A study of thermodynamic stability of deformation in visco-elastic fluids by Lyapunov function analysis. (English) Zbl 1084.76032
Summary: A positive definite thermodynamic Lyapunov function, \(L_s\), has been defined as the magnitude of excess rate of entropy production. The total time derivative of \(L_s\) in thermodynamic perturbation space then determines the stability or instability of a process. In the present paper the thermodynamic stability of deformation in visco-elastic fluids has been investigated using the above proposed thermodynamic Lyapunov function and Lyapunov’s direct method of stability of motion. For this purpose, in the present case the thermodynamic space based on extended irreversible thermodynamics has been used to construct the thermodynamic perturbation space. Three different models of deformation in viscoelastic fluids have been tested for the stability that establishes the regions of asymptotic stability and the stability under constantly acting small disturbances in each case. The case of instability also surfaces out.
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