2020 年 68 巻 8 号 p. 726-736
This study investigated the particle adhesion mechanism in a capsule of dry powder inhaler (DPI) based on a combined computational fluid dynamics and discrete element method (CFD–DEM) approach. In this study, the Johnson–Kendall–Roberts (JKR) theory was selected as the adhesion force model. The simulation results corroborated the experimental results—numerous particles remained on the outlet side of the capsule, while a few particles remained on the inlet side. In the computer simulation, the modeled particles were placed in a capsule. They were quickly dispersed to both sides of the capsule, by air fed from one side of the capsule, and delivered from the air inlet side to the outlet side of the capsule. It was confirmed that vortex flows were seen at the outlet side of the capsule, which, however, were not seen at the inlet side. Numerous collisions were observed at the outlet side, while very few collisions were observed at the inlet side. These results suggested that the vortex flows were crucial to reduce the amount of residual particles in the capsule. The original capsule was then modified to enhance the vortex flow in the area, where many particles were found remaining. The modified capsule reduced the number of residual particles compared to the original capsule. This investigation suggests that the CFD–DEM approach can be a great tool for understanding the particle adhesion mechanism and improving the delivery efficiency of DPIs.
In recent years, dry powder inhalers (DPIs) that directly deliver powdered drugs to human lungs have attracted much attention.1–9) Currently, DPIs are used for treating pulmonary diseases, in addition to being used as a new administration method for high molecular drugs, which are difficult to be absorbed in the gastrointestinal tract.10) In treatments involving powder inhalation formulations, the drug particles introduced from the inhaler device are directly delivered to the patient’s lungs through the patient’s breath. However, those patients who do not have enough suction ability owing to their small lung capacity or bronchial stenosis cannot completely inhale the DPIs. This results in the drug particles remaining in the device.11) This is because their weak breathing capacity does not have enough force to disperse the drug particles, which exhibit strong cohesion among themselves and adhesion to the device’s wall.12,13)
One of the major approaches to improving the emitted dose of drug particles from the device is the carrier method, in which large particles such as, lactose and mannitol are covered with the drug particles to increase the drug transportability and flowability.14,15) In the carrier method, the important factors for the desirable dispersion of the drug particles are the type of the particle,16) particle size,17) shape, and surface conditions.18,19) The particle design and the device design are critical to improve the delivery efficiency of the DPIs. Furthermore, understanding the mechanism of cohesion among the particles and the adhesion between the particles and the device is essential to maximize the drug release from the device.
So far, the inhalation performance from the devices has been mainly evaluated by in vitro experiments using a cascade impactor or a twin impinger. However, to evaluate the precise inhalation performance, an accurate particle release mechanism from the device should be devised. To achieve this, analyses of the adhesive forces between the particles and the device, and of the fluid and particle behaviors in the device is necessary. The experimental approach cannot fully investigate the fluid and particle behavior in the device because of their complicated behaviors.
Recently, a computational fluid dynamics (CFD) method has been used to analyze the fluid behavior in the device. Matida et al. demonstrated the role of CFD on the optimization of the device design and demonstrated that a spacer with a buffer region could reduce the turbulence kinetic energy more effectively than a straight spacer.20) Boer et al. investigated the effect of the branch flow in Twincer™ on the dispersion efficiency, and revealed that a block of bypass channel reduced the total flow rate and pressure in the device with an unchanged classification performance and powder flow rate.21) They concluded that CFD analysis was very useful for the design of devices; however, the CFD investigations were not adequate owing to the lack of available information on the particle behaviors.
Some researchers studied not only the fluid behaviors, but also the particle trajectories by using a discrete phase model (DPM). Coates et al. calculated the behavior of particles in an Aerolizer® using the DPM and determined the average particle impaction velocity.22) Donovan et al. analyzed the particle trajectories inside a Handihaler® and an Aerolizer, in which the particle size had no impact on the collisions between particles and the wall in the Handihaler, while the number of collisions in the Aerolizer increased as the particle size became large.23) This result suggested that the particle behavior depended on the physical particle properties, as well as the structure of the device. Shur et al. performed a CFD–DPM analysis using four different devices, Handihaler, Cyclohaler®, Mod 1, and Mod 2, which have different inlet shapes.24) The pressure drops of Mod 1 and Mod 2 almost agreed with that of the Handihaler, while the flow velocity in the chamber became larger than that in the Cyclohaler. These results suggested that the inlet shape had a large impact on the particle behavior in the device. Although the DPM calculates the particle behavior in the devices, it cannot explicitly incorporate the inter-particle adhesion in the fluid.
