Numerical investigation of the de-agglomeration ... - Semantic Scholar
Journal of Aerosol Science 42 (2011) 811–819
Contents lists available at ScienceDirect
Journal of Aerosol Science journal homepage: www.elsevier.com/locate/jaerosci
Numerical investigation of the de-agglomeration mechanisms of fine powders on mechanical impaction Z.B. Tong a, S. Adi b, R.Y. Yang a,n, H.K. Chan b, A.B. Yu a a
Labarotary for Simulation and Modelling of Particulate System, School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia Faculty of Pharmacy, University of Sydney, NSW 2006, Australia
b
a r t i c l e i n f o
abstract
Article history: Received 8 February 2011 Received in revised form 8 July 2011 Accepted 8 July 2011 Available online 19 July 2011
This paper numerically investigated the mechanisms of powder de-agglomeration on mechanical impaction, aiming to explain the experimental observations in our previous study (Adi et al., 2010). A numerical model based on a coupled computational fluid dynamics (CFD) and discrete element method (DEM) approach was developed to simulate the dispersion of drug mannitol agglomerates in the customised impaction throats containing one or two angles with different flow rates. Information in terms of particlethroat and particle-fluid interactions, number of fragments, fine particle fraction (FPF) and powder deposition was monitored over the whole process and quantitatively analysed. The results indicated that the breakage of the agglomerate was mainly attributed to the mechanical impaction and less affected by the shear effect from the flow-particle interaction. While the first impaction caused the major damage to the agglomerate, the second impaction in fact generated more fine particles with size less than 5 mm, resulting much improved dispersion performance for the throats with two angles. Powder deposition, which is dependent on impaction velocity and angle and fragment size, was another important factor affecting the dispersion. The analysis of dispersion mechanisms indicated that de-agglomeration at different conditions can be characterised by the ratio of the particle-wall impaction energy and agglomerate strength. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Powder dispersion Impact angle Agglomerates Computational fluid dynamics Discrete element method
1. Introduction Powder dispersion in dry powder inhalers (DPIs) is a complex process controlled by interparticle cohesion, powder-flow interaction and powder-device impaction. It has been widely reported that the mechanical impaction with device is a major contribution to agglomerate breakage (Dunbar et al., 1998; Finlay, 2001; Voss & Finlay, 2002; Xu & Zhu, 2006). Moreno et al. (2003) and Moreno and Ghadiri (2006) studied the effect of impact angle on the breakage of agglomerates and found the normal component of impact velocity is the dominant factor. However, using more plastic and softer particles, Samimi et al. (2004) found that at low impact velocity the normal component of impact velocity determines the extent of breakage, independent of the impact angle. At high impact velocity, its tangential component becomes increasingly important. Our recent attempts to understand mannitol agglomerate break-up using numerical simulations showed that increasing impact velocity improves agglomerate breakage and a 451 impact angle results in the maximum breakage for a given velocity (Tong et al., 2009; Yang et al., 2008). However, a few important issues, such as the effects of air flow, powder deposition and multiple impactions, were not considered in those studies. In fact, air flow can be very important as it is the main driving force for powder movements
n
Corresponding author. E-mail address: [email protected] (R.Y. Yang).
0021-8502/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2011.07.004
812
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
(Tong et al., 2010). Powder deposition (powders retained by devices) and multiple impactions also affect the final results. To address these issues, we recently carried out experimental studies on the de-agglomeration of powders in the specially designed impaction throats containing one or two angles (Adi et al., 2010). The results showed that mechanical impaction had a significant effect on agglomerate breakage. For the two-angle throats, there existed an optimal throat angle (451) and air flow (120 l min 1) to obtain maximum dispersion efficiency characterised by maximum fine particle fraction (FPF), a balanced result between improved breakage and increased deposition with increasing air flow rates. The throats with two angles had better agglomerate breakage than those with a single angle. Several questions, however, remain from that study. For example, what are the exact roles of the first and second impactions? How does the turbulence affect the powder dispersion and why does the larger flow rate not always improve the amount of fine powders (o5 mm) coming out from the throats? To answer these questions, the detailed knowledge of the particle and flow information over the process is required. Such information, however, is impossible to obtain from experiments. Therefore, while possible hypotheses/explanations were proposed, they were not confirmed in our previous work. This work is the follow up of our previous experimental study (Adi et al., 2010) by carrying out the coupled computational fluid dynamics (CFD) and discrete element method (DEM) simulations of dispersion process. The microdynamic information of particles and flow is analysed to understand the underlying mechanisms and to be used to explain the experimental observations. Furthermore, a quantitative index based on the ratio of interparticle cohesion and mechanical impaction is proposed to describe the dispersion performance. 2. CFD-DEM modelling and validation A coupled CFD-DEM model was developed to simulate the dispersion process. Detailed description of the model has been given in our previous studies (Tong et al., 2010) and is not repeated here. However, it should be noted that a fully coupled method was adopted here, which means the data from DEM and CFD were exchanged at each time step. Therefore, the full dynamics and instantaneous variation of particles and flow can be captured. The simulation conditions were similar to those in the experiments (Adi et al., 2010). The setup of the de-agglomeration apparatus is shown in Fig. 1. In the simulations, air of different flow rates entered the impaction throat from the right side air inlet and an agglomerate was introduced via the feed apparatus (as indicated by ‘‘B’’ in Fig. 1). The agglomerate moved along with the air flow and impacted with throats containing two angles (Fig. 1a and b) or a single angle (Fig. 1c–e). The agglomerate used in this work was formed with mannitol powders under an assumed centripetal force as described in our previous work (Yang et al., 2008). The mannitol powder had the size distribution as shown in Fig. 2a with the mass mean diameter of 3.27 mm. The formed agglomerate (Fig. 2b) had a diameter of 51 mm with porosity of 0.5 and a theoretical tensile strength of 1.21 kPa from the Rumpf’s model (Rumpf, 1962; Yang et al., 2008). Details of the parameters used in the simulations are provided in Table 1. As reported in our previous work (Adi et al., 2010), the numerical model was validated by comparing the simulated results, such as the trajectory of the agglomerates and the amount of fine particles less than 5 mm (FPF) generated, with those from the experiments. The comparisons on FPF are shown in Fig. 3 to provide a background for the later discussion. Here FPFload is defined as the mass fraction of particles smaller than 5 mm in the exiting aerosol, referenced against the total mass of powder loaded into the impaction throat. The powders deposited on the throat wall are not considered. The simulated results are qualitatively comparable with the experimental observations. For the two-angle throats (A and B) and the single angle throat C with 901 impaction angle, FPF increases with impact angles at low flow rates (60 and 120 l min 1) but decreases at the high flow rates of 150 l min 1. For the single angle throats D and E, FPF increases monotonically with flow rate. As shown later on,
60 cm 15 °
60 cm 45 °
B
A
60 cm
B
B
20 cm
A
A 30 cm
30cm
A
30 cm
A 30 cm
30 cm
Fig. 1. Schematics of impaction throats: (a) throat A; (b) throat B; (c) throat C; (d) throat D; and (e) throat E. A is the impact point, which is located 60 cm from the inlet of the main section. B is feed apparatus used to feed agglomerate into the throat via a 4 mm opening.
