Two-phase flows for sedimentation of suspensions
- Peschka, Dirk
- Rosenau, Matthias
2010 Mathematics Subject Classification
- 35M33 76T20 76M10 76N99
- Two-phase suspension flow, free boundary problem, non-smooth dissipation, generalized gradient structure based on flow maps
We present a two-phase flow model that arises from energetic-variational arguments and study its implication for the sedimentation of buoyant particles in a viscous fluid inside a Hele--Shaw cell and also compare corresponding simulation results to experiments. Based on a minimal dissipation argument, we provide a simplified 1D model applicable to sedimentation and study its properties and the numerical discretization. We also explore different aspects of its numerical discretization in 2D. The focus is on different possible stabilization techniques and their impact on the qualitative behavior of solutions. We use experimental data to verify some first qualitative model predictions and discuss these experiments for different stages of batch sedimentation.