The discrete element method (DEM),25) which can analyze the particle adhesion behavior, is a straightforward approach to understand the particle adhesion mechanism in the device. Tong et al. studied the dispersion mechanism of agglomerated particles in an Aerolizer by a CFD–DEM coupled model.26) In our previous study, a CFD–DEM coupled model was conducted to analyze the particle transportation in a human lung model.27) However, very few studies on the particle behavior have been conducted on the device by using the CFD–DEM coupled model, as the amount of particle emissions from the device seriously affects the particle transport in the human lung.
In this study, the CFD–DEM coupled model with the consideration of adhesive forces among the particles and the particle − capsule wall were considered to numerically analyze the fluid and particle behaviors in the capsule of the device, and to find the key factors affecting the amount of residual particles. Furthermore, a modified capsule was developed to reduce the residual amount by leveraging the knowledge obtained from the CFD–DEM simulation.
Mannitol (Mitsubishi Shoji Foodtech Co., Ltd., Tokyo, Japan) powder, which was prepared using a small spray dryer (CPL-2, OHKAWARA KAKOHKI Co., Ltd., Yokohama, Japan), was used as the model DPI particles for the experiments. The spray drying experimental conditions are summarized in the Supplementary Material. The scanning electron microscopy (SEM) image of the prepared powder was obtained using a field emission SEM (JXA-8530F, JEOL Ltd., Tokyo, Japan). The particle size distribution was measured with a laser diffraction particle analyzer (SALD-2100, SHIMADZU Co., Kyoto, Japan).
Figure 1 shows an SEM image and the size distribution of the spray dried mannitol powder. The median size and standard deviation of the particles were 4.77 µm and 2.0, respectively.
Figure 2 shows a schematic diagram of the powder inhalation experimental apparatus. A Jethaler® (Tokico System Solutions, Ltd., Kanagawa, Japan) was used as a device, and was connected to a cascade impactor via a throat in order to collect particles emitted from the device. The experimental system was hermetically sealed using a glove bag, in which humidity was controlled at 50 ± 5% by introducing an aqueous glycerin solution. The mannitol powder (20 mg) was filled in a No. 2 hydroxypropylmethylcellulose (HPMC) hard capsule (Shionogi Qualicaps, Nara, Japan) which was set into the device, followed by the powder suction for 5 s at a flow rate of 28.3 L/min.28–30)
The residual mass of the powder in the capsule was measured (n = 3).
Simulation MethodIn this study, a combined CFD and DEM (CFD–DEM) model was used to analyze the particle and fluid bahavior.31) The CFD–DEM calculation was performed with a DEM simulation software (EDEM™ Ver. 2018, DEM Solutions, Ltd., Edinburgh, U.K.) and a fluid dynamics analysis software (Fluent® Ver. 18.0, ANSYS, Inc., Canonsburg, PA, U.S.A).
CFD–DEM ModelIn the CFD–DEM model,31) the fluid phase is governed by the continuity and Navier–Stokes equations, while the translational and rotational motions of the particles are governed by the Newton’s second law. The continuity and the Navier–Stokes equations are defined as
 | (1) |
 | (2) |
where εvoid, u, ρ, p, τ, and g are the void fraction, vector of gas velocities, gas density, static pressure, fluid viscous stress tensor, and gravitational force, respectively. Here, fi is the volumetric particle–fluid interaction force, which is described as
 | (3) |
where Ff and VCell are the drag force exerted on the particle and volume of the cell, respectively. The fluid flow was solved using a standard k-ε model.32) Here, k denotes the turbulent kinetic energy, which is described as
 | (4) |
where u′ is the mean fluctuating velocity. k is used for dispersion metrics for DPIs as seen in previous studies.33,34)
The Newton’s second low is defined as
 | (5) |
 | (6) |
where mp, vp, and ωp are the mass, translational velocity vector, and angular velocity vector of the particle, respectively. Fc, l, and T are the contact force, moment of inertia, and resultant contact torque acting on the particle, respectively. Here Ff is described as
 | (7) |
where Vp is the particle volume. For the calculation of β, the equation advocated by Ergun and Wen–Yu is used,35) which is shown in Eqs. (8) and (9).
 | (8) |
 | (9) |
where dp is particle diameter. The coefficient CD is described as
 | (10) |
where Rep is Reynolds number of the particle.
