Lattice Boltzmann study on sedimentation behavior of two porous particles with different Darcy numbers in a narrow channel

This study investigates the sedimentation behavior of two porous particles under gravity in a two-dimensional (2D) infinite channel using the multiple-relaxation-time lattice Boltzmann method. Three cases of initial configurations are considered for the Darcy number (Da) of particles, i.e., two particles with identical Da (case 1); the trailing particle with higher Da than the leading particle (case 2); and the leading particle with higher Da than the trailing particle (case 3). The dynamics of the drafting, kissing, and tumbling (DKT) process are examined during the particle-pair sedimentation. The results show that the increase in Da reduces the settling velocity and weakens the wake-induced hydrodynamic effects between particles, which enhances their ability to maintain the vertical alignment upon contact. When the Darcy number becomes sufficiently large, the increased fluid penetration through the particles enhances the flow velocity in their wake, which makes the two porous particles no longer come into contact while maintain a stable gap. Depending on the combination of Da for the particle pair, several sedimentation modes are identified in a phase diagram, including periodic, staggered equilibrium, aligned equilibrium, and individual settling modes during the DKT process. Especially, when the trailing particle holds a large Da, the two porous particles may span multiple transitions from periodic state to individually settling state. These findings provide new insight into porous particle interactions and may guide the control of particle settling in engineering applications, such as fluidized beds and mineral separation.