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
813
0.3 0.8
0.6
0.2
0.4 0.1 0.2
0.0
Cumulative mass distribution
Probability density function (mass)
1.0
0.0 0
1
2
3
5 6 4 Diameter (μm)
7
8
9
Fig. 2. (a) Mass based size distribution and cumulative mass distribution of parimary powder; and (b) the morphology of the formed agglomerates (colours represent particle diameters). Table 1 Values of the key parameters used in the simulations. Parameter
Value
Number of particle, Np Particle density, rp Young’s modulus, Y Poisson’s ratio, s~ Sliding friction coefficient, ms Rolling friction coefficient, mr Normal damping coefficient, g Hamaker constant, Ha Air flow rate, Q
3000 1490 kg m 3 1 108 N m 2 0.29 0.3 0.0002 m 2 10 6 s 1 1.2 10 19 J 60, 120, 150 l min 1
the decrease in FPF at high flow rate for throats A, B and C is caused by the increased powder deposition. In general, the throats with two angles (A and B) result in better dispersion than those with a single angle (C, D and E), showing that the multiple impactions can improve powder de-agglomeration. In the following, the micro-dynamics of the dispersion process will be analysed to investigate the roles of fluid flow, mechanical impactions and powder dispersion. Finally, an energy based equation will be given to quantify these effects. 3. Results and discussion 3.1. Effect of fluid flow It has been reported that turbulence can be a major cause for the agglomerate break-up because of the aerodynamic lift, drag and shear force generated by the eddies (Brown et al., 2003; Coates et al., 2005; French et al., 1996; Li et al., 1996; Timsina et al., 1994). To investigate the effect of air flow on dispersion under the current condition, Fig. 4 shows the
814
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
60 L/min
FPFloaded (% Mass)
40
120 L/min
Second impaction
150 L/min Experiments
30
20
10
0 A
B
C Impaction throat
D
E
Fig. 3. FPF generated at different impaction conditions and flow rates. The experimental data (Adi et al., 2010) are also plotted for comparison.
Fig. 4. Contour of integral scale strain rate of throat C at 150 l min 1.
integral scale strain rate (ISSR) of throat C with a flow rate of 150 l min 1. ISSR is a measure of the velocity gradient across the integral scale eddies (the most energetic occurring in a turbulence flow) and has been demonstrated to be more relevant to powder dispersion (Finlay, 2001). It can be seen that ISSR is larger near the wall and has a maximum value at the inner intersection where the flow starts to change direction. ISSR shows similar patterns for other throats but the maximum ISSR decreases with decreasing flow rate and impaction angle. Since flows consisting of eddies that exhibit large ISSR exert large aerodynamic forces on the agglomerate, the agglomerate is more likely to be broken in this region. Therefore, the effect of flow on powder dispersion can be quantified in terms of the maximum shear stress generated from the flow on the agglomerate. As proposed by Bagster and Tomi (1974), the maximum shear stress, tmax, acting on a spherical particles is in the central plane parallel to fluid direction, given by
tmax ¼ ðFf Fi Þ=A
ð1Þ
where Ff and Fi are the total particle-fluid force and inertial force, respectively, applied on the half of the agglomerate above the central plane with the area A. Fig. 5 shows the maximum shear stress on the agglomerate under different conditions. Similar to the maximum ISSR, the maximum shear stress also increases with the air flow rate and impaction angle (throat C4A 4B4E 4D). Comparing with the tensile strength of the agglomerate, however, the maximum shear
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
815
Maximum shear stress (kPa)
1.2 1.0 0.8
Throat A Throat B Throat C Throat D Throat E
Agglomerate tensile strength
0.6 0.4 0.2 0.0 60
90
120
150
Airflow rate (l/min)
480 240
Fragment number
0 1000
120 60 0 400
Number Force
(a)
(b)
500
200
0 520 260 0 480
0 720 480 240 0 80
240 0 720 480 240 0
(c)
(d)
40 0 400
(e)
Normal contact force particle-wall (mN)
Fig. 5. Agglomerate tensile stress and maximum shear stress of throats A–E at different air flow rates.
