Extra stress tensor in fiber suspensions: Mechanics and thermodynamics
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en
Article de revue
Este ítem está publicado en
Journal of Rheology. 2011, vol. 55, p. 17-42
American Institute of Physics
Resumen en inglés
Formulas expressing the extra stress tensor, $\boldsymbol\sigma$, in fiber suspensions in terms of microstructural state variables are derived by using two types of arguments: mechanical and thermodynamical. Results are ...Leer más >
Formulas expressing the extra stress tensor, $\boldsymbol\sigma$, in fiber suspensions in terms of microstructural state variables are derived by using two types of arguments: mechanical and thermodynamical. Results are compared for the distribution function ($\psi$) and the orientation tensor, $\mathbf A$, playing the role of state variables. The main results are the following: (i) In the thermodynamical analysis the formulas arise as compatibility conditions between the time evolution of the fluid velocity and the time evolution of the internal structure. (ii) A complete agreement among the formulas arising in mechanics and thermodynamics is seen only in kinetic theory (i.e. with $\psi$ as the state variable) and only with the Chan-Terentjev mechanical formula. (iii) Theoretical arguments as well as numerical illustrations indicate that the larger is the role of the reversible part of the time evolution of the microstructure the larger is the difference in predicted stresses (i.e. the formulas for $\boldsymbol \sigma$ evaluated at solutions of the microstructural equations) calculated with the thermodynamic and the Dinh-Armstrong mechanical formulas.< Leer menos
Palabras clave en inglés
Suspensions
Kinetic theory
Free energy
Tensor methods
Cumulative distribution functions
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