The Stickiness
2.5 Particulate drying kinetics
Correct quantitative prediction of the droplet and particle behaviour in the dryer requires proper modelling of the drying behaviour of the droplets. The temperature and moisture content of the droplets and particles affect all subsequent reactions, including crystallization. It is important to allow properly for hindered drying due to the presence of the solids. Various approaches exist in the literature, including the characteristic drying curve
[19][22], A shortcut solution to the diffusion equation [23][24] and other diffusion models [25][26], Receding-plane type models [20] and others that include both convection and diffusion as transport processes [27] and reaction engineering approaches [28][29]. Both a characteristic drying curve (CDC) and the reaction engineering approach (REA) have been used to simulate drying behaviour and compared [28] with experimental data for whole and skim milk droplets, finding that the predictions from the REA model are closer to the experimental results from using CDC.
Although the predicted results from the REA model were closer to the experiments than those predicted by the CDC model, the difference was small, remaining under 5% for both models. Chen & Lin [28] recognised that the CDC model provided a good approximation to the experimental results, despite its simplicity. In addition, they recognised that the REA model includes initially incorrect activation energies, higher than the actual one, because the milk droplets initially behave in the same way as water, where the activation energy of drying is close to zero. The REA model overpredicts this value, thus underestimating the initial drying rate and predicting droplet temperatures that rise faster than in reality. This initial period of time, where over-prediction of the activation energy occurs, was found by Chen & Lin to be approximately the first 10% of the total drying time. Patel & Chen [29] used a parallel-flow approach to compare the two models, suggesting that the REA model gave better predictions at high relative humidities and high feed concentrations, but that the two models were similar under other conditions.
The extent of crystallization of a powder has a profound effect on properties relating to both use and handling. Studies of the properties of powders[30], have shown that fully crystalline powders have improved flowability and decreased wall deposition, whereas completely amorphous powders have the greatest bioavailability and adsorptive capacity [31] at the expense of flowability and stability[32]. A particle with a crystalline surface but an amorphous interior will retain much of the adsorptive capacity and bioavailability of an amorphous particle, with the crystalline flowability and decreased deposition characteristics. Hence the ability to control the degree
3.1 A physical transformation 3.0 Crystallization in drying
2.5 Particulate drying kinetics
of crystallization will have significant benefits for those using spray-dried products as well as those operating the processes.
Background
Water-induced crystallization of lactose in storage has been known for a long time [33][34], but recently we have shown that water-induced crystallization of lactose occurs in spray dryers [5][6], due to the high temperatures involved and the control of humidity and product moisture content that is possible in this equipment. We have also shown [35] that water-induced crystallization occurs for a wide range of materials, including sucrose, coffee, tea, skim milk, maltodextrin and hibiscus extract. Most recently, we have shown [2] that sucrose can be fully crystallized inside a laboratory-scale (Buchi) spray dryer (small scale).
Basic Theory
Actual measurements of, and correlations for, the rate of crystallisation of polymers, organic glasses and inorganic were reported by Williams, Landel and Ferry[1] (WLF) and used to form the WLF equation. Roos and Karel [36]
were able to apply the equation to food polymers, such as lactose. They found that the ratio (r) of the time for crystallisation (θcr) (time taken for the material to become 100% crystalline) at any temperature (Tp) to the time for crystallisation (θg) at the glass-transition temperature (Tgt) could be correlated by the following equation (the WLF equation):
( )
compared with the crystallisation rate at the glass-transition temperature. The inverse of this ratio can be described as the “impact” of the particle temperature, Tp, and the glass-transition temperature, Tgt, which is a function of the particle moisture content, X, through the Gordon-Taylor equation. Both the particle temperature, Tp, and the particle moisture content, X, change through the dryer, as described in the previous sections, so the glass-transition temperature, Tgt, also changes as the droplets and particles dry out when they move through the dryer.The Gordon-Taylor equation [37] can be used to predict the glass-transition temperature of food mixtures and pharmaceutical solids as a function of the composition and the glass-transition temperatures of the individual components that make up the mixture:
2 components, Tgt1 is the glass-transition temperature of one component, Tgt2 is the glass-transition temperature of the other component, and k is a curvature constant, which can be determined empirically. One of these components
may be the solid material that is spray dried, while the other might be the moisture in the particle, and the equation can be extended to three or more components in the particle (Arvanitoyannis et al., 1993). This equation is based on the assumption of perfect volume additivity, that is, the liquids mix without any change in volume, and there is no specific interaction between the components of the mixture. The equation has been used by many workers to predict that the glass-transition temperature decreases with increasing moisture content, as is found experimentally. The glass-transition temperature is affected by the nature and composition of the components
[36][38]
. The weight fraction of water, w, is related to the moisture content, X, expressed on a dry basis, through the equation w = X / (1 + X).
Both the particle temperature and the particle moisture content change through the dryer, and these changes are predicted by the simulation. These changes mean that the local value of the “impact”, the inverse of the ratio of crystallisation times, needs to be integrated over the residence time for each particle in the dryer. In effect, this procedure treats the WLF equation (24) as representing the inverse of a rate equation for crystallisation, where the inverse of the ratio is equivalent to a relative rate for crystallisation, and the inverse of the ratio is integrated over the residence time of each particle in the dryer to predict the overall increase in crystallinity. It is important to note that the WLF equation (equation 24) makes no distinction between nucleation and crystal growth, meaning that it is implicitly assumed that nucleation of the material is non-rate limiting.
Figure 6 Typical drying prediction form the parallel flow design equations Distance through Particle moisture
content, gas humidity, kg/kg solid or gas
Gas humidity, kg/kg
Solids moisture content, kg/kg
Figure 6 shows the typical drying prediction obtained form the parallel flow model. Chiou et al. [5][6] have found that this simulation predicted the correct trends in terms of lactose crystallinity when lactose was spray dried in a Buchi B-290 spray dryer. Islam and Langrish [2] and Islam et al. [4] have found that the simulation also predicts the correct trends when spray drying lactose, sucrose and ascorbic acid, since the order of their glass-transition temperatures (a key part of the Gordon-Taylor equation) is 101oC for lactose, around 60-65oC for sucrose and -50oC for ascorbic acid. However, the simulation clearly does not allow for recirculation of particles, so its quantitative accuracy is likely to be modest.
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