Contact ModelHertz–Mindlin contact model is used to express the contact force between particle–particle and particle–wall.36,37) The contact force Fc is divided into normal and tangential components. The contact force in the normal direction is composed of the elastic force, based on the Johnson–Kendall–Roberts (JKR) model and the damping force.38) On the other hand, the contact force in the tangential direction is composed of the elastic and damping forces.
 | (11) |
 | (12) |
 | (13) |
The normal elastic force based on the JKR model is defined by Eq. (14).
 | (14) |
Here γE, E*, a, and R* are the surface energy, equivalent Young’s modulus, contact radius, and the equivalent radius, respectively. E* and R* are expressed by
 | (15) |
 | (16) |
where E, ν, and R are the Young’s modulus, Poisson’s ratio, and particle radius, respectively. Subscripts i and j identify the particles. Moreover, the normal overlap δn is expressed by
 | (17) |
In this study, the normal damping force Fdn, the tangential elastic force Fet and the tangential damping force Fdt were used according to Herz–Mindlin contact model.36,37)
Design of the Device and Simulation ConditionFigure 3 shows the internal structure of the original device and the analysis area for the numerical simulation. The analysis region was set inside the capsule and the air inlet portion. The major and minor axis lengths of the capsule were 18.0 and 6.4 mm, respectively. In this study, particle and fluid behaviors were analyzed by dividing the capsule into 20 parts with respect to X axis. The average drag force on the particles at each position in the capsule was calculated to investigate the emission mechanism of particles from the capsule. In addition, the turbulence kinetic energies at four regions (outlet side: X <−6.3, outlet: −4.5 < X < −1.8, inlet: 1.8 < X < 4.5 and inlet side: X > 6.3) in the capsules were calculated from Eq. (4). Here, the average turbulent kinetic energies at the outlet side, the outlet, the inlet and the inlet side were defined as koutlet side, koutlet, kinlet, and kinlet side, respectively. This study investigated the turbulent kinetic energy using the ratio of k at the inlet side to the inlet (k*inlet) and the ratio of k at the outlet side to the outlet (k*outlet). The collision was defined as a momentary contact caused by a rebound. Based on the calculation results using the original capsule, the present study proposed modified capsule to improve the powder emission as shown in Fig. 4. The modified capsules had two holes on the capsule wall at the outlet side, where many particles remained and collided (the details are given in Results and Discussion). The hole diameters were 0.8, 0.4, 1.6, 0.8, 0.8, and 1.6 mm for cases 1, 2, 3, 4, 5, and 6, respectively. The horizontal positions of the holes were at X = −7.65, 0, and 7.65 for cases 1, 4, and 5, respectively. The other modified capsule had one hole in the top of capsule (case 6). The position of each hole was set at the center in direction of the capsule’s height. The number of computational cells in the original and modified capsules were approximately 70000 and 80000, respectively. For the boundary conditions in the original capsule, the fluid velocity at the outlet and pressure at the inlet were set to 37.5 m/s (28.3 L/min) and standard atmospheric pressure, respectively. On the other hand, for the boundary conditions in the modified capsule, the fluid velocity at the outlet was set to 37.5 m/s (28.3 L/min); however, the pressures at the inlet and holes were set to the standard atmospheric pressure as the inlet pressure. In this simulation, the initial location of particles was −5 < X < 5. The adhesion of the particles would vary with different surface energies. The CFD–DEM calculation parameters are summarized in Table 1. In this simulation, fluid was assumed as the incompressible air. For the powder physical properties for the DEM simulation, we followed a previous study.39)
In this study, the range of the outlet side was X < −6.3, the outlet was −4.5 < X < −1.8, the Inlet Was 1.8 < X < 4.5 and the outlet side was X > 6.3
The hole diameters: 0.8 mm (case 1, 4, 5), 0.4 mm (case 2), and 1.6 mm (case 3, 6). Position of holes: (X, Z) = (−7.65, 0) (case 1, 2 and 3), (X, Z) = (0, 0) (case 4) and (X, Z) = (7.65, 0) (case 5). The other modified capsule: one hole at the capsule edge (case 6).
