Abstract

Respiratory diseases debilitate more than 250 million people around the world. Among available inhalation devices, the soft mist inhaler (SMI) is the most efficient at delivering drugs to ease respiratory disease symptoms. In this study, we analyzed the SMI performance in terms of the aerosol's velocity profiles, flow pattern, size distribution, and deposition by employing computational fluid dynamics (CFD) simulations. We modeled two different simplified mouth geometries, idealized mouth (IM), and standard mouth (SM). Three different locations (x = 0, x = 5, and x = 10 mm) for the SMI nozzle orifice were chosen along the mouth cavity centerlines, followed by two different SMI nozzle angles (10 deg and 20 deg) for IM geometry. A flowrate of 30 L/min was applied. The simulation results were evaluated against experimental data. It was found that the SMI could be simulated successfully with a level of error of less than 10%. The inhalation flowrate significantly impacted the aerosol's velocity profile and deposition efficiency on both the IM and SM walls. The lowest particle deposition on the mouth wall occurred when a fixed flowrate (30 L/min) was applied inside both geometries, and the SMI nozzle position moved forward to x = 10 mm from the IM and SM inlets. An increase in the SMI nozzle angle increased particle deposition and decreased the deposition fraction for particles with a diameter above 5 μm inside the IM.

1 Introduction

Despite substantial research on drug delivery to the human respiratory tract for treating asthma and chronic obstructive pulmonary disease, inhaler device efficiency is still under study. The geometric design of inhaler devices and the inaccuracy in coordination between the actuation and inhalation play significant roles in drug wastage [1]. Pharmaceutical aerosol delivery to human lungs is inefficient due to about a 40% drug loss in the extra-thoracic region and approximately 22–27% in the device mouthpiece [24]. This amount varies for different inhaler devices. Pressurized metered dose inhalers (pMDIs), which deliver drug droplets under liquid propellant pressure, and dry powder inhalers (DPIs) that deliver drug particles by the act of a patient's inspiratory effort result in 10–20% lung deposition [5]. Soft mist inhalers (SMIs), which were made commercially available in 2003 [6], atomize the drug solution through a tiny nozzle into small droplets [7,8]—these inhalers result in almost 40% drug deposition into the lungs. This enhanced drug delivery is attributed to the patient's inhalation dependency reduction, improved usability, and the SMIs' propellant-free nature [6]. These advantages have enabled many researchers to investigate and perform further experimental and computational fluid dynamics (CFD) studies using SMI [911].

For in vivo functionality, inhalers must produce fine aerosols of a suitable size (typically 5 μm in diameter) [12]. Converting a drug solution to appropriately sized droplets involves using electrical energy to generate mechanical energy in the form of vibration [13]. New SMIs generate fine aerosol droplets and deliver a metered dose of the drug solution to the target site of action by mechanical energy derived from a metal spring located at the device's base. Twisting the base of the SMI about 180 deg compresses the spring, simultaneously withdrawing a predefined dose of liquid inhalation solution from the reservoir into the capillary tube [12]. The drug solution is then forced through two converging (at an angle of approximately 90 deg), 10 μm-diameter microchannels, generating two high-speed liquid streams. The streams then collide downstream of the precisely engineered nozzle system (uniblock) to form a slow-moving, inhalable aerosol plume [14]. The high pressure (hundreds of atmospheres) at the orifice nozzle [15] and the resulting fine droplets lead to a longer generation time and lower velocity. This high-pressure stream results in more drug droplets reaching the lungs rather than being wasted in the oral cavity, pharynx, and larynx, as is the case with traditional inhalers [16,17].

Among pharmaceutical inhalers' variables, the drug aerosol's diameter and velocity are the two most important factors in drug deposition in the human respiratory tract [18,19]. These factors themselves depend on environment temperature, relative humidity, coordination of inhalation, and the patient's respiratory tract [20].

