Border between layering and agglomeration

In particle formation processes in spray fluidized beds, usually both size enlargement mechanisms (layering and agglomeration) occur simultaneously. However, in order to achieve the required product quality, only one mechanism depending on the application of the product is desired. In this case, the material properties as well as the process parameters need to be adjusted to favor either layering or agglomeration. The amount of properties and parameters influencing the dominating mechanism opens up a wide field of investigation.

Many studies investigating the border of the size enlargement mechanisms experimentally can be found in literature. Some investigations focus on the detection of defluidization [59, 60] occurring when agglomeration leads to very large particles and the mass flow rate of the fluidization gas cannot maintain the fluidized state. Others deal with the direct measurement of the mass fraction of agglomerated particles [34, 37, 61, 62]. In any case, these studies are focused on coating experiments, where agglomeration is undesired and should be avoided. According to the mentioned works,

Chapter 2 Particle formation in spray fluidized beds

agglomeration is more pronounced if particle size, bed temperature, mass flow rate, and evaporation capacity of the fluidization gas are decreased and the spraying rate and droplet size are increased.

Theoretical studies regarding the border of layering and agglomeration are also available in the literature. Below, the criteria presented by Akkermans et al. [63], Davis et al. [64] and Barnocky and Davis [65] are discussed.

Akkermans et al. [63] presented a criterion predicting the dominant size enlargement mechanism for the production of detergent agglomerates. A dimensionless number called Flux-number FN was introduced, which is defined as:

FN=log 𝜚_p 𝑢_g −𝑢_mf𝐴_spray 𝑀¤_spray

!

. (2.3)

In this equation,𝜚_pis the density of the particles,𝑢_g−𝑢_mf is the difference between the gas velocity and the minimum fluidization velocity (also known as excess gas velocity),𝑀¤_sprayis the mass flow rate of the spray, and𝐴_spray is the contact area between each spray cone and the particle bed. A classification of the size enlargement mechanisms based on the works of Wasserman et al. [49] and Akkermans et al. [63] is given by Boerefijn and Hounslow [21] and Boerefijn et al. [50]:

• Flooding: Flooding will occur if FN<2. The result is rapid agglomeration leading to defluidiza-tion.

• Agglomeration: In order to achieve agglomeration without defluidization, the condition 2≤ FN≤ 3.5 must be fulfilled.

• Layering: Particle growth by layering will occur if FN>3.5.

Hede et al. [61] suggest that higher values for the Flux-number are needed to ensure size enlargement by layering since they found layering to be the dominant size enlargement mechanism for FN ≥ 4.5. . .4.7.

Further investigations focus on the description of binary, normal collisions between particles in spray fluidized beds. In these studies, two spherical particles with a radius𝑅approaching each other with a velocity𝑢_colland covered with a liquid layer of thicknessℎ_l and viscosity𝜂are considered.

Davis et al. [64] consider particles with a smooth surface (no surface roughness). Upon collision, the approaching particles are slowed down due to viscous forces of the liquid. A large pressure develops in the liquid, which may additionally lead to elastic deformation of the particles. Barnocky and Davis [65] consider two colliding spherical particles with a surface roughnessℎ_acovered by a liquid layer, based on a theory presented by Davis [66]. In this case, the particles are also slowed down by the liquid layer. When the particles come into contact at the surface roughness elements, they may also deform elastically. In both cases, particles will stick together and agglomerate if their kinetic energy is dissipated during the collision. Otherwise, rebound will occur.

