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Creeping flow of a Herschel–Bulkley fluid with pressure-dependent material moduli

Published online by Cambridge University Press:  11 July 2017

L. FUSI  and
F. ROSSO
L. FUSI
Affiliation:
Dipartimento di Matematica e Informatica “U. Dini”, Viale Morgagni, 67/a, 50134 Firenze, Italy emails: lorenzo.fusi@unifi.it, fabio.rosso@unifi.it
F. ROSSO
Affiliation:
Dipartimento di Matematica e Informatica “U. Dini”, Viale Morgagni, 67/a, 50134 Firenze, Italy emails: lorenzo.fusi@unifi.it, fabio.rosso@unifi.it
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Abstract

We model the axisymmetric unidirectional flow of a Herschel–Bulkley fluid with rheological parameters that depend linearly on pressure. Adopting an appropriate scaling, we formulate the mathematical problem in cylindrical geometry exploiting an integral formulation for the momentum equation in the unyielded part. We prove that, under suitable assumptions on the data of the problem, explicit solutions can be determined. In particular, we determine the position of the yield surface together with the pressure and velocity profiles. With the aid of some plots, we finally discuss the dependence of the solution on the physical parameters of the problem.

Keywords

Non-Newtonian fluidsHerschel–BulkleyPoiseuille flowBessel functionsnon-linear constitutive equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 2 , April 2018 , pp. 352 - 368
Copyright
Copyright © Cambridge University Press 2017 

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