200 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Normalized time (τ) Fig. 6. Time evolution of the number of fragments and agglomerate-wall impact force for agglomerates impacted at 120 l min 1 using different throats A–E. Note different scales are used.
stress is much lower. Even the largest value (throat C at 150 l min 1) is less than half of the agglomerate tensile strength of 1.21 kPa. Therefore, the break-up of the agglomerate due to the turbulence flow is minimum in the current work.
3.2. Mechanical impactions and effect of second impaction The dispersion process can be further investigated by plotting the variations of the number of fragments and particlewall impact force with dispersion time as shown in Fig. 6. Note different scales are used for different throats. The dispersion time is normalised against the residence time of the agglomerate in the throat when the particles are discharged from the outlet. As mentioned above, the fluid has no visible effect on the powder dispersion so there is no breakage for the agglomerate before the first impaction with the throats. During the first impaction, a strong spike is shown in the agglomerate-wall impact force. In the mean time, there is a rapid increase in the number of fragments. The fragment numbers gradually become saturated for throats C, D and E. For throats A and B, there are second impaction at the normalised time of 0.72 and 0.37, respectively, which causes a step change in the number of fragments. For throat A, the second impaction is even stronger than the first one (125 mN vs. 65 mN). The second impaction also lasts longer, and therefore causes more severe breakage as reflected from the sharp increase in the number of fragments. In contrast, the second impaction for throat B is much weaker than the first one. This is because the agglomerate has already broken into
816
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
Before impaction First impaction Before second impaction Second impaction
Fig. 7. Snapshots of agglomerate dispersion at 120 l min 1 (a) throat A and (b) throat B. (The colours represent the magnitude of particle velocity.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
many small fragments on the first impaction. This is evident from Fig. 7 which superimposes the breakage conditions after the first and second impactions for the throats A and B. It was postulated in our previous paper (Adi et al., 2010) that the first impaction more likely causes major breakage while the second one acts as a facilitator for further break-up. To test this assumption, the cumulative mass distributions of the fragments after each impaction are plotted in Fig. 8. For throat A, the total fraction of fine particles less than 5 mm (including those deposited on the wall) is 8% and 35%, respectively, after the first and second impactions (also see Fig. 3). For throat B, the total fine particle fraction after the first and second impaction is 14% and 38%, respectively. It demonstrates that the second impaction is more important in generating fine powders, which improves the dispersion efficiency significantly.
3.3. Effect of powder deposition Powder deposition (amount of powder retained in the throats) also affects the dispersion performance. As shown in Fig. 3, although larger flow rates have better breakage, FPF actually decreases at the high flow rate of 150 l min 1 for throats A, B and C. This is mainly due to the increased deposition on throat wall at large flow rates, which reduces the amount of fine powders exiting from the outlet and thus leads to an overall reduction in FPF. An optimal dispersion is the combined result of de-agglomeration and deposition. Fig. 9 shows the powder deposition under different impaction conditions. Again the simulated total depositions are comparable with experimental results, further confirming the validity of the model. It is observed that the deposition is dependent on both impaction angle and inertial energy (mass and velocity) of fragments. The general trend is that smaller impaction angles have less powder deposition for single impaction (i.e. throats A EDoB EEoC). However, the second impaction also plays an important role in the deposition. For throat A with the second impact angle of 751, large deposition occurs at the second impaction region, which is consistent with the experimental observation (Adi et al., 2010). In comparison, the deposition in throat B is smaller in the second impaction than in the first one because of the relatively smaller fragment size in the second impaction. This can be further confirmed in Fig. 10, which shows the amount of deposition at different positions for throats A and B. The dotted-lines show the starting points of the two impactions. While throat A has more particle deposition after the second impaction, throat B shows a large amount of deposition after
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
817
Fragment mass cumulative (%)
100
80
60
40 After 1st impaction (throat A) After 2nd impaction (throat A) After 1st impaction (throat B) After 2nd impaction (throat B)
20
0 0
2
4
6
8 10 12 14 16 Fragment diameter (μm)
18
20
22
Fig. 8. Cumulative mass distribution of fragments after first and second impactions for throat A and B at 120 l min 1 (powders deposited on the wall are also considered).
70 60 L/min Throat deposition (% Mass)
60
150 L/min
120 L/min
Experiments
Second impaction
50 40 30 20 10 0 A
B
C
D
E
Impaction throat Fig. 9. Mass fraction of powder deposition in different impaction throats at different flow rates. The experimental results (Adi et al., 2010) are shown for comparison.
20
Deposition (% Mass)
Throat A
First impaction
15 10
Second impaction
5 0
Throat B
5 4 3 2
First impaction
Second impaction
1 0 0.40
0.45 0.50 0.55 0.60 Distance from feeding point (m)
0.65
Fig. 10. Deposition mass distribution on the axial direction in throats A and B.