In both approaches, the particles are characterized by their viscous Stokes number Stv. The condition for rebound is met if a critical value Stcritis exceeded. Therefore, the general condition for successful

2.2 Size enlargement of particles in spray fluidized beds

agglomeration can be expressed as:

Stv ≤Stcrit. (2.4)

The viscous Stokes number is defined as:

Stv= 2 3

𝑀_p𝑢_coll

𝜋𝜂𝑅² , (2.5)

where𝑀_pis the mass of the colliding particles,𝑢_coll is the collision velocity,𝜂 is the viscosity of the liquid layer, and𝑅is the radius of the colliding particles. If size and mass of colliding particles are not equal, the harmonic mean values of the individual masses and radii can be used as shown in literature, see Terrazas-Velarde [15] and Tardos et al. [67]. The definition of the critical viscous Stokes number depends on the morphology of the particles (smooth or rough surfaces). For smooth surfaces, Stcrit becomes [68]:

Stcrit = 2

5 ln 4√ 3𝜋 𝛱2

!

. (2.6)

In this equation,𝛱 is a dimensionless elasticity parameter, which is defined as:

𝛱 = 4𝛩𝜂𝑢_coll𝑅^3/2

ℎ_l^5/2 with 𝛩 = 1−𝜈₁⁰²

𝜋𝐸₁ + 1−𝜈₂⁰²

𝜋𝐸₂ . (2.7)

The parameter𝛩can be calculated using Poisson’s ratio𝜈⁰and the Young’s modulus𝐸 of particle 1 and 2. For rough surfaces, Stcrit becomes [65]:

Stcrit = 1+ 1

𝑒⁰ lnℎ_l

ℎ_a

. (2.8)

In this equation,𝑒⁰is the coefficient of restitution of the particles andℎ_ais the height of the surface asperities (surface roughness).

The criterion for the collision of two particles with rough surfaces was later used by Ennis et al. [69]

two derive a classification of the size enlargement mechanisms:

• Noninertial regime: In this regime Stv/Stcrit →0. This means that Stvis always smaller than Stcritand consequently all collisions lead to agglomeration as long as a liquid layer is present.

The distribution of the liquid controls the agglomeration process.

• Inertial regime: The largest Stokes numbers equal the critical value (Stv,max ≈Stcrit). The kinetic energy of the particles and the layer viscosity start to play a role.

• Coating regime: The average Stokes number equals the critical value (Stv ≈ Stcrit). Particle growth by agglomeration is not achieved since coalescence and rebound compensate each other. Instead, the particles grow only by layering.

Chapter 2 Particle formation in spray fluidized beds

An extended criterion taking plastic deformation of the colliding particles into account has been presented by Liu et al. [70]. However, the present work focuses on non-deformable, elastic particles, which is why a detailed discussion of the model by Liu et al. [70] is omitted.

In contrast to theoretical approaches dealing with normal collisions described above, Donahue et al.

[71, 72] present theoretical and experimental work on oblique collisions between particles. They have found that the above shown Stokes criterion (derived for normal collisions) is able to describe the outcome of oblique collisions as well. However, when a certain impact angle is exceeded, particles may separate after successful agglomeration, although the Stokes criterion is met. This observation is attributed to centrifugal forces arising from rotation of the agglomerate, leading to breakage of the liquid bridge. A dimensionless number (i.e., the centrifugal number) is proposed to characterize the influence of centrifugal forces.

The above shown criteria allow an estimation of the dominant size enlargement mechanism based on parameters on the single particle level. The decision whether a collision is successful depends on the properties of the particles (i.e., size, density, surface roughness, velocity, elasticity) and the liquid film (i.e., height and viscosity). As shown by Tsotsas [56], drying influences the liquid film properties, but also the area covered by deposited droplets. The latter also plays a role since wet spots must be present at the contact points for agglomeration to occur. In this way, drying influences not only the kinetics of the particle formation process, but also which size enlargement mechanism dominates.

Both criteria (Flux-number and Stokes criterion for normal collisions) have been tested experimen-tally in the frame of spray fluidized bed layering granulation by Hede et al. [61] and Villa et al. [73]

using urea and sodium sulfate, respectively. In both cases, layering was the desired size enlargement mechanism, which was also predicted by both criteria. However, in some cases high percentages of agglomerates were measured, indicating that more complex criteria are required. For example, the wet particle surface also plays a role as discussed above and should therefore be included in such an extended criterion.