci A, Ouari N, Racineux G, Chaouche M (2011) Flow and blockage of highly concentrated granular suspensions in non-Newtonian fluid. Eur J Mech B Fluids 30:129–134
Krieger IM (1972) Rheology of monodisperse lattices. Adv Colloid Interf Sci 3:111–136
Laun HM, Rady M, Hassager O (1999) Analytical solution for squeeze flow with partial wall slip. J Non-Newtonian Fluid Mech 81:1–15
Leighton D, Acrivos A (1987) The shear-induced migration of particles in concentrated suspensions. J Fluid Mech 181:415–439
Li XY, Logan BE (2001) Permeability of fractal aggregates. Water Res 35:3373–3380
Mascia S, Wilson DI (2008) Biaxial extensional rheology of granular suspensions: the HBP (Herschel–Bulkley for Pastes) model. J Rheol 52:981–998
Mascia S, Seiler C, Fitzpatrick S, Wilson DI (2006) Extrusion-spheronisation of microcrystalline cellulose pastes using a non-aqueous liquid binder. Int J Pharm 389:1–9
Meeten GH (2004) Effects of plate roughness in squeeze-flow rheometry. J Non-Newtonian Fluid Mech 124:51–60
Meeten GH (2007) Radial filtration during constant-force squeeze flow of soft solids. Rheol Acta 46:803–813
Mueller S, Llewellin EW, Mader HM (2010) The rheology of suspensions of solid particles. Proc R Soc A 466:1201–1228
Navier CL, Sur MH (1827) Les lois du mouvement des fluides. Mem Acad R Sci Inst Fr 6:389–440
Nikkhoo M, Khodabandehlou K, Brozovsky L, Gadala-Maria F (2013) Normal stress distribution in highly concentrated suspensions undergoing squeeze flow. Rheol Acta 52:155–163
Nikkhoo M, Hofman A, Gadala-Maria F (2014) Correlation between radial filtration and normal stress distribution in highly concentrated suspensions undergoing constant-force squeeze flow. Rheol Acta 53:303–314
O’Donovan EJ, Tanner RI (1984) Numerical study of the Bingham squeeze film problem. J Non-Newtonian Fluid Mech 15:75–83
Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31:385–404
Phillips RJ, Armstrong RC, Brown RA (1992) A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys Fluids A 4:30–40
Poitou A, Racineux G (2001) A squeezing experiment showing binder migration in concentrated suspensions. J Rheol 45:609–625
Roussel N, Lanos C (2004) Particle fluid separation in shear flow of dense suspensions: experimental measurement on squeezed clay paste. J Rheol 51:493–515
Sherwood JD (2002) Liquid–solid relative motion during squeeze flow of pastes. J Non-Newtonian Fluid Mech 104:1–32
Sherwood JD, Durban D (1998) Squeeze flow of a Herschel–Bulkley fluid. J Non-Newtonian Fluid Mech 77:115–121
Smyrnaios DN, Tsamopoulos JA (2001) Squeeze flow of Bingham plastics. J Non-Newtonian Fluid Mech 100:165–190
Toutou Z, Roussel N, Lanos C (2005) The squeezing test: a tool to identify firm cement-based material’s rheological behavior and evaluate their extrusion ability. Cem Concr Res 35:1891–1899
Yang SP, Zhu KQ (2006) Analytical solutions for squeeze flow of Bingham fluid with Navier slip condition. J Non-Newtonian Fluid Mech 138:173–180
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We are grateful to Sarah Rough of the Department of Chemical Engineering and Biotechnology at the University of Cambridge for her helpful comments on an earlier draft of this paper.
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Nikkhoo, M., Gadala-Maria, F. Modeling radial filtration in squeeze flow of highly concentrated suspensions. Rheol Acta 53, 607–619 (2014). https://doi.org/10.1007/s00397-014-0782-2
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DOI: https://doi.org/10.1007/s00397-014-0782-2