818
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
0.25
FPF (% Mass)
0.20
0.15
0.10
Throat A Throat B Throat C Throat D Throat E
0.05
0.00 0
1
2
3
Fig. 11. Correlation between fine particle fraction (FPF) and the ratio between the impact energy and agglomerate cohesion energy (f) in different throats.
the first impaction but before the second one. Therefore to reduce deposition, both device design (e.g. impaction angle) and the flow condition (e.g. flow rate) have to be carefully considered. 3.4. Dispersion mechanisms The above results show that the breakage of the agglomerate in the throats is mainly due to the particle-wall impaction while the flow has no obvious effect on the breakage. Another important property to affect the breakage is the strength of the formed agglomerate. Our previous studies (Tong et al., 2009, 2010) indicated that the dispersion performance can be characterised in terms of particle-wall impaction energy Epw and agglomerate tensile energy Ead. The particle-wall impact energy is given by Epw ¼
K Z X i
0
Z
t
ðvi,n UFi,n Þdt þ
0
t
ðvi,t UFi,t Þdt
ð2Þ
where K is the number of particles impacting on the wall, and Fi,n, Fi,t, vi,n and vi,t are the forces and velocities of particle i in the normal and tangential directions, respectively. The tensile energy of an agglomerate Ead is calculated from the Rumpf’s model (Rumpf, 1962). Details can be found from our previous papers (Tong et al., 2009; Yang et al., 2008). Fig. 11 shows FPFload obtained under different conditions as a function of the ratio of impaction and tensile energy f( ¼Epw/Ead). It is observed the results collapse on a single master curve which can be fitted by an error function, given by n
FPFload ¼ FPFload,1 erf ðkf Þ
ð3Þ
where FPFload,N is the limiting value when the energy ratio f is infinitely large, k and n are two empirical parameters. With the current results, FPFload,N ¼0.25, k¼0.92 and n ¼0.86. The results further indicate that agglomerate breakage is governed by the same mechanisms at different throats. 4. Conclusions This work studied the effect of impact angles on powder dispersion at the presence of air flow by using CFD-DEM approach. By analysing the flow field and micro-dynamics of particles, the dispersion mechanisms were investigated at the particle level. The main findings can be summarised as follows:
The generation of fine particles with size less than 5 mm was mainly attributed to the second impaction instead of the
first one. After the first impaction, the agglomerate was broken up into many small fragments with weak strength; second impaction further disintegrated them into smaller fragments. Powder deposition was dependent on impaction angle and the inertial energy (mass and velocity) of fragments. While increasing flow rate and the number of impactions increased breakage, they also resulted in larger powder deposition. To have optimal dispersion, both device design and flow condition should be considered. Agglomerate breakage at different conditions was governed by the same mechanisms, which can be described by a unified error function in terms of the ratio of agglomerate-wall impaction and agglomerate strength.
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
819
Acknowledgements Authors are grateful to the Australia Research Council (ARC) for the financial support for this work. References Adi, S., Tong, Z.B., Chan, H.K., Yang, R.Y., & Yu, A.B. (2010). Impact angles as an alternative way to improve aerosolisation of powders for inhalation? European Journal of Pharmaceutical Sciences, 41, 320–327. Bagster, D.F., & Tomi, D. (1974). The stresses within a sphere in simple flow fields. Chemical Engineering Science, 29, 1773–1783. Brown, D.P., Kauppinen, E.I., & Jokiniemi, J.K. (2003). Agglomerate deaggregation potential during dry powder inhaler operation and characterization under steady and unsteady conditions. Journal of Aerosol Science, 34, 1417–1428. Coates, M.S., Fletcher, D.F., Chan, H.-K., & Raper, J.A. (2005). The role of capsule on the performance of a dry powder inhaler using computational and experimental analyses. Pharmaceutical Research, 22, 923–932. Dunbar, C.A., Hickey, A.J., & Holzner, P. (1998). Dispersion and characterization of pharmaceutical dry powder aerosols. Kona, 16, 7–45. Finlay, W.H. (2001). The Mechanics of Inhaled Pharmaceutical Aerosols, An Introduction. Academic Press: London. French, D.L., Edwards, D.A., & Niven, R.W. (1996). The influence of formulation on emission, deaggregation and deposition of dry powders for inhalation. Journal of Aerosol Science, 27, 769–783. Li, W.-I., Perzl, M., Heyder, J., Langer, R., Brain, J.D., Englmeier, K.H., Niven, R.W., & Edwards, D.A. (1996). Aerodynamics and aerosol particle deaggregation phenomena in model oral-pharyngeal cavities. Journal of Aerosol Science, 27, 1269–1286. Moreno, R., & Ghadiri, M. (2006). Mechanistic analysis and computer simulation of impact breakage of agglomerates: effect of surface energy. Chemical Engineering Science, 61, 2476–2481. Moreno, R., Ghadiri, M., & Antony, S.J. (2003). Effect of the impact angle on the breakage of agglomerates: a numerical study using DEM. Powder Technology, 130, 132–137. Rumpf, H. (1962). The Strength of Granules and Agglomerates. Interscience: New York. Samimi, A., Moreno, R., & Ghadiri, M. (2004). Analysis of impact damage of agglomerates: effect of impact angle. Powder Technology, 143, 97–109. Timsina, M.P., Martin, G.P., Marriott, C., Ganderton, D., & Yianneskis, M. (1994). Drug delivery to the respiratory tract using dry powder inhalers. International Journal of Pharmaceutics, 101, 1–13. Tong, Z.B., Yang, R.Y., Chu, K.W., Yu, A.B., Adi, S., & Chan, H.K. (2010). Numerical study of the effects of particle size and polydispersity on the agglomerate dispersion in a cyclonic flow. Chemical Engineering Journal, 164, 432–441. Tong, Z.B., Yang, R.Y., Yu, A.B., Adi, S., & Chan, H.K. (2009). Numerical modelling of the breakage of loose agglomerates of fine particles. Powder Technology, 196, 213–221. Voss, A., & Finlay, W.H. (2002). Deagglomeration of dry powder pharmaceutical aerosols. International Journal of Pharmaceutics, 248, 39–50. Xu, C.B., & Zhu, J. (2006). Parametric study of fine particle fluidization under mechanical vibration. Powder Technology, 161, 135–144. Yang, R.Y., Yu, A.B., Choi, S.K., Coates, M.S., & Chan, H.K. (2008). Agglomeration of fine particles subjected to centripetal compaction. Powder Technology, 184, 122–129.
