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

Kalogirou, Anna; Poyiadji, Stella; Georgiou, Georgios C.

Abstract

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. © 2011 Elsevier B.V.

Citation

Kalogirou, A., Poyiadji, S., & Georgiou, G. C. (2011). Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity. Journal of Non-Newtonian Fluid Mechanics, 166(7-8), 413-419. https://doi.org/10.1016/j.jnnfm.2011.01.006

• Journal Article Type: Article
• Acceptance Date: Jan 12, 2011
• Online Publication Date: Jan 19, 2011
• Publication Date: 2011-04
• Deposit Date: Jun 13, 2019
• Journal: Journal of Non-Newtonian Fluid Mechanics
• Print ISSN: 0377-0257
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 166
• Issue: 7-8
• Pages: 413-419
• DOI: https://doi.org/10.1016/j.jnnfm.2011.01.006
• Keywords: Mechanical Engineering; General Materials Science; Applied Mathematics; General Chemical Engineering; Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/2138198
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0377025711000231