The flow birefringence of the Rivlin-Ericksen viscoelastic fluid and of Noll's simple fluid is theoretically investigated. The Maxwell-Lorentz field equations, the mechanical field equations and the constitutive equations are reduced to simplified ones in the weak limit of the electromagnetic plane wave. In this limit the stress tensor and the index tensor are expressed as functions or functionals depending on the mechanical state-variables. The birefringences and the extinction angles in Couette flow are formulated as functions of the shearing-rate. These formulae are identical with Kuhn and Kuhn's necklace model theory. Thus the two viscoelastic fluids correspond to a suspention of linear molecules whose valency-angle is freely movable.
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