Pressure-driven flow of a rate type fluid with stress threshold in an infinite channel
Résumé
In this paper we extend some our previous works on continua with stress threshold. In particular here we propose a mathematical model for a continuum which behaves as a nonlinear upper convected Maxwell fluid if the stress is above a certain threshold and as a Oldroyd-B type fluid if the stress is below such a threshold. We derive the constitutive equations for each phase exploiting the theory of natural configurations (introduced by rajagopal and co-workers) and the criterion of the maximization of the rate of dissipation. We state the mathematical problem for a one-dimensional flow driven by a constant pressure gradient and study two peculiar cases in which the velocity of the inner part of the fluid is spatially homogeneous.
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PEER_stage2_10.1016%2Fj.ijnonlinmec.2011.04.015.pdf (625.1 Ko)
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