Conservation laws and constitutive relations for density-gradient-dependent viscous fluids

Abstract.Conservation laws and constitutive relations for a density-gradient-dependent viscous fluid as a multipolar continuum obeying an entropy inequality with generalized entropy flux and supply density are considered in this paper. A decomposition of the rate of work of dipolar stress, which reveals the contribution of various parts of this stress to the energy equation, is used to discuss the inconsistencies between the results obtained here and those obtained by Bluestein and Green [1] on the basis of the pioneering work of Green and Rivlin [8]. Furthermore, we discuss the connection between the model presented here and the materials of Korteweg type considered by Dunn and Serrin [6]. In particular, we relate the rate of work of dipolar stress and the interstitial working introduced by Dunn and Serrin [6].

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