The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. A linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated, and the connections to the stability problem for the related classical Bingham flow problem are discussed.
%0 Journal Article
%1 ahnert2018stability
%A Ahnert, Tobias
%A Münch, Andreas
%A Niethammer, Barbara
%A Wagner, Barbara
%D 2018
%J Journal of Engineering Mathematics
%K 76e05-parallel-shear-flows 76t20-suspensions
%N 1
%P 51--77
%R 10.1007/s10665-018-9954-x
%T Stability of concentrated suspensions under Couette and Poiseuille flow
%U https://link.springer.com/article/10.1007%2Fs10665-018-9954-x
%V 111
%X The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. A linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated, and the connections to the stability problem for the related classical Bingham flow problem are discussed.
@article{ahnert2018stability,
abstract = {The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. A linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated, and the connections to the stability problem for the related classical Bingham flow problem are discussed.},
added-at = {2020-07-08T05:16:03.000+0200},
author = {Ahnert, Tobias and M{\"u}nch, Andreas and Niethammer, Barbara and Wagner, Barbara},
biburl = {https://www.bibsonomy.org/bibtex/23365c2c494bcbfad8edc612ba61f32f3/gdmcbain},
day = 01,
doi = {10.1007/s10665-018-9954-x},
interhash = {6cc514dd32410558c9afdebfe8be94de},
intrahash = {3365c2c494bcbfad8edc612ba61f32f3},
issn = {1573-2703},
journal = {Journal of Engineering Mathematics},
keywords = {76e05-parallel-shear-flows 76t20-suspensions},
month = aug,
number = 1,
pages = {51--77},
timestamp = {2020-07-08T05:17:22.000+0200},
title = {Stability of concentrated suspensions under {C}ouette and {P}oiseuille flow},
url = {https://link.springer.com/article/10.1007%2Fs10665-018-9954-x},
volume = 111,
year = 2018
}