Next Article in Journal
Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations
Next Article in Special Issue
Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid
Previous Article in Journal
A 3D Numerical Study of Interface Effects Influencing Viscous Gravity Currents in a Parabolic Fissure, with Implications for Modeling with 1D Nonlinear Diffusion Equations
Previous Article in Special Issue
The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel
Open AccessArticle

Lubrication Approximation for Fluids with Shear-Dependent Viscosity

Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1959-007 Lisboa, Portugal
Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
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;
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
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop