Viscoelastic fluids in thin domains: a mathematical proof
Guy Bayada (ICJ), Laurent Chupin (LaMCoS), B\'er\'enice Grec (ICJ)
TL;DR
This paper rigorously proves the convergence of the Navier-Stokes/Oldroyd-B system to an asymptotic model for non-Newtonian viscoelastic flows in thin domains, relevant to lubrication and similar applications.
Contribution
It provides a rigorous mathematical justification for the asymptotic model of Oldroyd-B viscoelastic flows in thin geometries, extending previous heuristic approaches.
Findings
Mathematically proved convergence of the Navier-Stokes/Oldroyd-B system
Validated the asymptotic model for thin domain flows
Applicable to lubrication and similar thin geometries
Abstract
The present paper deals with non Newtonian viscoelastic flows of Oldroyd-B tye in thin domains. Such geometries arise for example in the context of lubrication. More precisely, we justify rigorously the asymptotic model obtained heuristically by proving the mathematical convergence of the Navier-Stokes/Oldroyd-B sytem towards the asymptotic model.
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Taxonomy
TopicsRheology and Fluid Dynamics Studies · Advanced Mathematical Modeling in Engineering · Fluid Dynamics and Thin Films