Abstract
In this paper we investigate the stability of some viscometric flows for a concentrated suspension model which allows for the effects of shear-induced migration, including plane and circular Couette and Poiseulle flows, and unbounded and bounded torsional flows. In the bounded torsional flow, where its radial outer boundary is assumed frictionless, an exact closeform solution is given. With the exception of torsional flows, we find that a limit point for all the steady-state solutions can exist for certain range in the parameter values. In all cases, disturbances can persist for a long time, O (H 2/a 2), where H is a dimension of the flow field, and a is the particles' radius.
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References
Avagliano A, Phan-Thien N (1996) Torsional flow: elastic instability in a finite domain. J Fluid Mech (in press)
Gadala-Maria F, Acrivos A (1980) Shear-introduced structure in a concentrates suspensions of solid spheres. J Rheol 24:799–811
Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stephens TS (1991) Note: NMR imaging of shear-induced diffusion and structure in concentrated suspensions undergoing Couette flow. J Rheol 35:191–201
Hampton R, Tetlow N, Altobelli SA, Graham AL, Mondy LA (1995) umpublished results
Iwamiya JH, Chow AW, Sinton SW (1994) NMR flow imaging of Newtonian liquids and a concentrated suspension through an axisymmetric sudden contraction. Rheol Acta 33:267–282
Jenkins JT, McTigue DF (1990) Transport processes in concentrated suspensions: the role of particles fluctuations. In: Joseph DD, Schaeffer DG (eds) Two phase flows and waves. Springer-Verlag, New York, pp 70–79
Koh CJ, Hookham P, Leal LG (1994) An experimental investigation of concentrated suspensions flows in a rectangular channel. J Fluid Mech 266:1–32
Krieger IM (1972) Rheology of monodisperse lattices. Adv Colloid Interface Sci 3:111–136
Kubíĉek M, Marek M (1983) Computational methods in bifurcation theory and dissipative structures. Springer-Verlag, New York
Leighton D, Acrivos A (1987) The shear-induced migration of particles in concentrated suspensions. J Fluid Mech 181:415–439
Lyon MK, Leal LG (1995) Experimental studies of the motion of concentrated suspensions in two-dimensional channel flow. IUTAM Symposium, Denver
Nott PR, Brady JF (1994) Pressure-driven flow of suspensions: simulation and theory. J Fluid Mech 275:157–199
Phan-Thien N (1995) Constitutive equation for concentrated suspensions in Newtonian liquids. J Rheol 39:679–695
Phan-Thien N, Graham AL, Altobelli SA, Abbott JR, Mondy LA (1995) Hydrodynamic particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders. Ind Eng Chem Res 34:3187–3194
Phillips RJ, Armstrong RC, Brown RA, Graham AL, Abbott JR (1992) A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys Fluid A 4:30–40
Ryskin G, Rallison JM (1980) appendix to Ryskin G, the extensional viscosity of a dilute suspension of spherical particles at intermediate microscale Reynolds numbers. J Fluid Mech 99:513–529
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Phan-Thien, N., Fang, Z. & Graham, A.L. Stability of some shear flows for concentrated suspensions. Rheol Acta 35, 69–75 (1996). https://doi.org/10.1007/BF00366554
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DOI: https://doi.org/10.1007/BF00366554