| Parameter | Value | |
|---|---|---|
| Time step for fluid | [s] | 5.0 × 10−6 |
| Time step for particle | [s] | 1.0 × 10−8 |
| Fluid density | [kg/m3] | 1.2 |
| Fluid viscosity | [Pa·s] | 1.8 × 10−5 |
| Particle diameter | [µm] | 50 |
| Particle density33) | [kg/m3] | 1500 |
| Mass of particle | [kg] | 20 × 10−3 |
| Young’s modulus of particle33) | [GPa] | 0.1 |
| Poisson’s ratio of particle33) | [—] | 0.3 |
| Coefficient of resistance33) | [—] | 0.85 |
| Sliding friction coefficient33) | [—] | 0.7 |
| Rolling friction coefficient33) | [—] | 0.1 |
| Surface energy | [J/m2] | 0–0.03 |
To qualitatively validate the simulation parameters, the simulated and experimental results were compared by using the residual mass of particles and the particle behavior in the capsule. Figure 5 shows the relationship between the surface energy and the residual mass of the particles in the capsule. It was found that the residual mass of the particles in the capsule almost linearly increased as the surface energy from the JKR theory increased. The relationship between the residual mass of the particles and the surface energy can be mathematically expressed through the following linear expression.
 | (18) |
Here, in the experiment, the residual mass of the particles in the capsule was measured to be 3.05 mg. By using the proposed expression, the surface energy could be determined as 0.0129 J/m2. The residual mass of particles calculated under the surface energy of 0.0129 J/m2 was 3.06 mg, which was in good agreement with the experimental data. Figure 6 indicates the experimental and simulated particle behavior in the capsule. In the simulation, the surface energy of the particles was set to 0.0129 J/m2. The experimental result showed that particles located at the center of the capsule (at −6.3 < X < 6.3) before the inhalation remained on the left side even after the inhalation. The simulated result also showed that the particles located at the center of the capsule before inhalation remained on the left side of the capsule. It was found that the numerical simulation could predict the particle residual behavior in the capsule reasonably even though the particle size was 50 µm.
(a) Experimental result and (b) simulated result. (Color figure can be accessed in the online version.)
Figure 7 illustrates the contour maps of the particle velocity, which was high in the center of the capsule between 0.0020 and 0.0100 s, and got reduced in the left side and the right sides of the capsule between 0.0100 and 0.0200 s. The particles were dispersed in the left side, as well as the inlet sides of the capsule. However, at 0.1000 s, almost particles remained on the left side. The mechanism of particle residual phenomenon in the left side could be explained from the fluid behavior as follows.
(Color figure can be accessed in the online version.)
Figure 8 shows the contour map of the fluid velocity and the streamlines in the capsule. The fluid velocity was high at the center of the capsule (inlet and outlet regions), while it was low at the inlet and outlet sides of the capsule. The particle velocity was affected by the fluid velocity and particles dispersed in the outlet side and inlet side between 0.0100 and 0.0200 s, as shown in Fig. 7. From the fluid streamlines, a vortex flow was observed at the right side, where few particles remained. However, a similar vortex flow was not observed at the left side, where several particles remained. From this finding, it appears that the vortex flow possibly reduced the collision between the particles and the capsule wall. To confirm this prediction, the relationship between the positions of the residual particles, the number of collisions, and the drag force was analyzed. Figure 9(a) shows the number of the residual particles at each position in the capsule. The number of particles having velocities of zero, which can be assumed as residual particles in the capsule, were counted. Few residual particles existed at X > 6.3 (inlet side), while many particles remined at X < −6.3 (outlet side). The residual particle number showed a peak at X = −7.65. Figure 9(b) indicates the number of collisions between the particles and the capsule wall at each position in the capsule. The numbers of collisions at the inlet and outlet sides were more than that at the center of the capsule (inlet and outlet regions), and the most collisions between the particles and the capsule wall were observed at X < −6.3 (the outlet side). The kinetic energy loss of particles due to the collision on the capsule wall would result in many residual particles at the outside. Figure 9(c) describes the average fluid drag force on the particles at each position in the capsule among inhalation. The drag force had two similar peaks at the center of the capsule (inlet and outlet regions). Focusing on the inlet side and outlet side, the drag force at X > 6.3 (the inlet side) was larger than that at X < −6.3 (the outlet side). These results suggest that the fluid drag force affected the particles at the inlet side, leading to a decrease in the opportunities for the particle collisions on the capsule wall. On the other hand, the drag force at the outlet side was so low that the particles tended to be accompanied by the flow at the previous position. It is considered that particles, which were not entrained by the outlet flow, were transported by the initial inlet flow to the capsule wall at the outlet side. Thus, many particles collided with each other and adhered to the capsule wall at the outlet side. In these results, the vortex flow and the high drag force of particles reduced the collisions, leading to a decrease in the number of residual particles at the inlet side. For the analysis of vortex the flow, following discussions were made focusing on the turbulence kinetic energy.
