Distribution nucleation: Quantifying liquid distribution on the particle surface using the dimensionless particle coating number
Graphical abstract
Highlights
► The five steps in distribution nucleation were defined. ► New dimensionless parameter, particle coating number, was derived and experimentally validated. ► Fractional coating can be predicted in advance based on simple parameters. ► Particle coating number is expected to improve modelling studies and to aid process control of fluidised bed granulation.
Introduction
Wet granulation is an important process which converts powders into structured granules by adding a liquid binder, and in so doing improves powder flow, increases bulk density, minimises dust and reduces segregation. Granulation is used in a broad range of industries, including in the chemical, pharmaceutical, food, and, mining industries. Each industry has its own specialised granulation equipment, including pans, drums, mixers, and fluidised beds (Litster and Ennis, 2004). During granulation, there are three general mechanisms that can occur simultaneously or in rapid succession: wetting and nucleation, growth and breakage (Iveson et al., 2001). The balance of these mechanisms depends on the equipment design, formulation, and operating conditions.
Nucleation is the first mechanism where the powder is wetted by the binder fluid and the initial “nuclei” granules are formed. The liquid binder usually is added via an atomised spray, particularly for fluid bed granulation (Boerefijn et al., 2009, Hede et al., 2008, Schaafsma et al., 1999, Schaafsma et al., 2000, Schæfer and Wørts, 1977, Seo et al., 2002).
There are two nucleation mechanisms which are distinguished by the relative ratio of binder droplet diameter ddrop to the particle diameter dparticle. The first mechanism, known as “immersion nucleation,” occurs when the small powder particles get immersed in a relatively large binder droplet (ddrop>dparticle). Over the last decade, research on immersion nucleation has become well established (Abberger et al., 2002, Ax et al., 2008, Chouk et al., 2009, Hapgood et al., 2010, Hapgood et al., 2002, Hapgood et al., 2003, Hapgood et al., 2004, Hapgood et al., 2009, Iveson et al., 2001, Johansen and Schæfer, 2001, Lee and Sojka, 2011, Litster et al., 2002, Litster et al., 2001, Marston et al., 2010, Nguyen et al., 2009, Oullion et al., 2009, Plank et al., 2003, Seo et al., 2002, Wildeboer et al., 2007, Wildeboer et al., 2005). The large droplet contacts the powder particles and produces a highly saturated initial nucleus, where the size is proportional to the size of the drop (Ax et al., 2008, Hapgood et al., 2003, Schaafsma et al., 2000, Waldie, 1991). There are generally five steps in immersion nucleation (see Fig. 1), starting with the (1) formation of the droplets; (2) droplet impact on the powder surface and possible breakage (Agland and Iveson, 1999, Chouk et al., 2009, Lee and Sojka, 2011, Marston et al., 2010); (3) droplet coalescence at the powder surface; and ending with the (4) penetration of the drop into the powder bed and/or the (5) mechanical dispersion of the droplet through the powder (Hapgood et al., 2003).
The second mechanism, known as “distribution nucleation”, occurs when a large powder particle is wetted by small binder droplets distributed over the particle surface (ddrop<dparticle). Distribution nucleation is poorly understood (Boerefijn and Hounslow, 2005, Štěpánek and Rajniak, 2006), although there is a wealth of literature on fluid bed coating of particles, where there are clear similarities (Hemati et al., 2003, Karlsson et al., 2011, Nienow, 1995, Panda et al., 2001, Teunou and Poncelet, 2002, Turton and Cheng, 2005), particularly since small atomised drops are used to form a coating layer around the exterior of larger particles. However, granulation (or agglomeration) of the coated particles is considered an undesirable side effect of coating processes (Boerefijn et al., 2009).
Coating begins with the droplet deposition on the particle surface, which includes the impact, wetting and spreading of the fluid over the surface (Karlsson et al., 2011, Link and Schlunder, 1997, Panda et al., 2001). Gradually, more and more drops cover the particle surface, gradually forming a wet coating layer. Simultaneous drying within the fluid bed causes the coating to dry and minimises agglomeration of the particles. However, if the flux of fluid is too high (Boerefijn et al., 2009, Hede et al., 2008), the bed will become too wet, allowing liquid bridges to form between colliding particles, which may results in agglomeration of the coated particles.
