Summary
Based on the incompressibleBKZ elastic fluid theory, a relation is obtained between two complex dynamic moduli which pertain to small oscillations superposed on a basic steady simple shearing flow. One of these moduli concerns oscillations parallel to the basic flow and the other concerns oscillations transverse or orthogonal to the basic flow. It is demonstrated that the relation holds for any incompressibleBKZ fluid, but a counterexample shows that the relation does not hold for the general incompressible simple fluid.
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Bernstein, B. A rheological relation between parallel and transverse superposed complex dynamic shear moduli. Rheol Acta 11, 210–215 (1972). https://doi.org/10.1007/BF01993022
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DOI: https://doi.org/10.1007/BF01993022