%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 }