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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

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


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
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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Additional Information

A. Farina
Affiliation: Università degli Studi di Firenze, Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy
Email: farina@math.unifi.it

A. Fasano
Affiliation: Università degli Studi di Firenze, Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy
Email: fasano@math.unifi.it

L. Fusi
Affiliation: Università degli Studi di Firenze, Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy
Email: fusi@math.unifi.it

K. R. Rajagopal
Affiliation: Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77845
Email: krajagopal@mengr-tamu.org

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01249-7
PII: S 0033-569X(2011)01249-7
Keywords: Non-Newtonian fluids, implicit constitutive relations, free boundary problems, parabolic equations.
Received by editor(s): March 24, 2010
Published electronically: May 9, 2011
Article copyright: © Copyright 2011 Brown University



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