Results

Interacting drops made of grains with an horizontal offset

Let us consider two drops made of grains falling one behind another with an horizontal offset in a viscous fluid. The classical evolution of each Stokes drop is perturbed by the presence of the other drop. Initially, each drop interacts with the fluid causing a circulating velocity field around them. The velocity field of the lower drop attracts the upper drop forcing the upper drop to lengthen while the lower one flattens. The interaction between the two circulating velocity fields forces the upper drop to drill the lower one and cross it. Then, the initially upper drop slows down and wrap the initially lower one. The grains mixed together to form an unstable open torus that could break up into two or three droplets.

Injection of water in immersed granular matrix

Fluidization of immersed granular flows is an important technique due to its use in drying, segregation, mixing, airing… processes. It is also possible to use air injection to deteriorate contaminants in soil remediation. Numerical simulations are of considerable interest to study injection area and observe invasion patterns. Particularly, it seems to be interesting to estimate, through simulations, what is the injection flow rate required to fluidize the granular bed. Studying the fluidization area, it is possible to observe that the injection flow rate required to fluidize the granular bed is greater than the injection flow rate required to maintain the fluidized area. This hysteretic behavior is often attributed to the friction that creates grains arches in the granular matrix. However, for granular matrices with equal radius grains geometrical effects are in competition with frictional effect. It explains why the hysteresis can also be observed without friction between grains.

Granular motion in tumbling mills

Tumbling mills are widely used in the industry in various processes such as mixing, centrifuging or crushing particles. The motion of the granular phase inside the mill has been shown to depend on the Froude number, that quantifies the centrifugal acceleration with respect to gravity. As this number increases, the grains undergo the four different regimes that can be seen in the upper part of the video below (respectively rolling, cascading, cataracting and centrifuging) that have different industrial applications. In the presence of a fluid, shown for the case of sand in ethanol in the lower part of the video below, the transition between the regimes is much faster. Indeed, at a low Froude number (0.1) the grains already are in a cascading regime, and for the above Froude numbers they experience centrifuging, with time to complete solid rotation decreasing with increasing Fr.

Granular drag on a cylinder

The drag force exerted on a cylinder that moves through a granular medium, dry or immersed exhibits a peculiar behaviour in terms of velocity. At low velocities, the drag force is independent of the velocity. This is because the grain network reorganisation that is necessary for the cylinder to move through dominates. At higher velocities, the momentum transfer between the grains takes over and the drag force strongly increases with velocity. The presence of an interstitial fluid reduces the drag force because of the modification of the apparent weight of the grains, and causes a velocity dependence at lower velocities.

Grain sorting using water jigging

A pile of grains with different densities can be sorted using water jigging, i.e. periodically injecting and pumping water through them in an oscillating motion. Indeed, the difference in suspension and settling velocities of the grains will lead to their respective segregation. Simulations show that the initial configuration of the pile is a key parameter. The density sorting is faster when the least dense grains are able to gather and form agglomerates rising to the top of the pile, instead of slowly diffusing through. The sorting rate also depends on the drag force intensity and the density ratio between the two types of grains. A sensitivity analysis on the friction coefficients revealed that the most significant one is the one between the denser grains and the walls. A higher value prevents the motion near the walls and favours the water flow at the centre, leading to a higher drag force and thus to a faster sorting.

Faraday waves

Faraday waves are standing waves that occur when a liquid is periodically shaken above a threshold frequency. The observed pattern depends on frequency, container shape and fluid properties. MigFlow is able to simulate such phenomena thanks to a free surface model based on an Arbitrary Lagrangian-Eulerian (ALE) method.