The one-dimensional flow of a fluid with limited strain-rate

Farina, A.; Fasano, A.; Fusi, L.; Rajagopal, K.

doi:10.1090/S0033-569X-2011-01249-7

Authors: A. Farina, A. Fasano, L. Fusi and K. R. Rajagopal
Journal: Quart. Appl. Math. 69 (2011), 549-568
MSC (2010): Primary 76A05, 74D10, 35R35, 35K10
DOI: https://doi.org/10.1090/S0033-569X-2011-01249-7
Published electronically: May 9, 2011
MathSciNet review: 2850745
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Abstract: We present a model for a continuum in which the strain rate depends linearly on the stress, as long as the latter is below a fixed threshold, but it is frozen to a constant value when the stress exceeds such a threshold. The constitutive equation is given in an implicit form as the stress is a multi-valued function of the strain rate. We derive the model in a general 3D setting and we study the one-dimensional case of a pressure-driven flow between two parallel plates. We prove some analytical results and describe a procedure to determine the main physical parameters (stress threshold and viscosity) by means of a rotational viscometer. Finally we show that the model can be obtained as the limit case of a piecewise linear viscous model.

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