Dumbbells Warner

Bird,R.B., Warner,Jr, H.R, and Evans,D.C. Kinetic Theory and Rheology of Dumbbell Suspensions with Brownian Motion. Vol. 8, pp. 1—90. 

Values of p22 — P33 = N2 appear to be negative and approximately 10-30% of Nj in magnitude (82). The conventional bead-spring models yield N2=0. Indeed, N2 in steady shear flow is identically zero for all free draining models, regardless of the force-distance law in the connectors (102a). Thus, finite extensibility and, by inference at least, internal viscosity do not in themselves provide non-zero N2 values. Bird and Warner (354) have recently analyzed the rigid dumbbell model with intramolecular hydrodynamic interaction, the latter represented by the Oseen approximation. In this case N2 turns out to be non-zero but positive. 

Bird,R.B., Warner,H.R.,Jr., Evans,D.G Kinetic theory and rheology of dumbbell suspensions with brownian motion. Advan. Polymer ScL 8,1-90 (1971). 

Warner, H.R., Jr. Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells. Ind. Eng. Chem. Fundam. 11,379-387 (1972). 

Warner HR (1972) Kinetic theory of dilute suspensions of finitely extendible dumbbells Ind Eng Chem Fundam 11 379... 

H. R. Warner, Jr., Kinetic Theory and Rheology of Dilute Suspensions of Finitely Extendible Dumbbells, Ind. Eng. Chem. Fundam., 11,379-387 (1972) also, R. L. Christiansen and R. B. Bird, Dilute Solution Rheology Experimental Results and Finitely Extensible Nonlinear Elastic Dumbbell Theory, J. Non-Newt. Fluid Mech., 3, 161-177 (1977/1978). 

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