Paper Info
Title
Analysis of a Two-Fluid Taylor-Couette Flow with One Non-Newtonian Fluid
Abstract
We study the dynamic behaviour of two viscous fluid films confined between two concentric cylinders rotating at a small relative velocity. It is assumed that the fluids are immiscible and that the volume of the outer fluid film is large compared to the volume of the inner one. Moreover, while the outer fluid is considered to have constant viscosity, the rheological behaviour of the inner thin film is determined by a strain-dependent power-law. Starting from a Navier-Stokes system, we formally derive evolution equations for the interface separating the two fluids. Two competing effects drive the dynamics of the interface, namely the surface tension and the shear stresses induced by the rotation of the cylinders. When the two effects are comparable, the solutions behave, for large times, as in the Newtonian regime. We also study the regime in which the surface tension effects dominate the stresses induced by the rotation of the cylinders. In this case, we prove local existence of positive weak solutions both for shear-thinning and shear-thickening fluids. In the latter case, we show that interfaces which are initially close to a circle converge to a circle in finite time and keep that shape for later times.
Year
DOI
Venue
2022
10.1007/s00332-021-09750-0
JOURNAL OF NONLINEAR SCIENCE
Keywords
DocType
Volume
Taylor-Couette flow, Non-Newtonian fluid, Power-law fluid, Degenerate parabolic equation, Weak solution, Long-time asymptotics, Thin-film equation
Journal
32
Issue
ISSN
Citations 
2
0938-8974
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Christina Lienstromberg100.34
Tania Pernas-Castaño200.34
J. J. L. Velázquez3138.41