Drug aerosol diameters range from nanometers to micrometers [11], but generally, droplets with a diameter range of 2–5 μm can reach and deposit in the lungs; thus, understanding the respirable size range is necessary [5]. Aerosol droplets bigger than 5 μm are deposited before entering the trachea on the oropharynx, mouth-throat, and upper tracheobronchial region due to inertial impact along their path to the lungs [19]. In comparison, droplets smaller than 2 μm have a great potential to be exhaled from the body [19].

Several studies have evaluated the effect of independent parameters, such as the SMI nozzle angle and position [21,22] and the inhalation flowrate [23], on the drug particles' velocity and diameter. Wasted medication at the back of the throat can be reduced by optimizing the nozzle's position [24]. A flowrate of 75 L/min results in the lowest and highest mouth-throat drug deposition for DPI and MDI at the nozzle angle of +10 deg and –20 deg (relative to the horizontal axis), respectively [25]. Drug deposition in the human respiratory tract by a pMDI can be varied with different angles of the actuator nozzle. Using a CFD approach, the best angle of the pMDI actuator nozzle was found to be 120 deg, leading to a higher particle velocity and a greater possibility of the drug reaching the alveoli [22]. Ocular and facial drug deposition can occur due to misuse, as when a patient holds a Respimat SMI at an angle, causing unwanted side effects from drug deposition of less than 1% of a dose deposited in the ocular area [21]. The aerosol plume's entrance angle strongly affects drug droplet penetration efficiency through a human oral airway. The aerosol penetration efficiency monotonically increases with a range of 0 deg–20 deg of the plume's entrance angle, with maximum efficiency occurring at 20 deg [26].

Though the SMI nozzle produces drug droplets in the diameter range of 100 nm–60 μm, the distribution is polydisperse [4]. This uneven drug particle distribution [27,28] is attributed to several factors: aerosol evaporation and condensation, relative humidity inside the mouth-throat, and drug deposition at the inhaler's mouthpiece. Droplet evaporation leads to finer particle sizes, while droplet condensation results in greater aerosol diameter [2].

The term aerodynamic diameter is commonly used by the pharmaceutical industry. It refers to the diameter of a spherical particle with a constant density of 1000 kg/m3, which has the same vertical velocity in the air as the particle of interest [29]. The aerodynamic diameter can be calculated using the following equation:
aerodynamicdiameter=geometricdiameter×(ρpρ0x)1/2
(1)

where ρp and ρ0 are the particle and unit densities, respectively, and x is the dynamic shape factor [30]. Earlier research has reported that SMI can generate aerosol drug droplets with a fine particle fraction of >60%, which can be defined as the mass fraction of particle size less than 5 μm; and mass median aerodynamic diameter of <5 μm, which means that 50% of particles have an aerodynamic diameter greater than 5 μm and 50% of the particles have an aerodynamic diameter less than 5 μm (D50) [31,32]. Several in vitro, in vivo, and in silico research studies have been conducted to assess the effect of different parameters on aerodynamic particle size distribution through the human respiratory tract [33,34].

The inhalation flowrate is one of the most critical parameters affecting aerosol velocity, diameter, and, consequently, aerosol deposition. A steady inhalation rate results in an approximately 20% improvement in aerosol drug deposition in a patient's lungs when the flowrate increases from 15 to 60 L/min; a flowrate increase also causes a higher (16%) throat deposition [35]. This result was confirmed by Ciciliani et al., who showed that a higher inhalation flowrate increases the inertial impaction of aerosol particles at bifurcations in the oropharynx in large central airways [1]. Mehri et al. showed that with an increase in the flowrate from 45 to 60 L/min, the total dose recovered using a mechanical ventilator increased by almost 16% (at constant relative humidity) [36]. The importance of the flowrate was better demonstrated in an in vitro study by Wei et al., showing that the mean mouth-throat particle deposition increased from 9.8 to 14.2 μg for flow rates of 15 to 45 L/min (representing weak to strong flow rates, respectively) [37]. They also showed that the impact of the mouth-throat geometry compared to the inhalation flow rates was higher for the MDI and SMI, but much less critical than inhalation strength for the DPI [37].

