The measurement of the sedimentation velocity of an ensemble of many spheres as a function of the volume fraction constitutes a more realistic test than the two above. As in the case of the fixed sphere arrangement in the two preceding tests we choose periodic boundary conditions on our sample cell that now, however, contains many spheres whose position and orientation can evolve dynamically without artificial kinematic constraints.
Gravitation acts as the driving force via the density difference of particles and fluid.
In 2D, we assured by test simulations on single falling discs that we are in the same range of Reynolds numbers. As motivated in Sec. Their number is taken to be the integer part of i.e., approximately equal to the number of fluid volume elements on the surface of each particle. The mean sedimentation velocity is measured in experiments either as the velocity with which the upper front of the particle rich phase settles or, when single particle velocities can be measured, as the mean velocity of the particle phase. This procedure takes some corrections due to finite cell size and Reynolds number into account.