Building on the existing work on coating, we define the five stages of distribution nucleation, as shown in Fig. 2. Initially, the binder fluid must be atomised into droplets which are significantly smaller than the particles to be granulated. Step 2 indicates a single droplet impacting on the particle and creating a solid–liquid interface, which will be affected by a range of processes including surface chemistry, fluid rheology, drop dynamic spreading and contraction, particle roughness, interaction with adjacent droplets, the overall drying rate etc. until the drop reaches a pseudo-equilibrium position on the particle surface.
Step 3 in Fig. 2 shows the particle coating stage, where the particle is gradually covered by more and more droplets. Each droplet successfully deposited increases the fraction of the particle surface area which is coated with droplets. The random distribution of the droplets landing of the particle surface will not be uniform, and as a result the particle will not be uniformly wetted (Karlsson et al., 2011, Panda et al., 2001, Rajniak et al., 2007, Štěpánek and Rajniak, 2006). Steps 1–3 of distribution nucleation have been investigated in numerical volume of fluid (VOF) and Monte-Carlo simulations by Štěpánek and Rajniak (2006). In a VOF simulation, droplets were deposited (stage 1) randomly onto particles of varying roughness. The drops were allowed to spread over the undulating particle surface and reach an equilibrium position before another drop was added. These simulations produced elegant 3D representations of droplets coating single particles as a function of droplet size, particle roughness, and the equilibrium contact angle of the fluid on the solid. They tracked the increase in the liquid coverage of the particle surface, called the “surface coverage”, as more drops were deposited on the particle. The surface coverage fraction was initially directly proportional to the number of drops deposited on the particle, but as the drop density increased, the probability of each new drop landing on the dry section of the particle decreased. As a result, the rate of increase of the particle surface coverage levelled off and asymptotically approached 100% (Štěpánek and Rajniak, 2006). The fraction of the particle surface covered ψ as a function of the liquid to solid ratio xLS was fitted to empirical curves of the form:where k is a fitting parameter, fitted for each set of experimental simulation condition (e.g., same roughness and contact angle). The simulations also showed that liquid is not uniformly distributed over the particle surface and that the surface coverage is affected by the particle roughness. These simulations were later used to model real pharmaceutical formulations and explain differences in the experimental growth curves (Rajniak et al., 2007, Štěpánek et al., 2009).
The final two steps of distribution nucleation shown in Fig. 2 are inter-particle collisions (step 4) and the formation liquid bridge (step 5) to create a nucleus granule. Nucleation is defined here as the beginning of agglomeration and therefore involves more than one particle held together by a liquid bridge. In the case of immersion, nucleation is initiated the instant that the droplet meets the powder as it covers more than one particle at collision. In the case of distribution nucleation, nucleation is not instantaneous; it requires two or more partially wetted particles colliding at their wetted region. This collision results in liquid bridges being formed between the particles, which form stronger and more rigid bonds as they dry. To increase the chances of two partially wetted particles forming a liquid bridge and initiating nucleation, adequate surface coverage is required. Particles with low surface coverage which collide may not form a liquid bridge after collision, either because they collided at a dry patch, or because the volume of liquid in the collision zone was insufficient to form a liquid bridge. However, adding excess liquid to create a high surface coating of the particles increases the cost, the granule growth rate and risk of uncontrolled granulation, and drying time and energy.
Whether a nucleus granule forms depends on several factors—the collision velocities, the fluid properties, the particle roughness and the amount of fluid present at the contact point (Ennis et al., 1990, Ennis et al., 1991). Specifically, the probability of a collision resulting in a stable liquid bridge between two particles i and j after a collision Cij can be written as (Štěpánek et al., 2009):where ψij are the physical and geometric success factors. The physical success factors can be calculated by the Stokes’ coalescence models (Ennis et al., 1991, Liu et al., 2000) and are relatively well described. A major contributor to the geometric success factor is the presence or absence of liquid at the collision point (Štěpánek et al., 2009). Determining whether there is liquid at the contact point has so far been impossible, let alone whether there is sufficient liquid at the contact point to form a liquid bridge. Whilst the sophisticated model of Štěpánek and Rajniak (2006) could, in theory, be applied during fluid bed simulations, the model would be extremely complex and this approach is currently impractical.