Contents lists available at ScienceDirect
Journal of Aerosol Science journal homepage: www.elsevier.com/locate/jaerosci
Numerical investigation of the de-agglomeration mechanisms of fine powders on mechanical impaction Z.B. Tong a, S. Adi b, R.Y. Yang a,n, H.K. Chan b, A.B. Yu a a
Labarotary for Simulation and Modelling of Particulate System, School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia Faculty of Pharmacy, University of Sydney, NSW 2006, Australia
b
a r t i c l e i n f o
abstract
Article history: Received 8 February 2011 Received in revised form 8 July 2011 Accepted 8 July 2011 Available online 19 July 2011
This paper numerically investigated the mechanisms of powder de-agglomeration on mechanical impaction, aiming to explain the experimental observations in our previous study (Adi et al., 2010). A numerical model based on a coupled computational fluid dynamics (CFD) and discrete element method (DEM) approach was developed to simulate the dispersion of drug mannitol agglomerates in the customised impaction throats containing one or two angles with different flow rates. Information in terms of particlethroat and particle-fluid interactions, number of fragments, fine particle fraction (FPF) and powder deposition was monitored over the whole process and quantitatively analysed. The results indicated that the breakage of the agglomerate was mainly attributed to the mechanical impaction and less affected by the shear effect from the flow-particle interaction. While the first impaction caused the major damage to the agglomerate, the second impaction in fact generated more fine particles with size less than 5 mm, resulting much improved dispersion performance for the throats with two angles. Powder deposition, which is dependent on impaction velocity and angle and fragment size, was another important factor affecting the dispersion. The analysis of dispersion mechanisms indicated that de-agglomeration at different conditions can be characterised by the ratio of the particle-wall impaction energy and agglomerate strength. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Powder dispersion Impact angle Agglomerates Computational fluid dynamics Discrete element method
1. Introduction Powder dispersion in dry powder inhalers (DPIs) is a complex process controlled by interparticle cohesion, powder-flow interaction and powder-device impaction. It has been widely reported that the mechanical impaction with device is a major contribution to agglomerate breakage (Dunbar et al., 1998; Finlay, 2001; Voss & Finlay, 2002; Xu & Zhu, 2006). Moreno et al. (2003) and Moreno and Ghadiri (2006) studied the effect of impact angle on the breakage of agglomerates and found the normal component of impact velocity is the dominant factor. However, using more plastic and softer particles, Samimi et al. (2004) found that at low impact velocity the normal component of impact velocity determines the extent of breakage, independent of the impact angle. At high impact velocity, its tangential component becomes increasingly important. Our recent attempts to understand mannitol agglomerate break-up using numerical simulations showed that increasing impact velocity improves agglomerate breakage and a 451 impact angle results in the maximum breakage for a given velocity (Tong et al., 2009; Yang et al., 2008). However, a few important issues, such as the effects of air flow, powder deposition and multiple impactions, were not considered in those studies. In fact, air flow can be very important as it is the main driving force for powder movements
n
Corresponding author. E-mail address: [email protected] (R.Y. Yang).
0021-8502/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2011.07.004
812
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
(Tong et al., 2010). Powder deposition (powders retained by devices) and multiple impactions also affect the final results. To address these issues, we recently carried out experimental studies on the de-agglomeration of powders in the specially designed impaction throats containing one or two angles (Adi et al., 2010). The results showed that mechanical impaction had a significant effect on agglomerate breakage. For the two-angle throats, there existed an optimal throat angle (451) and air flow (120 l min 1) to obtain maximum dispersion efficiency characterised by maximum fine particle fraction (FPF), a balanced result between improved breakage and increased deposition with increasing air flow rates. The throats with two angles had better agglomerate breakage than those with a single angle. Several questions, however, remain from that study. For example, what are the exact roles of the first and second impactions? How does the turbulence affect the powder dispersion and why does the larger flow rate not always improve the amount of fine powders (o5 mm) coming out from the throats? To answer these questions, the detailed knowledge of the particle and flow information over the process is required. Such information, however, is impossible to obtain from experiments. Therefore, while possible hypotheses/explanations were proposed, they were not confirmed in our previous work. This work is the follow up of our previous experimental study (Adi et al., 2010) by carrying out the coupled computational fluid dynamics (CFD) and discrete element method (DEM) simulations of dispersion process. The microdynamic information of particles and flow is analysed to understand the underlying mechanisms and to be used to explain the experimental observations. Furthermore, a quantitative index based on the ratio of interparticle cohesion and mechanical impaction is proposed to describe the dispersion performance. 2. CFD-DEM modelling and validation A coupled CFD-DEM model was developed to simulate the dispersion process. Detailed description of the model has been given in our previous studies (Tong et al., 2010) and is not repeated here. However, it should be noted that a fully coupled method was adopted here, which means the data from DEM and CFD were exchanged at each time step. Therefore, the full dynamics and instantaneous variation of particles and flow can be captured. The simulation conditions were similar to those in the experiments (Adi et al., 2010). The setup of the de-agglomeration apparatus is shown in Fig. 1. In the simulations, air of different flow rates entered the impaction throat from the right side air inlet and an agglomerate was introduced via the feed apparatus (as indicated by ‘‘B’’ in Fig. 1). The agglomerate moved along with the air flow and impacted with throats containing two angles (Fig. 1a and b) or a single angle (Fig. 1c–e). The agglomerate used in this work was formed with mannitol powders under an assumed centripetal force as described in our previous work (Yang et al., 2008). The mannitol powder had the size distribution as shown in Fig. 2a with the mass mean diameter of 3.27 mm. The formed agglomerate (Fig. 2b) had a diameter of 51 mm with porosity of 0.5 and a theoretical tensile strength of 1.21 kPa from the Rumpf’s model (Rumpf, 1962; Yang et al., 2008). Details of the parameters used in the simulations are provided in Table 1. As reported in our previous work (Adi et al., 2010), the numerical model was validated by comparing the simulated results, such as the trajectory of the agglomerates and the amount of fine particles less than 5 mm (FPF) generated, with those from the experiments. The comparisons on FPF are shown in Fig. 3 to provide a background for the later discussion. Here FPFload is defined as the mass fraction of particles smaller than 5 mm in the exiting aerosol, referenced against the total mass of powder loaded into the impaction throat. The powders deposited on the throat wall are not considered. The simulated results are qualitatively comparable with the experimental observations. For the two-angle throats (A and B) and the single angle throat C with 901 impaction angle, FPF increases with impact angles at low flow rates (60 and 120 l min 1) but decreases at the high flow rates of 150 l min 1. For the single angle throats D and E, FPF increases monotonically with flow rate. As shown later on,
60 cm 15 °
60 cm 45 °
B
A
60 cm
B
B
20 cm
A
A 30 cm
30cm
A
30 cm
A 30 cm
30 cm
Fig. 1. Schematics of impaction throats: (a) throat A; (b) throat B; (c) throat C; (d) throat D; and (e) throat E. A is the impact point, which is located 60 cm from the inlet of the main section. B is feed apparatus used to feed agglomerate into the throat via a 4 mm opening.