(a) Contour map and (b) streamlines. Outlet velocity is 37.5 m/s. In the contour map, dotted line shows the center of the capsule. Single black line shows inlet and outlet sides of the capsule. In the streamlines, single black line shows inlet side of the capsule. (Color figure can be accessed in the online version.)
(a) Residual particle numbers; (b) Number of collisions between the particles and the capsule wall; and (c) Fluid drag force on particle.
From above section, a modified capsule structure, which has adequate local vortices at the inlet and outlet sides, was proposed. The proposed capsule was made with two holes in the capsule for creating a vortex flow at X < −6.3 (outlet side). Since the airflow entered the capsule from the holes, no particles were emitted through the holes. Figures 10(a) and (b) show the residual mass of particles at the outlet side and inlet side. In the versions of the modified capsule with the holes at the outlet side (cases 1 and 6), the particles remained at the inlet side. On the other hand, in the remaining versions of the modified capsule (cases 4 and 5), the particles remained at the outlet side. The residual behavior of the particles was compared in the modified capsule among cases 1, 4, 5, and 6. Figure 10(c) indicates the ratio of k at the outlet side (X < −6.3) to that at the outlet (−4.5 < X < −1.8). Figure 10(d) describes the ratio of k at inlet side (X > 6.3) to that at the inlet (1.8 < X < 4.5) in the modified capsule. In terms of the position of the holes (cases 1, 4, and 5), the fewest particles remained in the capsule with holes at X = −7.65. From Figs. 10(c) and (d), the ratio of k at the outlet side to at the outlet (k*outlet = koutle side/koutlet) was low in the modified capsule with holes at X = 0 and 7.65. On the other hand, k*outlet was high in the modified capsule with holes at X = −7.65. In terms of the hole at outlet side (cases 1 and 6), case 1 had fewer mass of particles remaining than that case 6. From Figs. 10(c) and (d), in case 1, k*outlet was almost the same as the ratio of k at the inlet side to at the inlet (k*inlet = kinle side/kinlet). On the other hand, since k*outlet was too lower than k*inlet in case 6, the flow intensity was low at the inlet side, resulting in many residual particles at the inlet side. These results suggested that making holes with little difference of turbulent kinetic energies at the outlet side (k*outlet) and inlet side (k*inlet) was crucial for the particle emission. In the following discussion, we focus on case 1.
(a) Residual mass of particles at the outlet side in capsule; (b) Residual mass of particles at the inlet side in capsule; (c) Ratio of turbulence kinetic energy at the outlet side koutlet Side to turbulence kinetic energy at outlet koutlet; and (d) Ratio of turbulence kinetic energy at inlet side kinlet Side to turbulence kinetic energy at inlet kinlet.
