Abstract
A continuum theory of rigid suspensions is introduced. Balance laws and constitutive equations of micropolar continuum theory are modified and extended for the characterization of dense rigid suspensions. Thermodynamic restrictions are imposed. The general theory is specialized to the case of dense rigid fiber and spherical suspensions. Dilute suspensions in Newtonian fluids are obtained as special cases. Motions of rigid fiber suspensions in viscometric flows are determined as applications of the theory.
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References
Eringen A Cemal (1980) Theory of Anisotropic Micropolar Fluids. Int J Engng Sci 18:5–17
Eringen A Cemal (1966) Theory of Micropolar Fluids. J Math Mech 16:1–18
Eringen A Cemal (1972) Theory of Microfluids. J Math Anal and Appl 38:480–496
Eringen A Cemal (1984) A Continuum Theory of Rigid Suspensions. Int J Engng Sci 22:1373–1388
Eringen A Cemal (1985) Rigid Suspensions in Viscous Fluid. Int J Engng Sci 23:491–495
Batchelor GK (1970) The Stress System in a Suspension of Force-free Particles. J Fluid Mech 41:545–570
Batchelor GK (1971) The Stress Generated in a Nondilute Suspension of Elongated Particles by Pure Straining Motion. J Fluid Mech 46:813–829
Mewis J, Metzner AB (1974) The Rheological Properties of Suspensions of Fibres in Newtonian Fluids Subjected to Extensional Deformations. J Fluid Mech 62:593–600
Bark FH, Tinoco H (1978) Stability of Plane Poiseuille Flow of a Dilute Suspensions of Slender Fibres. J Fluid Mech 87:321–333
Shaqfeh Eric SG, Fredrickson GH (1990) The Hydrodynamic Stress in Suspension of Rods. Phy Fluids A2(1):7–24, Jan.
Russel WB, Gast AP: (1986) Nonequilibrium Statistical Mechanics of Concentrated Colloidal Dispersions: Hard Spheres in Weak Flows. J Chem Phys 84, No. 3, 1825–1826, Feb.
de Kruif CG, Vanlersel EMF, Vrij A (1985) Hard Sphere Colloidal Dispersions: Viscosity as a Function of Shear Rate and Volume Fraction. J Chem Phys 83 (9):4717–4725, 1 Nov.
Eringen A Cemal (1964) Simple Micro-fluids. Int J Engng Sci 2:189–203
Eringen A Cemal (1978) Micropolar Theory of Liquid Crystals. In: Johnson JF, Porter RS (eds) Liquid Crystals and Ordered Fluids, Vol. 3. Plenum Publishing Co
Jefferey GB (1922) Proc Roy Soc A 102:161
Leal LG, Hinch EJ (1973) Theoretical Studies of a Suspension of Rigid Particles Affected by Brownian Couples. Rheol Acta 12:127–132
Johnson SJ, PhD thesis Simultaneous Dichroism and Birefringence Measurements of Sheared Colloidal Suspensions in Polymeric Liquids. Stanford University, Stanford, CA
Fuller GG (1990) Optical Rheometry. Ann Rev Fluid Mechanics 22:387–417
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Eringen, A.C. Continuum theory of dense rigid suspensions. Rheol Acta 30, 23–32 (1991). https://doi.org/10.1007/BF00366791
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DOI: https://doi.org/10.1007/BF00366791