Extension of nonlinear Onsager theory of irreversibility

Abstract

Nonlinear Onsager theory in combination with Wang’s representation theorem is utilized to obtain nonlinear constitutive equations for fluid. The constitutive equations can be derived using the derivative of a dissipative function according to nonlinear Onsager’s theory. The requirement of the dissipative function is convexity in thermodynamic force and continuity in thermodynamic flux. An isothermal fluid is provided as an example. Objectivity is required for the constitutive equations of the fluid. Such an axiom permits that all response functions are isotropic functions and can be expressed by Wang’s representation theorem. Therefore, the dissipative part of Cauchy stress is obtained using (i) Wang’s representation theorem only and (ii) both nonlinear Onsager theory and Wang’s representation theorem. In method (i), the coefficients for the constitutive equations are only constrained by the Clausius–Duhem inequality, while in method (ii), these are not only constrained by Clausius–Duhem inequality but also by the positive semidefiniteness of the Hessian matrix of the dissipative function (convexity of the dissipative function).