Particle settling in yield stress fluids: Effect of porosity

Porous particles can be used for applications such as water purification. In certain applications, however, the working fluid might exhibit a yield stress. In this study, we have numerically investigated the effect of porosity on sedimentation behavior of a single circular porous particle immersed in a closed-ended two-dimensional vessel filled with a yield-stress liquid obeying Bingham–Papanastasiou (BP) model. Finite element software package COMSOL Multiphysics was used for the simulations. Volume-averaged macroscopic equations were used to model the flow of interstitial fluid through the porous particle. The interaction force between the interstitial fluid and the solid skeleton (modelled as a body force) was related to its porosity through Ergun's relationships. Simulations were carried out in a coupled Eulerian–Lagrangian framework. Numerical results obtained for centered particles suggest that porosity decreases the terminal velocity of particles in yield stress fluids. The impeding effect of porosity on particle terminal velocity is attributed to its effect on the viscosity field. Since a porous particle has a smaller weight, it exerts smaller stress on the surrounding liquid so that viscosity of BP fluid remains close to its zero-shear-viscosity. It is shown that, for any given yield stress, there exists a critical porosity at which the particle is practically arrested. For off-center particles undergoing non-monotonic migration toward the channel's centerline, it is shown that this behavior can be suppressed by increasing particle's porosity or fluid's yield stress. Non-uniform distribution of shear stress is shown to be the main driving force behind particle migration toward the centerline.