Figure 11 shows the residual particles after the inhalation, the fluid streamlines, the fluid velocity vectors, and the contour map of the fluid velocity in the modified capsule of case 1. From Figs. 11(a) and (b), in this capsule, the particles did not remain at the outlet side and a vortex flow was observed at the outlet side. The fluid velocity vectors in the modified capsule shown in Fig. 11(c) demonstrated that the airflow entered the capsule from the holes. In addition, from the fluid velocity contours in the modified capsule at different cross section shown in Figs. 11(d) and (e), the airflow from the hole had almost the same velocity as that from the original inlet. The kinetic energy of the modified capsule was compared with one of the original capsule to observe the change in the fluid. Figures 12(a) and (b) indicate the contour map of k in the original and the modified capsules. At the outlet side, k in the modified capsule was larger than that in the original capsule. Thus, k at the outlet side was increased by introducing two holes. Figure 12(c) shows the relationship between the position and k. At the outlet side (X < −6.3), k in the modified capsule increased significantly. However, at the inlet side (X > 6.3), k in the modified capsule agreed with that in the original capsule. Thus, by creating the vortex flow, k at the outlet side was increased, while it did not change significantly at the inlet side. Figure 13(a) shows the position and the number of particles in the original and modified capsules. Figure 13(b) indicates the position and the collision between the particles and the capsule wall in the original and the modified capsules, while Fig. 13(c) describes the relationship between the position and the fluid drag force in the original and the modified capsules. These figures show that the number of collisions between the particles and the capsule wall were reduced and the fluid drag force was larger at the outlet side (X < −6.3) in the modified capsule than that in the original capsule. On the other hand, at the inlet side (X > 6.3), more particles remained in the modified capsule than that in the original capsule. From these results, it was found that two holes at the outlet side reduced the collisions between the particles and the capsule wall, and also increased the fluid drag force at the outlet side. As k increased at the outlet side, the particles entrained by the initial inlet flow were disturbed at the outlet side and did not collide with the capsule wall at the outlet side. It was observed that creating a vortex flow in the location where the particles adhered was an important factor for the dispersion of particles in the capsule. Figure 14(a) explains the relationship between the hole diameter and the residual mass of the particles in the modified capsules. Bothe of the experimental and simulation data showed that the residual particle mass increased with the diameter of the hole. These results got the same tendency as the previous reports.40) Focusing on the absolute mass, calculated residual particle mass was a bit less than that in the experiment. This was attributed to that the pressure at holes was set to the standard atmospheric pressure in the simulation condition. However, the pressure at holes was smaller than the standard atmospheric pressure in the experiment. In case 3 (hole diameter: 1.6 mm), the residual mass of particles was higher than that in the original capsule. Since many particles remained at the inlet side in the modified capsule, the turbulent kinetic energy in the inlet side were analyzed. Figure 14(b) shows the ratio of k at the inlet side to that at the inlet and the residual mass of particles in the modified capsules (case 1, 2, and 3). The residual particles increased as k*inlet decreased. Thus, turbulent kinetic energy at the inlet side became lower than that at the inlet, and many particles collided against the capsule wall at the inlet side. It was considered that the relative intensity of k was important for the improvement of the emission dose of DPIs.
(a) Residual particle behavior after the inhalation; (b) Fluid Streamlines; (c) Vectors of Fluid Velocity on the cross section when viewed from the top; (d) Contour map of fluid velocity; and (e) Contour map of fluid velocity on the cross section when viewed from the top. the outlet side of the capsule shows single black line in (a) and (b). (Color figure can be accessed in the online version.)
(a) Contour map in the original capsule; (b) Contour map in the modified capsule; and (c) Relationship between the position of the capsule and the turbulent kinetic energy. (Color figure can be accessed in the online version.)
(a) Number of collisions between particle and capsule wall and (b) Fluid drag force.
(a) Hole diameter and (b) Ratio of turbulence kinetic energy at inlet side kinlet Side to turbulence kinetic energy at inlet kinlet.
In this study, the particle behavior and the particle adhesion mechanism in a capsule of dry powder inhaler device was numerically simulated by a coupled CFD–DEM model.
The conclusions obtained from the study are as follows:
It is considered more particles were emitted from the capsule in the case of little difference turbulence kinetic energy in the capsule between the inlet and outlet sides. From these results, it can be inferred that the CFD–DEM simulation is a great tool for investigating the key parameters for the design of DPIs.
This work is supported by Grant-in-Aid for Challenging Exploratory Research (JP18K19409).
The authors also acknowledge the partial support from Ansys Japan, Cybernet Systems, and Altair Engineering.
The authors declare no conflict of interest.
The online version of this article contains supplementary materials.
