Two-phase flow model for concentrated suspensions
- Ahnert, Tobias
- Münch, Andreas
- Wagner, Barbara
2010 Mathematics Subject Classification
- 35Q35 76T20
- concentrated suspension, jamming transition, phase space methods, free boundary problem, numerical methods
A new two-phase model is derived that make use of a constitutive law combining non-Brownian suspension with granular rheology, that was recently proposed by Boyer et al. [PRL, 107(18),188301 (2011)]. It is shown that for the simple channel flow geometry, the stress model naturally exhibits a Bingham type flow property with an unyielded finite-size zone in the center of the channel. As the volume fraction of the solid phase is increased, the various transitions in the flow fields are discussed using phase space methods for a boundary value problem, that is derived from the full model. The predictions of this analysis is then compared to the direct finite-element numerical solutions of the full model.
- European J. Appl. Math., 30 (2019), pp. 585--617 (published online on 04.06.2018), DOI 10.1017/S095679251800030X .