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
813
0.3 0.8
0.6
0.2
0.4 0.1 0.2
0.0
Cumulative mass distribution
Probability density function (mass)
1.0
0.0 0
1
2
3
5 6 4 Diameter (μm)
7
8
9
Fig. 2. (a) Mass based size distribution and cumulative mass distribution of parimary powder; and (b) the morphology of the formed agglomerates (colours represent particle diameters). Table 1 Values of the key parameters used in the simulations. Parameter
Value
Number of particle, Np Particle density, rp Young’s modulus, Y Poisson’s ratio, s~ Sliding friction coefficient, ms Rolling friction coefficient, mr Normal damping coefficient, g Hamaker constant, Ha Air flow rate, Q
3000 1490 kg m 3 1 108 N m 2 0.29 0.3 0.0002 m 2 10 6 s 1 1.2 10 19 J 60, 120, 150 l min 1
the decrease in FPF at high flow rate for throats A, B and C is caused by the increased powder deposition. In general, the throats with two angles (A and B) result in better dispersion than those with a single angle (C, D and E), showing that the multiple impactions can improve powder de-agglomeration. In the following, the micro-dynamics of the dispersion process will be analysed to investigate the roles of fluid flow, mechanical impactions and powder dispersion. Finally, an energy based equation will be given to quantify these effects. 3. Results and discussion 3.1. Effect of fluid flow It has been reported that turbulence can be a major cause for the agglomerate break-up because of the aerodynamic lift, drag and shear force generated by the eddies (Brown et al., 2003; Coates et al., 2005; French et al., 1996; Li et al., 1996; Timsina et al., 1994). To investigate the effect of air flow on dispersion under the current condition, Fig. 4 shows the
814
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
60 L/min
FPFloaded (% Mass)
40
120 L/min
Second impaction
150 L/min Experiments
30
20
10
0 A
B
C Impaction throat
D
E
Fig. 3. FPF generated at different impaction conditions and flow rates. The experimental data (Adi et al., 2010) are also plotted for comparison.
Fig. 4. Contour of integral scale strain rate of throat C at 150 l min 1.
integral scale strain rate (ISSR) of throat C with a flow rate of 150 l min 1. ISSR is a measure of the velocity gradient across the integral scale eddies (the most energetic occurring in a turbulence flow) and has been demonstrated to be more relevant to powder dispersion (Finlay, 2001). It can be seen that ISSR is larger near the wall and has a maximum value at the inner intersection where the flow starts to change direction. ISSR shows similar patterns for other throats but the maximum ISSR decreases with decreasing flow rate and impaction angle. Since flows consisting of eddies that exhibit large ISSR exert large aerodynamic forces on the agglomerate, the agglomerate is more likely to be broken in this region. Therefore, the effect of flow on powder dispersion can be quantified in terms of the maximum shear stress generated from the flow on the agglomerate. As proposed by Bagster and Tomi (1974), the maximum shear stress, tmax, acting on a spherical particles is in the central plane parallel to fluid direction, given by
tmax ¼ ðFf Fi Þ=A
ð1Þ
where Ff and Fi are the total particle-fluid force and inertial force, respectively, applied on the half of the agglomerate above the central plane with the area A. Fig. 5 shows the maximum shear stress on the agglomerate under different conditions. Similar to the maximum ISSR, the maximum shear stress also increases with the air flow rate and impaction angle (throat C4A 4B4E 4D). Comparing with the tensile strength of the agglomerate, however, the maximum shear
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
815
Maximum shear stress (kPa)
1.2 1.0 0.8
Throat A Throat B Throat C Throat D Throat E
Agglomerate tensile strength
0.6 0.4 0.2 0.0 60
90
120
150
Airflow rate (l/min)
480 240
Fragment number
0 1000
120 60 0 400
Number Force
(a)
(b)
500
200
0 520 260 0 480
0 720 480 240 0 80
240 0 720 480 240 0
(c)
(d)
40 0 400
(e)
Normal contact force particle-wall (mN)
Fig. 5. Agglomerate tensile stress and maximum shear stress of throats A–E at different air flow rates.
