Understanding the Major Mechanisms and Controlling Parameters of Size Segregation

Introduction

Size segregation is an important process in the quality control of granular products, where complicated mechanisms are involved from both the macroscopic and particle-scale perspectives. To understand the major mechanisms, as well as the main parameters controlling how fast and how much segregation would take place, is of great interest. With such knowledge, theoreticians can predict segregation with a more physics-based modeling that considers functional forms of real parameters^1,2, while practitioners in the industry can better control the handling and processing of the mixing/de-mixing of granular materials³. This study aims to provide in-depth understanding of the major mechanisms and controlling parameters of size segregation, at both the continuum (theoretical) and the particle scales.

Theoretical background

Different mechanisms have been proposed for segregation induced by vibration, shear, or other forms of agitation. For the shear-induced segregation occurring in a heap flow or a chute flow, kinetic sieving and squeeze expulsion are widely accepted mechanisms⁴. The former refers to the gravity-driven percolation of small particles through the opening of gaps due to shear, while the latter attributes the upward migration of large particles to the imbalanced contact forces. The squeeze expulsion mechanism has been refined by recent particle-scale measurements from both laboratory experiments and numerical simulations^5,6, which show that the preferential rise of large particles originates from the local shear within the anisotropic contact network of a shear flow. Subject to shear, larger particles tend to roll over the lower neighbors, thus a tendency of rising towards the surface. In contrast to large particles, the role of shear is not significant in the percolation of small particles. The distinct role of shear (thus of friction) seems to underlie the recently-reported asymmetric behavior of segregating large and small particles⁷. The asymmetry is known to depend on the concentration of particle species; a small particle in its dilute regime segregates faster than its large counterpart.

From the major mechanisms reviewed above, several controlling parameters can be inferred for the shear-induced size segregation, namely, shear rate, size ratio, constituent concentration, and the strength of friction. Noting that in a gravity-driven flow (e.g., a chute flow) the system’s shear rate level is determined by gravity and the angle of inclination, the controllable parameters become slope angle, size ratio, concentration, and the coefficient of friction. While the first three parameters are either explicitly or implicitly considered in the continuum theory of segregation, the role of friction has not been accounted for yet.

Methods

We perform numerical experiments using the discrete element method (DEM). The numerical setup consists of a simulation box with periodic boundaries in the side and the flow directions, a rigid base roughened by fixed particles, and a free surface. A binary mixture of large and small particles is generated. The setup mimics a steady, well-developed bidisperse granular flow down an inclined plane.

Four major parameters, namely, slope angle (θ), size ratio (sr) , the overall concentration of large particles (Φ_l) , and the coefficient of friction (µ), are varied systematically for detailed analyses. A reference case is configured as follows: θ = 25°, sr = 2, Φ_l = 0.5, and µ = 0.5. The parameter space is θ ∈ [20,36]°, sr ∈ [1.2,4], Φ_l ∈ (0,1), and µ ∈ [0.1,1]. While one parameter is varying, other parameters remain default as in the reference configuration.

We measure mechanical and kinematic properties with the progress of segregation. The major results regarding segregation is the final degree of segregation, α_f, and the time spent before segregation completes, t_seg. The main mechanical properties include the partial coordination number and contact forces in large and small particles.

Results

Slope angle – When the inclination is just sufficient to initiate the flow (θ<24°), it is the gap opening due to increasing slope angle (thus increasing shear rate) that promotes segregation; the time to segregation t_seg decreases rapidly. The dominant mechanism in this regime is kinetic sieving. As slope angle further increases, a significant negative effect on segregation is observed, which comes mainly from two mechanisms: on one hand, the normal component of gravity that drives the phase separation declines. On the other hand, the increasing diffusive strength largely balances the segregation process, especially near the dilation-induced dilute surface region.

Size ratio – When sr is small and α_f increases significantly with sr, kinetic sieving is the dominant mechanism for segregation to occur; the forces carried by large (small) particles start to rise (decline) with sr . When sr rises above 2, since the voids created by large particles are filled by small particles, the enhancing effect on the percolation of small particles tend to saturate; the portion of forces on small particles becomes insensitive to the change of sr; contacts among large particles possess only a very small percentage. When sr is beyond 3, small particles overfill the voids among large particles, leaving the large ones isolated from each other; the forces transmitted through large particles do not increase further, while a small rise can be observed on the forces taken by small particles. The effect of increasing size ratio reaches a saturation in this last regime.

Concentration – The global concentration of large particles, Φ_l, affects segregation by two major mechanisms. Firstly, a higher Φ_l means a thinner layer of small particles atop the larger ones in the initial configuration, thus a smaller distance for all large particles to travel before segregation finishes. Secondly, a different Φ_l may result in different distributions of local concentration that has a leading-order influence on the behavior of segregation. The latter changes segregation significantly only when Φ_l is close to the extreme values, i.e. the single intruder cases; in its moderate range, the average segregation behavior remains similar.

Friction – Friction tends to enhance the upward migration of large particles. A positive correlation is observed between the degree of segregation and the probability of a particle’s rotation relative to its neighbors, which is characterized by the width of the probability density function of rotational velocities. This supports the argument that the rotation associated with shear underlies the effects of friction on the maximum extent of segregation⁶.

Conclusion

This study explores the effects of four major parameters controlling the speed and the extent of segregation in chute flows, i.e., slope angle, size ratio, concentration, and friction. A wide parameter space is applied, ranging from the moderate values to extremes values. Interesting changes of trend are observed, indicating a change of the dominant mechanism(s) for segregation to occur. We explain these trends with the measurements from both the continuum and particle scales. The knowledge gained in this study is expected to be translated to more physics-based formularizations in the segregation theory, especially the role of friction, which is crucial for a better control of granular segregation in the application of powder technologies.

References

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