Search results for "law of thermodynamics"
showing 2 items of 12 documents
Geometric Aspects of Thermodynamics
2016
This chapter deals with mathematical aspects of thermodynamics most of which will be seen to be primarily of geometrical nature. Starting with a short excursion to differentiable manifolds we summarize the properties of functions, of vector fields and of one-forms on thermodynamic manifolds. This summary centers on exterior forms over Euclidean spaces and the corresponding differential calculus. In particular, one-forms provide useful tools for the analysis of thermodynamics. A theorem by Caratheodory is developed which is closely related to the second law of thermodynamics. The chapter closes with a discussion of systems which depend on two variables and for which there is an interesting a…
Analysis of a viscoelastic phase separation model
2020
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics, and we study well-posedness of the model, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. A good qualitative agreement with mesoscopic simulations is observed in numerical tests.