Continuum Thermodynamics of the Phase Transformation of Thermoelastic Fluids

 In this presentation we use continuum thermodynamics of pure thermoelastic fluids (such as water) to examine their phase transformation. We present a complete approach for formulating constitutive models for real gases and liquids, of the type used to populate thermodynamic tables, using virial expansions. Our approach employs the specific free energy as the main function of state that needs to be characterized to completely describe the properties of a thermoelastic fluid. By adopting an arbitrary reference pressure and reference temperature, we obtain relatively simple expressions for the specific free energy of real liquids and gases. To examine phase transformation kinetics, a special emphasis is placed on the jump condition for the axiom of entropy inequality, thereby recovering the conventional result that stable phase equilibrium coincides with continuity of temperature, pressure, and free enthalpy across the phase boundary. Moreover, this jump condition leads to the formulation of a constitutive relation for arbitrary phase transition kinetics under non-equilibrium conditions, showing that phase transformations must be accompanied by a jump in temperature across the phase boundary. Encouraging agreement is found between the formulation of this study and limited available experimental data. Further evidence is needed to conclusively validate this proposed constitutive model. This continuum framework is well suited for implementation in a computational framework, such as the finite element method.

Gerard Ateshian is the Andrew Walz Professor of Mechanical Engineering and Professor of Biomedical Engineering at Columbia.  His primary research is in the field of soft tissue mechanics, with an emphasis on cartilage mechanics, lubrication, and tissue engineering, the formulation of growth theories for biological tissues, and the implementation of computational frameworks to solve challenging problems in these fields.  His primary clinical interest focuses on the treatment of osteoarthritis.

This seminar is in-person and virtual. Please see below for Zoom details.

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