Separation by Gravity

Segregation refers to the separation of bulk materials, powders or granules, which can occur after a mixing process or during transport, storage or conveying. In this process, the particles separate from one another due to their differing properties, such as particle size, density, shape or surface texture.

Typical segregation mechanisms include percolation (also known as sieve segregation), density segregation, inertial segregation, and segregation due to differences in angle of repose and flow behaviour. Segregation frequently occurs during the filling of silos, during pouring, during pneumatic conveying, or as a result of vibrations. It can significantly impair the homogeneity of a product. Kinetic models, continuum mechanics models and empirical parameters are usually employed to describe segregation in solid powders. A frequently used approach is the advection-diffusion-segregation model. This model describes the interplay between directed segregation and counteracting mixing.

∂c/∂t = − ∇· (v_s c) +∇·(D_(eff) ∇c)

Here, c represents the local concentration of a particle fraction, v_s the segregation velocity and D_(eff) the effective dispersion coefficient. The term −∇·(v_s c) describes directed segregation, for example due to percolation or the influence of gravity. The term ∇·(D_(eff) ∇c) represents compensatory mixing due to random particle motion.

In size-driven segregation, where smaller particles trickle through larger ones, a proportional relationship is often assumed.

v_s = k · g · (Δd/d_m) ; Δd = d_g−d_k)

Here, v_s represents the segregation velocity, g represents gravitational acceleration, d_g represents the diameter of large particles, d_k represents the diameter of small particles, Δd represents the particle size difference, d_(mean) represents a characteristic mean diameter, and k represents an empirical proportionality factor.

In the case of density-driven segregation, the equation can be formulated analogously:

v_s ∝ g ((ρ_s − ρ_L)/ρ_L)

Here, ρ_s is the density of the solid particles and ρ_L is the density of the surrounding phase. This relationship corresponds to a granular buoyancy analysis. A segregation index is often defined for the quantitative assessment of segregation.

S = σ / σ_(max)

Here, σ is the standard deviation of the concentration, and σ_(max) is the maximum possible standard deviation. When S = 0, the mixture is ideal; when S = 1, complete segregation occurs. For free-flowing bulk materials in inclined layers, the Gray-Thornton model is frequently used.

∂c/∂t +∇·(c · u) + ∂/∂z (w_s · c · (1 - c)) = ∇·(D · ∇c)

Here, u is the mean flow velocity, w_s the characteristic segregation velocity and D a diffusion coefficient. The term w_s c (1 − c) describes a non-linear segregation flow, as occurs in granular avalanche flows.

In the practice of the bulk materials industry, segregation generally arises from the interaction of several mechanisms.

• Percolation,
• density differences,
• trajectory separation,
• air-induced fluidisation, and
• wall and boundary zone flows.

In this respect, practical mixing and filling trials often provide more reliable results than purely theoretical models, particularly for cohesive powders whose flow behaviour varies. Amixon GmbH offers testing facilities at well-equipped technical centres in Germany, India, Japan, China, Korea, Thailand and the USA.