5.2 Simulation study
5.2.2 Influence of process parameters
The influence of process parameters (inlet gas temperature and spraying rate) and a material pa-rameter (DE value of maltodextrin) on the three agglomeration criteria considered in the model is presented. Therefore, further parameters are considered: drying time (cf. Equation (3.35)), glass transition temperature (cf. Equation (3.47)), temperature of the solid (cf. Equation (3.52)), and viscosity (cf. Equation (3.50)). The agglomeration behavior is quite complex, as changes in these parameters lead to opposing trends on the microscopic level. These trends are discussed below, while the governing trend on the macro-scale is discussed later using the simulation and experimental results. The used simulation parameters are summarized in Table 5.2. To show the influence of the above mentioned parameters on agglomeration, the following simulations are performed:
• simulations with𝑇g,in =60 °C and𝑇g,in =95 °C (DE 12,𝑀¤spray =0.4 kg h−1),
• simulations with𝑀¤spray =0.3 kg h−1and𝑀¤spray =0.5 kg h−1(DE 12,𝑇g,in =80 °C), and
• simulations with DE 6 and DE 47 (𝑇g,in =80 °C,𝑀¤spray =0.4 kg h−1).
The results are shown in Figure 5.4 to Figure 5.6 and summarized in Table 5.3.
Figure 5.4 shows the influence of the inlet gas temperature on the agglomeration behavior. Figure 5.4a shows the mean number of wet droplets (scaled up to the real particle system) during the process and Figure 5.4b to Figure 5.4d depict the transient behavior of the water mass fraction𝑤w, the glass transition temperature𝑇gt, and the viscosity of the wet spots𝜂during the drying time of a droplet.
An increase in temperature leads to a shorter drying time and therefore to a smaller number of wet droplets. This directly influences the first agglomeration criterion negatively and leads to less successful collisions. Additionally, the water mass fraction is reduced faster in case of a high inlet gas temperature leading to a faster increase of the glass transition temperature of the wet spot. That is why in case of a high inlet gas temperature it is more likely that the calculated glass transition temperature during a collision is higher, which generally inhibits the second agglomeration criterion from being
Chapter 5 Monte Carlo model for binder-less agglomeration due to glass transition
50 60 70 80 90 100
0 0.2 0.4 0.6 0.8
1 ·107 (a)
𝑇g,in [°C]
𝑁drop,wet,real[−]
𝑇g,in=60 °C 𝑇g,in=95 °C
0 0.4 0.8 1.2 1.6 0
0.1 0.2 0.3 0.4 (b)
𝑡 [s]
𝑤w[−]
𝑇g,in=60 °C 𝑇g,in=95 °C
0 0.4 0.8 1.2 1.6
−100
−50 0 50 100 150 200
𝑇s−20 K
(c)
𝑡 [s]
𝑇gt[°C]
0 0.4 0.8 1.2 1.6 10−2
102 106 1010 1014 (d)
𝑡 [s]
𝜂[Pas]
Figure 5.4:Influence of the inlet gas temperature on parameters of the agglomeration citeria: number of wet droplets (a), water mass fraction (b), glass transition temperature (c), and viscosity (d).
fulfilled and impedes agglomeration. At the same time, the temperature of the particles𝑇sis also higher if the inlet gas temperature is increased, promoting agglomeration. The combination of both effects is shown in Figure 5.4c. According to the second agglomeration criterion, the glass transition temperature must be smaller than the temperature of the solid material reduced by 20 K (indicated by the dashed lines in Figure 5.4c) to ensure stickiness of the material. The intersection of the curves for𝑇gt and𝑇s −20 K yields the time interval, in which the second agglomeration criterion is fulfilled.
This time interval is reduced in case of a high temperature, which means that the negative influence on the second criterion (higher glass transition temperature) prevails, leading to less agglomeration events. The third agglomeration criterion (Stokes criterion) is influenced by the viscosity of the material. Figure 5.4d shows that the viscosity is lower at the beginning of the drying process in case of a high inlet gas temperature due to a higher particle temperature. At the same time, drying is faster in this case and therefore the viscosity increases faster. Depending on the time of the collision, the viscosity may be smaller or larger in case of a higher inlet gas temperature and agglomeration may be impeded or promoted.