Aerosol interaction with the continuous phase can change the spray plume formation, affecting particle deposition inside the human respiratory tract. Gavtash et al. explored the effects of hydrofluoroalkane MDI spray injection into a stabilized airflow field inside a mouth-throat geometry on an aerosol plume [38]. They showed that a shield-like particle-embedded configuration formed at the early stages of the plume's spatial development. This formation happened due to the existence of an extremely high drag force. As the mass loading of the droplets was low at the initial stages of actuation, an upward trend of the plume was observed that resulted in the formation of recirculation regions inside the mouth-throat.

Although designing an appropriate experimental setup to evaluate drug deposition in mouth-throat is essential, testing processes and developing new SMI nozzles at different positions cost time and material resources. CFD can make the analysis and simulation of multiphase flow faster by avoiding the need for real-time experiments [3941]. In a CFD study by Ma and Lutchen, total particle deposition was evaluated based on different flow rates and particle sizes in human airways [42]. As expected, the deposition fraction was increased with an increase in flowrate. However, deposition efficiency was found to be more sensitive to particle diameter than to flowrate, showing the importance of aerodynamic particle size distribution through the human respiratory tract. Bass and Longest went further and examined the effect of airflow conditions on particle deposition in the mouth-throat path [43]. They found that higher flow rates and a consequently higher Reynolds number increased the sensitivity of the fine aerosols' deposition [43]. This result was also confirmed by Ahookhosh et al., who used a pMDI in a CFD study to evaluate the deposition fraction of particles in mouth-throat at four constant inhalation flow rates [44]. The significant increase in deposition fraction at higher flow rates was attributed to a higher turbulence level and particle inertia. However, Yousefi et al. studied the effects of flow rates (15, 30, and 60 L/min) on the particle deposition rate by a pMDI, and the optimum deposition rate in the lung was acquired at 30 L/min [28].

It's apparent from the literature mentioned earlier that very few studies deal with the analysis of the effect of the nozzle angle on aerosol deposition inside the human mouth. This is paramount because it can frequently occur when an SMI is misused. Furthermore, although a few studies shed light on spray performance, there is a significant lack of research that helps understand the flowrate and nozzle position effects on respiratory aerosol delivery. In this study, we used CFD to explore the impact of flowrate, SMI nozzle position, and the angle on the aerosol's velocity, size distribution, and deposition inside the mouth. Two mouth geometries, i.e., the idealized mouth (IM) and standard mouth (SM), were modeled in our study.

2 Computational Fluid Dynamics Model Development

2.1 Geometry Design and Mesh.

The three-dimensional geometries of a simplified mouth cavity based on both IM and SM were created using the geometry module available in the ANSYS workbench [45]. Figure 1(a) shows the mouth cavity portion of IM as described by Zhang et al. and Fig. 1(b) shows the midplane view of the Andersen cascade impactor induction port (only horizontal section) representing the SM [46]. As seen in Fig. 1, we considered three locations for the SMI nozzle near the mouth inlet along the x-axis (i.e., x0, x1, and x2) and two SMI nozzle angles (10 deg and 20 deg). The SMI nozzle was located at the inlet (x0) due to the SMI insertion through the mouthpiece connector. The mouthpiece connector was excluded from the mesh and did not affect the results of this study.

Fig. 1
Geometry schematics (side views) of (a) IM and (b) SM, with defined x0, x1, and x2 as nozzle positions at x = 0, x = 5, and x = 10 mm, respectively, and nozzle angles of 10 deg and 20 deg
Fig. 1
Geometry schematics (side views) of (a) IM and (b) SM, with defined x0, x1, and x2 as nozzle positions at x = 0, x = 5, and x = 10 mm, respectively, and nozzle angles of 10 deg and 20 deg
Close modal

A hexahedral structured mapped mesh was applied to both IM and SM geometries to ensure a high-quality computational solution. Figures 2(a) and 2(b), respectively, show the front and side views of the meshed IM and SM geometries. Both the average skewness and orthogonal quality measurements were ensured to be in an acceptable range (see Ref. [47] for more information). Additionally, in both models with 162 k and 158 k cells, an inflation layer meshing with a maximum of 15 layers and a growth rate of 1.2 was adopted to capture the effect of velocity fluctuations near the wall.

