Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity

The pressure-dependence of the viscosity becomes important in flows where high pressures are encountered. Applications include many polymer processing applications, microfluidics, fluid film lubrication, as well as simulations of geophysical flows. Under the assumption of unidirectional flow, we der...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2011-04, Vol.166 (7), p.413-419
Main Authors: Kalogirou, Anna, Poyiadji, Stella, Georgiou, Georgios C.
Format: Article
Language:English
Subjects:
Annular Poiseuille flow
Coefficients
Exact sciences and technology
Flows in ducts, channels, nozzles, and conduits
Fluid dynamics
Fluid films
Fluid flow
Fundamental areas of phenomenology (including applications)
Geophysics
Laminar flow
Lubrication
Microfluidics
Newtonian flow
Newtonian liquids
Physics
Poiseuille flow
Pressure-dependent viscosity
Viscosity
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Summary:The pressure-dependence of the viscosity becomes important in flows where high pressures are encountered. Applications include many polymer processing applications, microfluidics, fluid film lubrication, as well as simulations of geophysical flows. Under the assumption of unidirectional flow, we derive analytical solutions for plane, round, and annular Poiseuille flow of a Newtonian liquid, the viscosity of which increases linearly with pressure. These flows may serve as prototypes in applications involving tubes with small radius-to-length ratios. It is demonstrated that, the velocity tends from a parabolic to a triangular profile as the viscosity coefficient is increased. The pressure gradient near the exit is the same as that of the classical fully developed flow. This increases exponentially upstream and thus the pressure required to drive the flow increases dramatically.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2011.01.006