In addition, there will also be a distribution of the number of drops deposited per particle, which adds a further level of variation in the liquid coating of the fluidised particles. Understanding both the variation in liquid coating between particles as well as over the surface of a single particle has, to date, been an extremely complex undertaking. In this paper, we are focussing on the liquid distribution over the surface of a single particle—separate work on understanding inter-particle coating variability is underway.
Although there are several dimensionless design groups for immersion nucleation, including dimensionless spray flux (Hapgood et al., 2004, Litster et al., 2001) and drop penetration time (Hapgood et al., 2002, Nguyen et al., 2009) which have been applied to a variety of processes (Ax et al., 2008, Cavinato et al., 2011, Chouk et al., 2009, Hapgood et al., 2010, Plank et al., 2003, Tan et al., 2009), there are currently no dimensionless groups which describe distribution nucleation. This is a serious gap in knowledge because nucleation in fluid beds tends to occur via the distribution mechanism (Boerefijn and Hounslow, 2005). Further study of distribution nucleation is required to develop a suite of design rules equivalent to the design rules developed for immersion nucleation.
There is currently no method to quantify the fractional surface coverage of a particle or to accurately predict whether two colliding particles will have sufficient local liquid to form a liquid bridge between the particles. This paper investigates distribution nucleation by deriving and validating a new dimensionless particle coating number Φp to predict the fractional coverage of a particle with liquid as a function of particle size, particle surface area, number of drops, and drop footprint area. The ability to accurately predict particle coating and surface coverage will have immediate applications in granulation modelling, process design and troubleshooting of fluid beds. In addition, it will advance our understanding of processes which involve either particle coating or distribution nucleation.
Section snippets
Bernoulli model for coating coverage F
The model system consists of a single particle being bombarded sequentially with droplets from uniformly random directions. This system is similar in concept to that of Štěpánek and Rajniak (2006); however, once deposited (ignoring overlap) all droplets cover the same footprint area on the surface of the particle. Theoretical model development then follows similarly to Freireich and Wassgren (2010) and Freireich et al. (2011); except the fractional area coated per coating event is smaller,
Materials and methods
To validate the dimensionless particle coating number Φp (Eq. (12)) and its relationship with the actual particle coating coverage fraction F (predicted using Eq. (13), (14)), experiments were conducted by depositing drops randomly on particles of different sizes and measuring the fraction of the surface coated with drops using image analysis. The particles used in this study were ping pong balls (PP) and polystyrene foam balls (FB) as summarised in Table 1.
Drops of polyethylene glycol
Selection of footprint area estimation method
The single droplet footprint areas measured and given in Table 2 may be compared to the models derived in Section 2.2.1 (Fig. 4). This figure shows that the projected footprint area given by Eq. (17) always under-predicts the measured droplet footprint. As expected the ping pong ball and foam balls seem to follow similar but separate trends. By adjusting the contact angle until the experimentally measured single footprint area agreed with the calculated footprint areas, the ping pong ball has
Deviations from predicted coating coverage
There are several causes of experimental variation which should be considered. First, the manual rotation of the ball between drop additions is unlikely to be truly random and will therefore result in some deviations from the theoretical coverage. We have now designed and built a robot manipulator which will be able to rotate the ball to a new random position after each drop has been added. In addition, the coating process is inherently a discrete, stochastic, Monte-Carlo type process. Many
Conclusions
The five steps of distribution nucleation indicated that the particle coating step was a critical precursor to particle coalescence. The particle coating number Φp derived here is able to predict the fractional surface coating F, including variations in particle size and drop size, and represents the first quantitative design approach to distribution nucleation and coating. Whilst some experimental variations in drop footprint area resulted in some bias and scatter, using the footprint size as
Acknowledgements
This project was supported financially by an Australian Research Council Discovery Project DP0877961.
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- 1
Now at The Dow Chemical Company, Midland, MI, USA
- 2
Now at Department of Chemical and Biological Engineering, Sheffield University, Sheffield, UK