Fig. 2
Geometries mesh views (side and front views) of (a) IM and (b) SM, including vertical (y-direction) and horizontal (z-direction) lines on front views
Fig. 2
Geometries mesh views (side and front views) of (a) IM and (b) SM, including vertical (y-direction) and horizontal (z-direction) lines on front views
Close modal

2.2 Transport Equations and Methods.

The commercial code ansysfluent v19.1 was employed to solve the continuity and momentum equations. The multiphase flow involves a continuous phase (air) and aerosol particles. The multiphase volume of the fluid method was adopted to simulate the liquid injection and atomization process from an SMI nozzle. This method is a well-established Eulerian numerical approach based on the solution of transport equations by tracking the volume fraction of the target fluid in the grid unit [48]. The key feature of the volume of fluid method is its ability to capture the surface tension's effect and the interphase's behavior [49].

The flow inside the geometries is laminar to turbulent and highly vortical (300 < Re<2050). By considering the velocity at a single point as a sum of the mean (Ūi) and the fluctuating (ui) component in the three coordinates' directions (i.e., i= 1, 2, and 3), the momentum equation can be expressed as follows:
ui=Ūi+ui
(2)
Equally, the continuity equation accounting for mass conservation can be expressed as below:
ρairt+ρairŪixi=0
(3)

where ρair is the continuous phase density and t is the time [50].

Physical properties of the continuous phase and aerosol used in this simulation include air density ρair =1.225 kg/m3, air viscosity μair = 1.789 × 10−5 kg/m s, aerosol density ρp = 998.2 kg/m3, and aerosol viscosity μp = 0.00103 kg/m s. The continuous phase flow is solved using an unsteady Reynolds-averaged Navier–Stokes (URANS) two-equation turbulent model. The URANS equations are highly functional in simulating aerosol spray behavior due to their time-efficient particle trajectories and flow field calculations [3,14]. One of the most popular URANS turbulence models is the low Reynolds number k–ω shear stress transport approximation employed in this study to simulate turbulent effects. The k–ω turbulence model has been widely used in models of multiple bifurcations and oral airways [1,51]. This is due to its advantages in predicting velocity profile, pressure drop, and shear stress for turbulent and transitional flows. The required equations are presented below [50]:
(ρairŪi)t+(ρairŪiŪj)xi=Pxj+xj(μair(Ūixj+Ūjxi))+ρairgixj(ρairuiuj¯)
(4)

where P is the time-average pressure, gi is the component of gravitational acceleration in the xi-axis direction, and the last term, ρairuiuj¯ is known as Reynolds stress.

The k–ω model was used to increase accuracy based on using both the near wall region calculation of kω model and the freestream calculation of k–ε model [52,53]. In the kω model, an extended Boussinesq relationship has been used to relate the Reynolds stress term in URANS equations to the velocity gradient in the flow as presented below [50]:
ρairuiuj¯=νt(Ūixj+Ūjxi)23ρairkδij
(5)
where vt is the turbulent viscosity term, k is the turbulent kinetic energy per unit mass, and δij is Kronecker delta constant (in three coordinate directions, i.e., i,j = 1, 2, and 3). The corresponding equations are read as
νt=Cuρairk2ε
(6)
k=12(Ūi2)
(7)
δij=1,wheni=jδij=0,whenij
(8)
where Cu is a model constant and ε is the dissipation rate calculated using the following equation [50]:
ε=νŪixiŪjxj
(9)
From the above equation, ν is the kinematic eddy viscosity. The governing transport equations for the k-ω turbulence model are as below:
kt+ūjkxj=τijuixjβ*kω+xj((ν+σkνt)(kxj))
(10)
ωt+ūjωxj=αωkτijuixjβω2+xj((ν+σkνt)(ωxj))
(11)

where ω is the specific rate of dissipation, τij is the Reynolds stress tensor, and the other shear stress transport equation coefficients are β* = 0.9, β = 0.075, αk = 0.31, σω = 0.5, and σk = 0.85 [52].

