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Preprint 39-2014

Models for the two-phase flow of concentrated suspensions

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Author(s) : Tobias Ahnert , Andreas Münch , Barbara Wagner

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 39-2014

MSC 2000

35Q35 Other equations arising in fluid mechanics

Abstract :
A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model naturally exhibits a Bingham-type flow property. This property is investigated in detail for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady state of this problem, the governing equation are reduced to a boundary value problem for a system of ordinary differential equations and the dependence of its solutions are analyzed by using phasespace methods. For the general time-dependent case a new drift-flux model is derived for the first time using matched asymptotic expansions that take account of the boundary layers at the walls and the interface between the yielded and unyielded region. Using the drift-flux model, the behavior of the suspension flow, in particular the appearance and evolution of unyielded or jammed regions is then studied numerically for different choices of the parameters.

Keywords : Suspensions, jamming, yield stress, averaging, multiphase model, phasespace methods, matched asymptotics, drift-flux

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