A GENERIC formalism for Korteweg-type fluids: I. A comparison with classical theory. (12th March 2020) - Suzuki, Yukihito
Abstract: We investigated a mathematical model for Korteweg-type fluids, formulated in the form of the General equation for the non-equilibrium reversible–irreversible coupling (GENERIC) as proposed by Grmela and Öttinger, in comparison with the classical work of Dunn and Serrin. Interstitial working introduced by Dunn and Serrin reappeared in the formulation and proved to be necessary if we claim that the work done by the Korteweg stress is 'isentropic'. Indeed, the GENERIC formalism provides a fairly simple derivation of the governing equations with the interstitial working for Korteweg-type fluids. In the accompanying paper, and within this formalism, we derived a higher-order model including the second-order gradient of the density. We also discussed the relation of the interstitial working to the microforces introduced by Gurtin.