Avalanche Mixing Research Articles

Avalanche mixing and the simultaneous collapse of two media under uniaxial stress.

Avalanches in coal and sandstone samples under common uniaxial stress serve as a model for mixing of avalanche exponents in ceramics, multiferroics, and alloys. The two media are sandwiched together and subjected to common uniaxial stress using high- and low-stress compression. Each medium collapses individually through avalanches that often coincide with secondary avalanches into the other medium. The total avalanche time sequence allows a detailed investigation of the mixing by superposition and delayed coincidence. Correlations can be described by an inter-media Båth's law.

Time of avalanche mixing of granular materials in a half filled drum

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference $\delta$ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time $\tau$ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when $\delta$ is an integer part of $\pi$. Introduction of fluctuations of $\delta$ supresses the singularities of $\tau(\delta)$ and smoothes the dependence $\tau(\delta)$.

Modeling continuous mixing of granular solids in a rotating drum

We consider the avalanche mixing of a monodisperse collection of granular solids in a slowly rotating drum. Although not yet well understood, this process has been studied experimentally for the case where the drum rotates slowly enough that each avalanche ceases completely before a new one begins. We develop a mathematical model for the mixing in both the discrete avalanche case and in the more useful case where the drum is rotated quickly enough to induce a continuous avalanche in the material but slowly enough to avoid significant inertial effects. This continuous model in turn provides a more plausible model of the discrete avalanche case. Although avalanches are inherently a nonlinear phenomenon, the mathematical model developed here reduces to a linear integral equation. The asymptotic behavior of the solution for an arbitrary initial distribution is consistent with those obtained experimentally.

Characteristic time of avalanche mixing of granular materials

Fractions of a granular material are mixed in a cylinder rotating slowing about its horizontally oriented longitudinal axis. The cylinder is not completely full, and at any instant, mixing occurs only on the free surface of the material. The complete dependence of the characteristic time of such so-called avalanche mixing on the fill level of the cylinder is constructed within a simple geometric approach. This dependence faithfully describes the actual experimental curve. Near the critical point of half-filling, at which mixing to a homogeneous state does not occur, the reciprocal of the characteristic mixing time is proportional to δ2 ln(|δ|−1), where δ is the deviation of the fill level from half-filling.

Avalanche mixing of granular materials: Time taken for disappearance of the pure fraction

An analysis is made of the mixing of two fractions of granular material in a slowly rotating drum: a partially filled cylinder rotates slowly about its longitudinal axis, which is positioned horizontally, and the granules can only pour onto the free surface of the material. The time taken for both of the pure fractions to disappear completely in the regions adjacent to the surface of the drum is obtained and its stepped dependence on the degree of filling of the drum and on the volume ratio of the mixed fractions is constructed.

Anomalies in avalanche mixing of granular material at half filling

Two fractions of granular material mix in a drum rotating slowly about its longitudinal axis arranged horizontally. The drum is filled not to full capacity, and mixing occurs at each moment of time only on the free surface of material. It is shown that in a half-filled drum the material will never reach uniformly mixed state. Near this critical point, the inverse characteristic mixing time is proportional to δ2 ln(|δ|−1), where δ is the deviation from the half-fill level.

Kinetics of avalanche mixing of granular materials

The problem of the avalanche mixing of two fractions of granular material is solved. Mixing of the fractions takes place in a cylinder that rotates slowly about its longitudinal axis, which is positioned horizontally. The cylinder is not filled completely and at all times mixing only occurs in the surface layer of granules. It is shown that, depending on the relation of the volumes of the fractions and the volume of the empty space, mixing can take place slowly, over a large number of rotations, in a diffusive regime with convection or rapidly, by the time the cylinder has turned through a small angle. The mixing process is described analytically in terms of a purely geometrical approach and can, in a number of situations, be reduced to a sequence of discrete mappings. The characteristic mixing times are determined, including the times over which one or the other of the pure fractions no longer exists in the regions adjacent to the surface of the cylinder. Their dependence on the degree of filling of the cylinder and on the ratio of the volumes of the fractions is found.

Mixing of granular materials in a half-filled rotating drum

The process of avalanche mixing of two fractions of granular material in a half-filled rotating drum is described accurately and it is shown that under these conditions, the fractions do not generally undergo complete mixing.

Avalanche mixing of granular solids

THE production of many goods, ranging from pharmaceuticals and foods to polymers and semiconductors, depends on reliable, uniform mixing of solids. Although there have been several notable recent advances1–6, solid mixing processes are still poorly understood. We can neither qualitatively nor quantitively determine the effectiveness of any given mixing process in advance. In contrast to the case of liquid mixing7, we do not have a widely accepted theoretical basis that describes the mixing of solids. Moreover, we cannot determine whether a given set of solids will mix or separate during a specified stirring process8–23. As a step towards uncovering the basic physical principles, it is helpful to analyse systems that are both experimentally and theoretically tractable. Here we describe a geometric technique for the analysis of slow granular mixing processes, as are commonly encountered in industry. By comparing our calculations with experiments on thin rotating containers partially filled with coloured particles, we demonstrate that the mixing behaviour of powders in slow flows can be divided into geometric and dynamic parts. For monodisperse, weakly cohesive particles, geometric aspects dominate.