Diffusional mixing in an ideal system

Shape dynamics of interfacial front in rotating cylinders

“…[15] was a radial segregated core of small particles and not a mixture as in Refs. [10,17]." It was found experimentally [2,6] and numerically [18] that a nearly complete radial segregation can be achieved after only a few rotations.…”

“…Assuming random particle motion in the axial direction (z axis), one component systems could be well described by a diffusion process according to Fick's Second Law [10,17]. The interface of a two component system can also be studied in this fashion and the diffusion equation reads…”

“…Hogg et al [10] solved a similar diffusion problem for a single component system by replacing the time derivative with the derivative with respect to the number of rotations thus assuming that the dynamic effects on the diffusion process was not significant within the range of the rotation rates studied. Nakagawa et al [15] investigated a mixing process of 50-50 mixtures of liquid filled pharmaceutical pills of different sizes.…”

Mixing and Segregation in Powders: Evaluation, Mechanisms and Processes

“…At the same time, however, the increase in the expected variance can mask the effects of small, but significant long-range variations. For example, in a study of axial mixing in a rotating cylinder 9) it was found, using samples of about 500 particles, that the observed sample variance became equal to the expected value after about 70,000 revolutions of the drum. At that stage, however, there remained a small but detectable and significant variation in composition along the length of the cylinder.…”

Resolving a paradox of anomalous scalings in the diffusion of granular materials

“…For decades this macroscopic approach has been the accepted engineering model for granular diffusion (28)(29)(30). Moreover, Barenblatt's intermediate asymptotics theory (31) indicates that solutions to Eq.…”