Analysis of hydrodynamic drag forces acting on suspended fine particle in porous media

Abstract

An important class of flow and transport problems occurring in porous media involves the interactions between suspended fine particles and the moving fluid at Stokes limit. Historically, due to the complicated geometries of porous media, researchers have had to resort to simplifying assumptions to conceptualize the underlying physics. However, the advent of high performance computing, in recent decades, has made it possible to vigorously investigate this problem at the streamline scale level. In this work, the flow problem is solved by means of a finite-element model. The simulations results are used to compute the drag forces experienced by suspended fine particles. The drag force distributions experienced by suspended fine particles of different sizes in various compact granular porous media – ordered (simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC)) and monodisperse disordered packs are reported and discussed. It is concluded that, overall, the trends of the drag force distribution in the face centered cubic (FCC) pack are the closest to those of the disordered pack, despite the considerable difference in their porosity values (~10). Moreover, analyzing the pressure and viscous fractions of the hydrodynamic force experienced by each individual fine particle, it is concluded that the locations where the largest deviations from the Stokes law occur in all the domains have the same spatial characteristic, such as close proximity to grain-to-grain contact points. Similar spatial characteristic is also seen regarding the locations of the smallest and the largest ranges of the drag force in all the different granular domains. It is also seen that the polar circulation zones, which only forms in the SC and the BCC packs, causes unexpected trends in the drag force distributions of particle, which are fully or partially inside these zones. Furthermore, the simulation results are compared with the drag force predictions obtained via the Happel model. The results of the semi-analytical approach, more or less, capture the trend of the drag force distribution obtained via simulation in the FCC and ordered packs, however, the semi-analytical results can significantly underestimate the drag force experienced by the suspended, fine particles.The influence of neighboring suspended fine particles on each other is also briefly analyzed using our direct numerical approach.