200 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Normalized time (τ) Fig. 6. Time evolution of the number of fragments and agglomerate-wall impact force for agglomerates impacted at 120 l min 1 using different throats A–E. Note different scales are used.
stress is much lower. Even the largest value (throat C at 150 l min 1) is less than half of the agglomerate tensile strength of 1.21 kPa. Therefore, the break-up of the agglomerate due to the turbulence flow is minimum in the current work.
3.2. Mechanical impactions and effect of second impaction The dispersion process can be further investigated by plotting the variations of the number of fragments and particlewall impact force with dispersion time as shown in Fig. 6. Note different scales are used for different throats. The dispersion time is normalised against the residence time of the agglomerate in the throat when the particles are discharged from the outlet. As mentioned above, the fluid has no visible effect on the powder dispersion so there is no breakage for the agglomerate before the first impaction with the throats. During the first impaction, a strong spike is shown in the agglomerate-wall impact force. In the mean time, there is a rapid increase in the number of fragments. The fragment numbers gradually become saturated for throats C, D and E. For throats A and B, there are second impaction at the normalised time of 0.72 and 0.37, respectively, which causes a step change in the number of fragments. For throat A, the second impaction is even stronger than the first one (125 mN vs. 65 mN). The second impaction also lasts longer, and therefore causes more severe breakage as reflected from the sharp increase in the number of fragments. In contrast, the second impaction for throat B is much weaker than the first one. This is because the agglomerate has already broken into
816
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
Before impaction First impaction Before second impaction Second impaction
Fig. 7. Snapshots of agglomerate dispersion at 120 l min 1 (a) throat A and (b) throat B. (The colours represent the magnitude of particle velocity.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
many small fragments on the first impaction. This is evident from Fig. 7 which superimposes the breakage conditions after the first and second impactions for the throats A and B. It was postulated in our previous paper (Adi et al., 2010) that the first impaction more likely causes major breakage while the second one acts as a facilitator for further break-up. To test this assumption, the cumulative mass distributions of the fragments after each impaction are plotted in Fig. 8. For throat A, the total fraction of fine particles less than 5 mm (including those deposited on the wall) is 8% and 35%, respectively, after the first and second impactions (also see Fig. 3). For throat B, the total fine particle fraction after the first and second impaction is 14% and 38%, respectively. It demonstrates that the second impaction is more important in generating fine powders, which improves the dispersion efficiency significantly.
3.3. Effect of powder deposition Powder deposition (amount of powder retained in the throats) also affects the dispersion performance. As shown in Fig. 3, although larger flow rates have better breakage, FPF actually decreases at the high flow rate of 150 l min 1 for throats A, B and C. This is mainly due to the increased deposition on throat wall at large flow rates, which reduces the amount of fine powders exiting from the outlet and thus leads to an overall reduction in FPF. An optimal dispersion is the combined result of de-agglomeration and deposition. Fig. 9 shows the powder deposition under different impaction conditions. Again the simulated total depositions are comparable with experimental results, further confirming the validity of the model. It is observed that the deposition is dependent on both impaction angle and inertial energy (mass and velocity) of fragments. The general trend is that smaller impaction angles have less powder deposition for single impaction (i.e. throats A EDoB EEoC). However, the second impaction also plays an important role in the deposition. For throat A with the second impact angle of 751, large deposition occurs at the second impaction region, which is consistent with the experimental observation (Adi et al., 2010). In comparison, the deposition in throat B is smaller in the second impaction than in the first one because of the relatively smaller fragment size in the second impaction. This can be further confirmed in Fig. 10, which shows the amount of deposition at different positions for throats A and B. The dotted-lines show the starting points of the two impactions. While throat A has more particle deposition after the second impaction, throat B shows a large amount of deposition after
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
817
Fragment mass cumulative (%)
100
80
60
40 After 1st impaction (throat A) After 2nd impaction (throat A) After 1st impaction (throat B) After 2nd impaction (throat B)
20
0 0
2
4
6
8 10 12 14 16 Fragment diameter (μm)
18
20
22
Fig. 8. Cumulative mass distribution of fragments after first and second impactions for throat A and B at 120 l min 1 (powders deposited on the wall are also considered).
70 60 L/min Throat deposition (% Mass)
60
150 L/min
120 L/min
Experiments
Second impaction
50 40 30 20 10 0 A
B
C
D
E
Impaction throat Fig. 9. Mass fraction of powder deposition in different impaction throats at different flow rates. The experimental results (Adi et al., 2010) are shown for comparison.
20
Deposition (% Mass)
Throat A
First impaction
15 10
Second impaction
5 0
Throat B
5 4 3 2
First impaction
Second impaction
1 0 0.40
0.45 0.50 0.55 0.60 Distance from feeding point (m)
0.65
Fig. 10. Deposition mass distribution on the axial direction in throats A and B.
818
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
0.25
FPF (% Mass)
0.20
0.15
0.10
Throat A Throat B Throat C Throat D Throat E
0.05
0.00 0
1
2
3
Fig. 11. Correlation between fine particle fraction (FPF) and the ratio between the impact energy and agglomerate cohesion energy (f) in different throats.
