A thermodynamical suspension model for blood

TL;DR

This paper develops a comprehensive thermodynamical model of blood as a suspension of red blood cells in plasma, incorporating temperature effects and dissipative phenomena, validated through thermodynamic restrictions.

Contribution

It introduces a novel thermodynamical framework for blood modeling based on mixture theory with internal variables and temperature effects, ensuring thermodynamic consistency.

Findings

Derived thermodynamic restrictions using Clausius-Duhem inequality.

Established thermodynamic admissibility via extended Coleman-Noll procedure.

Provided a one-dimensional solution satisfying all constraints.

Abstract

A complete thermodynamical analysis for a blood model, based on mixture theory, is performed. The model is developed considering the blood as a suspension of red blood cells (solid component) in the plasma (fluid component), and taking into account the temperature effects. Furthermore, two independent scalar internal variables are introduced accounting for additional dissipative effects. Using Clausius-Duhem inequality, the general thermodynamic restrictions and residual dissipation inequality are derived. The thermodynamic admissibility with the second law of thermodynamics is assessed by means of the extended Coleman-Noll procedure; in one space dimension we exhibit a solution of all the thermodynamical constraints.