During spray atomization, the density of air (ρair = 1.225 kg/m3) and aerosol particles (ρp = 998.2 kg/m3) remain-almost unchanged. This is because of the low density of the continuous phase and sufficiently small mass flowrate of aerosol particles (1 × 10−5 kg/s) that keeps the total volume of phases almost constant. Also, continuous phase compressibility has a negligible effect on the spraying process, making the model incompressible. Although droplet evaporation at a relative humidity below 90% is low, the small aerosol droplet size in SMI makes droplet evaporation inevitable [4]. Droplet evaporation can affect relative humidity, temperature, and continuous field properties inside an IM and SM. To put evaporation into effect, a species transport model (Eqs. (12) and (13)) with mass transfer between the water vapor (relative humidity) and the air was employed
YVt+(ujYV)xj=xj((DV+vtScT)(YVxj))+SV
(12)
where YV is the mass fraction of water vapor in the mixture (air and water vapor); DV is the diffusion coefficient of water vapor in the mixture; ScT is the turbulent Schmidt number (ScT = 0.9); and SV is the water vapor (mass) source term which accounts for the increase or decrease in water vapor mass fraction in the mixture from evaporating or condensing aerosols. A thermal energy equation is also needed to determine the temperature field inside the geometries, which is expressed as
ρCP(Tt+ujTxj)=xj((kg+ρCPvtPrT)(Txj)+shs(ρDV+ρvtScT)Ysxj)+Se
(13)

In this equation, ρ is the mixture density; CP is constant specific heat; kg is air conductivity; PrT is turbulent Prandtl number (PrT = 0.9); hs is the enthalpy of each species (air and aerosol); and finally, Se is air energy source term due to the presence of a discrete phase. The first term on the right-hand side of Eq. (13) accounts for conductive transport due to turbulent mechanism and the second term represent energy transport due to species diffusion. The presence of mass and energy source terms in Eq. (12) and Eq. (13) is due to evaporation and condensation at the aerosol surface (for more information, see Ref. [3]).

2.3 Discrete Phase Model.

The aerosol particles were considered as the discrete phase since the volume fraction of the liquid is small (<10%). The SMI nozzle atomizes aerosols in a wide range of diameters (100 nm–60 μm), and nozzle actuation in different positions results in varied particle trajectories [54]. The unsteady Lagrangian particle tracking method was employed to address this broad range of particle paths [55].

A random walk method was also implemented to consider the effect of random velocities on particle trajectories [54]. However, this model does not account for reduced turbulent fluctuations in the wall-normal direction, which affect particle deposition. An anisotropic turbulence correction can be applied to better approximate the effects of turbulence on particle deposition. Therefore, near-wall fluctuating velocities are calculated from the following equations:
ui=Fλi(23)k
(14)

where F is an anisotropic correction factor which computes as F = 1 × 10−0.02n while n value ranges from 0 to 60 and λi is a normally distributed random number [3]. The effect of aerosol droplets on the continuous phase (air), referred to as two-way coupling [56], was also included. Previous studies showed a noticeable difference when comparing two-way coupling with one-way coupling to predict the particle deposition rate onto the wall [16].