the first impaction but before the second one. Therefore to reduce deposition, both device design (e.g. impaction angle) and the flow condition (e.g. flow rate) have to be carefully considered. 3.4. Dispersion mechanisms The above results show that the breakage of the agglomerate in the throats is mainly due to the particle-wall impaction while the flow has no obvious effect on the breakage. Another important property to affect the breakage is the strength of the formed agglomerate. Our previous studies (Tong et al., 2009, 2010) indicated that the dispersion performance can be characterised in terms of particle-wall impaction energy Epw and agglomerate tensile energy Ead. The particle-wall impact energy is given by Epw ¼
K Z X i
0
Z
t
ðvi,n UFi,n Þdt þ
0
t
ðvi,t UFi,t Þdt
ð2Þ
where K is the number of particles impacting on the wall, and Fi,n, Fi,t, vi,n and vi,t are the forces and velocities of particle i in the normal and tangential directions, respectively. The tensile energy of an agglomerate Ead is calculated from the Rumpf’s model (Rumpf, 1962). Details can be found from our previous papers (Tong et al., 2009; Yang et al., 2008). Fig. 11 shows FPFload obtained under different conditions as a function of the ratio of impaction and tensile energy f( ¼Epw/Ead). It is observed the results collapse on a single master curve which can be fitted by an error function, given by n
FPFload ¼ FPFload,1 erf ðkf Þ
ð3Þ
where FPFload,N is the limiting value when the energy ratio f is infinitely large, k and n are two empirical parameters. With the current results, FPFload,N ¼0.25, k¼0.92 and n ¼0.86. The results further indicate that agglomerate breakage is governed by the same mechanisms at different throats. 4. Conclusions This work studied the effect of impact angles on powder dispersion at the presence of air flow by using CFD-DEM approach. By analysing the flow field and micro-dynamics of particles, the dispersion mechanisms were investigated at the particle level. The main findings can be summarised as follows:
The generation of fine particles with size less than 5 mm was mainly attributed to the second impaction instead of the
first one. After the first impaction, the agglomerate was broken up into many small fragments with weak strength; second impaction further disintegrated them into smaller fragments. Powder deposition was dependent on impaction angle and the inertial energy (mass and velocity) of fragments. While increasing flow rate and the number of impactions increased breakage, they also resulted in larger powder deposition. To have optimal dispersion, both device design and flow condition should be considered. Agglomerate breakage at different conditions was governed by the same mechanisms, which can be described by a unified error function in terms of the ratio of agglomerate-wall impaction and agglomerate strength.
Z.B. Tong et al. / Journal of Aerosol Science 42 (2011) 811–819
819
Acknowledgements Authors are grateful to the Australia Research Council (ARC) for the financial support for this work. References Adi, S., Tong, Z.B., Chan, H.K., Yang, R.Y., & Yu, A.B. (2010). Impact angles as an alternative way to improve aerosolisation of powders for inhalation? European Journal of Pharmaceutical Sciences, 41, 320–327. Bagster, D.F., & Tomi, D. (1974). The stresses within a sphere in simple flow fields. Chemical Engineering Science, 29, 1773–1783. Brown, D.P., Kauppinen, E.I., & Jokiniemi, J.K. (2003). Agglomerate deaggregation potential during dry powder inhaler operation and characterization under steady and unsteady conditions. Journal of Aerosol Science, 34, 1417–1428. Coates, M.S., Fletcher, D.F., Chan, H.-K., & Raper, J.A. (2005). The role of capsule on the performance of a dry powder inhaler using computational and experimental analyses. Pharmaceutical Research, 22, 923–932. Dunbar, C.A., Hickey, A.J., & Holzner, P. (1998). Dispersion and characterization of pharmaceutical dry powder aerosols. Kona, 16, 7–45. Finlay, W.H. (2001). The Mechanics of Inhaled Pharmaceutical Aerosols, An Introduction. Academic Press: London. French, D.L., Edwards, D.A., & Niven, R.W. (1996). The influence of formulation on emission, deaggregation and deposition of dry powders for inhalation. Journal of Aerosol Science, 27, 769–783. Li, W.-I., Perzl, M., Heyder, J., Langer, R., Brain, J.D., Englmeier, K.H., Niven, R.W., & Edwards, D.A. (1996). Aerodynamics and aerosol particle deaggregation phenomena in model oral-pharyngeal cavities. Journal of Aerosol Science, 27, 1269–1286. Moreno, R., & Ghadiri, M. (2006). Mechanistic analysis and computer simulation of impact breakage of agglomerates: effect of surface energy. Chemical Engineering Science, 61, 2476–2481. Moreno, R., Ghadiri, M., & Antony, S.J. (2003). Effect of the impact angle on the breakage of agglomerates: a numerical study using DEM. Powder Technology, 130, 132–137. Rumpf, H. (1962). The Strength of Granules and Agglomerates. Interscience: New York. Samimi, A., Moreno, R., & Ghadiri, M. (2004). Analysis of impact damage of agglomerates: effect of impact angle. Powder Technology, 143, 97–109. Timsina, M.P., Martin, G.P., Marriott, C., Ganderton, D., & Yianneskis, M. (1994). Drug delivery to the respiratory tract using dry powder inhalers. International Journal of Pharmaceutics, 101, 1–13. Tong, Z.B., Yang, R.Y., Chu, K.W., Yu, A.B., Adi, S., & Chan, H.K. (2010). Numerical study of the effects of particle size and polydispersity on the agglomerate dispersion in a cyclonic flow. Chemical Engineering Journal, 164, 432–441. Tong, Z.B., Yang, R.Y., Yu, A.B., Adi, S., & Chan, H.K. (2009). Numerical modelling of the breakage of loose agglomerates of fine particles. Powder Technology, 196, 213–221. Voss, A., & Finlay, W.H. (2002). Deagglomeration of dry powder pharmaceutical aerosols. International Journal of Pharmaceutics, 248, 39–50. Xu, C.B., & Zhu, J. (2006). Parametric study of fine particle fluidization under mechanical vibration. Powder Technology, 161, 135–144. Yang, R.Y., Yu, A.B., Choi, S.K., Coates, M.S., & Chan, H.K. (2008). Agglomeration of fine particles subjected to centripetal compaction. Powder Technology, 184, 122–129.
