The theory of the bulk viscosity of polymer solutions is considered for cases of low and moderate concentrations of phantom chains under Vthgr; conditions. It is shown that the familiar preaveraging approximation for the hydrodynamic interactions imposes the constraint that the polymer contribution to the bulk viscosity is minus onehyphen;third of its contribution to the shear viscosity, thereby providing an experimental means for testing this widely used approximation. Particular application is made to the theory of sound attenuation in polymer solutions as one potential means for measuring the bulk viscosity. At higher frequencies the longitudinal (sound) modes of the solvent introduce an additional exponentially decaying contribution to the hydrodynamic interactions which leads to a renormalization of the relaxation times of the polymer.
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