The Lagrangian equation (Eq. (15)) accounts for the governing forces on the particles. The governing forces that are employed in this study include the drag force, the gravitational force, Brownian motion, and lift force or lift due to shear [57,58]. The virtual mass force, pressure gradient force, and thermophoretic force are excluded from this study due to the very small size of particles, negligible pressure, and temperature differences [3,59]
εvit=aDuiDt+fτp(uivi)+gi(1a)+fi,Brownian+fi,liftdxidt=vi(t)
(15)
τp=Ccρpdp218μ
(16)

where vi is the component of the particle velocity, ui is the component of local continuous velocity, a is the ratio of mixture density to droplet density (a =ρair/ρp 10−3), τp is the particle relaxation time, f is the drag factor, Cc is the Cunningham correction factor; dp is the particle diameter, and μ is the absolute viscosity. Injection characteristics used in this simulation are given in Table 1.

Table 1

Summary of physical characteristics of materials and DPM injection model

ParameterValue
Injection duration [60]1.5 s
Velocity magnitude [2]17.5 m/s
Cone angle [61]22.57°
Particle size range [54]100 nm–60 μm
Total mass flow rate [3]1 × 10–5 kg/s
Time step size1 × 10–5 s
ParameterValue
Injection duration [60]1.5 s
Velocity magnitude [2]17.5 m/s
Cone angle [61]22.57°
Particle size range [54]100 nm–60 μm
Total mass flow rate [3]1 × 10–5 kg/s
Time step size1 × 10–5 s

2.4 Boundary Conditions and Flow Systems.

This study consists of two different configurations for boundary conditions. For the first configuration, while the air flowrate is zero, the prespecified outlet pressure for the inlet and outlet was assigned for both the IM and SM geometries based on the experimental system and the zero-pressure gradient inside the geometries. For the second configuration, while there is an airflow rate in the system, an inlet velocity was selected at the outlet to account for the effect of flowrate on drug aerosol velocity and deposition. A stationary wall with zero slip shear and a trap discrete phase model (DPM) condition was considered to capture drug particles while accounting for drug deposition when they hit the mouth wall so that there is no bounce. A constant temperature of 23 °C was considered during the simulations with a normal relative humidity level of 50% inside both geometries to meet the experimental procedure [2].

2.5 Numerical Controls and Computational Power.

For numerical accuracy, a second-order upwind scheme was employed for momentum, k, and ω [49]. In this study, the convergence of the flow field was determined when continuity, k, and ω residuals reached below 1 × 10−5. To perform computational tasks, the supercomputing facility at Lakehead University was used. This supercomputer was equipped with Intel Xeon Gold 6148 CPU at 2.40 GHz with 16 cores. In addition, parallel processing was used on Intel Xeon Silver 4214 CPU at 2.20 and 2.19 GHz processors with 16 cores. The simulation duration varied between 3 and 7 days.

2.5.1 Mesh Independency Study.

Mesh independency studies were carried out for both geometries using a mesh adaptation technique. Table 2 shows four cell sizes and a corresponding number of meshes for both IM and SM geometry.

Table 2

Cell sizes and the number of cells for IM and SM

GeometryMeshAverage cell size (mm)Number of cellsComparisonNRMSE in X = 15 mm %NRMSE in X = 30 mm %
IMMesh A2.1037,488Meshes A and B3.811.1
Mesh B1.5081,472
Meshes B and C2.39.4
Mesh C1.10162,360
Meshes C and D1.63.5
Mesh D0.81320,044
SMMesh E2.1042,336Meshes E and F12.211.3
Mesh F1.6079,040Meshes F and G3.54.9
Meshes G and H2.33.0
Mesh G1.15158,752
Mesh H0.83312,301
GeometryMeshAverage cell size (mm)Number of cellsComparisonNRMSE in X = 15 mm %NRMSE in X = 30 mm %
IMMesh A2.1037,488Meshes A and B3.811.1
Mesh B1.5081,472
Meshes B and C2.39.4
Mesh C1.10162,360
Meshes C and D1.63.5
Mesh D0.81320,044
SMMesh E2.1042,336Meshes E and F12.211.3
Mesh F1.6079,040Meshes F and G3.54.9
Meshes G and H2.33.0
Mesh G1.15158,752
Mesh H0.83312,301