Figure 5.5 shows the influence of the spraying rate on the agglomeration behavior. A higher spraying
5.2 Simulation study
0.2 0.3 0.4 0.5 0.6 0
0.2 0.4 0.6 0.8
1 ·107 (a)
𝑀¤spray kg h−1 𝑁drop,wet,real[−]
¤
𝑀spray =0.3 kg h−1
¤
𝑀spray =0.5 kg h−1
0 0.25 0.5 0.75 1
0 0.1 0.2 0.3 0.4 (b)
𝑡 [s]
𝑤w[−]
¤
𝑀spray=0.3 kg h−1
¤
𝑀spray=0.5 kg h−1
0 0.25 0.5 0.75 1
−100
−50 0 50 100 150 200
𝑇s−20 K
(c)
𝑡 [s]
𝑇gt[°C]
0 0.25 0.5 0.75 1
10−2 102 106 1010 1014 (d)
𝑡 [s]
𝜂[Pas]
Figure 5.5:Influence of the spraying rate on parameters of the agglomeration citeria: number of wet droplets (a), water mass fraction (b), glass transition temperature (c), and viscosity (d).
rate leads to an increased number of wet droplets (see Figure 5.5a) due to a higher number flow rate of droplets (see Equation (3.15)) and an increased drying time. This directly influences the first agglomeration criterion, leading to more agglomeration events. As drying is slower in case of a higher spraying rate, the reduction of the water mass fraction is slower (see Figure 5.5b) and correspondingly the glass transition temperature increases slower during the drying process. This leads to lower values for𝑇gtduring collisions and therefore positively influences the second agglomeration criterion.
However, the temperature of the solid material is lower, which inhibits the fulfillment of the second agglomeration criterion. Considering both effects simultaneously in Figure 5.5c, it can be seen that the time interval in which the second agglomeration criterion is fulfilled increases with an increasing spraying rate, which ultimately promotes agglomeration as the positive influence (lower glass transition temperature) prevails. Figure 5.5d shows that the viscosity at the beginning of the drying process is larger in case of a high spraying rate, but increases slower during drying. Similar to the case shown in Figure 5.4d, a higher spraying rate may lead to higher or smaller viscosities during collisions. Depending on the time of the collision, agglomeration may be promoted or inhibited according to the third agglomeration criterion.
Figure 5.6 shows the influence of the DE value of the maltodextrin on the agglomeration behavior.
Chapter 5 Monte Carlo model for binder-less agglomeration due to glass transition
0 10 20 30 40 50
0 0.2 0.4 0.6 0.8
1 ·107 (a)
DE [−]
𝑁drop,wet,real[−]
DE 6DE 47
0 0.2 0.4 0.6 0.8 0
0.1 0.2 0.3 0.4 (b)
𝑡 [s]
𝑤w[−]
DE 6DE 47
0 0.2 0.4 0.6 0.8
−100
−50 0 50 100 150 200
𝑇s−20 K
(c)
𝑡 [s]
𝑇gt[°C]
0 0.2 0.4 0.6 0.8 10−2
102 106 1010 1014 (d)
𝑡 [s]
𝜂[Pas]
Figure 5.6:Influence of the DE value on parameters of the agglomeration citeria: number of wet droplets (a), water mass fraction (b), glass transition temperature (c), and viscosity (d).
As stated in Section 3.2.3, the drying model assumes gas-side controlled drying, neglecting material influence such as hygroscopicity. Therefore, the drying time is not influenced when varying the DE value and the number of wet positions does not change. The small difference in Figure 5.6a results from the stochastic nature of the model. Note that the simulation for DE 47 was performed with the same initial particle size distribution as the simulation for DE 6 in this case, since the larger particle size (cf. Table 5.2) would otherwise lead to a slightly larger drying time due to a smaller mass transfer coefficient for DE 47, interfering with the impact of the DE value. Since the drying time is identical, the first agglomeration criterion is not influenced. The reduction of the water mass fraction is not changed as well, see Figure 5.6b. However, a higher DE value leads to smaller glass transition temperatures, promoting agglomeration. As the temperature of the solid material is not changed, the time interval in which the second agglomeration criterion is fulfilled is larger when the DE value is increased. Consequently, the combination of both effects results in more successful collisions according to the second agglomeration criterion in case of a higher DE value, see Figure 5.6c. Figure 5.6d shows that the viscosity of a wet spot will be lower if the DE value increases.
Therefore, the third agglomeration criterion predicts less agglomeration events in this case.