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Open AccessArticle

Lubrication Approximation for Fluids with Shear-Dependent Viscosity

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Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1959-007 Lisboa, Portugal
2
Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
3
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 98; https://doi.org/10.3390/fluids4020098
Received: 30 April 2019 / Revised: 16 May 2019 / Accepted: 20 May 2019 / Published: 28 May 2019
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing. View Full-Text
Keywords: power-law fluid; shear-dependent viscosity; Reynolds equation; lubrication approximation power-law fluid; shear-dependent viscosity; Reynolds equation; lubrication approximation
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MDPI and ACS Style

Pereira, B.M.; Dias, G.A.; Cal, F.S.; Rajagopal, K.R.; Videman, J.H. Lubrication Approximation for Fluids with Shear-Dependent Viscosity. Fluids 2019, 4, 98.

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