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Anil A. Bhalekar, Chandrakant S. Burande

A study of thermodynamic stability of deformation in visco-elastic fluids by Lyapunov function analysis

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 (EIT) 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.

Journal of Non-Equilibrium Thermodynamics, Walter de Gruyter

Print ISSN: 0340-0204
Volume: 30, 03/2005
Pages: 53 - 65

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