Figure 3 shows the particles' velocity for different meshes (meshes A–H, see Table 2) for both IM and SM geometry on two lines in the y-direction (vertical) at x = 15 mm and x = 30 mm from the SMI nozzle on the x-axis. We selected these lines close to the nozzle because of high turbulence and velocity fluctuations in that area. The normalized root-mean-square error (NRMSE), defined as NRMSE(%)=(i,j=1N(uiuj)2)/N(i=1N(ui)2)/N×100 where i,j are the variables, N is the number of data points which is seven in this case,ui and uj are two different sets of particles' velocity value, was utilized to quantify the differences among the particles' velocity profiles. All the measured velocity in this study is velocity magnitude. Table 2 shows the NRMSE between the meshes [62].

Fig. 3
Particles' magnitude velocity for different meshes in IM for (a) vertical (y-direction) at x = 15 mm, (b) vertical (y-direction) at x = 30 mm; particles' magnitude velocity for different meshes in SM for (c) vertical (y-direction) at x = 15 mm, (d) vertical (y-direction) at x = 30 mm (legend shows the number of cells)
Fig. 3
Particles' magnitude velocity for different meshes in IM for (a) vertical (y-direction) at x = 15 mm, (b) vertical (y-direction) at x = 30 mm; particles' magnitude velocity for different meshes in SM for (c) vertical (y-direction) at x = 15 mm, (d) vertical (y-direction) at x = 30 mm (legend shows the number of cells)
Close modal

As can be seen in Figs. 3(a) and 3(b) and NRMSEs reported in Table 2; at both distances from the SMI nozzle (x = 15 mm and x = 30 mm, respectively), particles' velocity changes significantly between meshes A and B and meshes B and C. However, for the third refinement (from meshes C to D), increasing the number of cells two times (162 k–320 k) resulted in the NRMSEs = 1.6 and 3.5% for lines at x = 15 mm and x = 30 mm, respectively (see Table 2). For the SM geometry, shown in Figs. 3(c) and 3(d), the NRMSEs reported in Table 2 were 2.3 and 3.0% between meshes G and H for x = 15 mm and x = 30 mm distance from the SMI nozzle, respectively. Therefore, the IM and SM mesh contained 162 k cells (mesh C) and 158 k cells (mesh G), respectively.

3 Results and Discussion

The numerical results of particles' velocity at the outlets of both the IM and SM geometries when the nozzle position was at x0, and the flowrate was 0 L/min were compared with the previous experimental data [2]. The experimental particles' magnitude velocities were measured at the outlets of IM and SM at seven radial distances (i.e., 6, 3, 2, 0, –2, –3, and –6 mm) in the vertical and horizontal directions, that is y and z, respectively.

Figure 4 shows a good agreement between CFD and experimental results of Ref. [2] at the outlets of both geometries at the zero-flux of air and nozzle position of x0. The maximum NRMSEs calculated were 6.5% and 9.6% for both CFD and experimental particles' velocity for the IM and SM geometries, respectively. The discrepancy between experimental results and the simulations can be attributed to imperfect replications of determining locations in simulations and/or experimental uncertainties at the outlet related to particles' velocity and distributions.

Fig. 4
Model validation for particles' magnitude velocity at zero-flux of air and nozzle position of x0 at the outlet of IM geometry for (a) vertical (y-direction), and (b) horizontal (z-direction); and model validation for particles' magnitude velocity at zero-flux of air and nozzle position of x0 at the outlet of SM geometry for (c) vertical (y-direction), and (d) horizontal (z-direction)
Fig. 4
Model validation for particles' magnitude velocity at zero-flux of air and nozzle position of x0 at the outlet of IM geometry for (a) vertical (y-direction), and (b) horizontal (z-direction); and model validation for particles' magnitude velocity at zero-flux of air and nozzle position of x0 at the outlet of SM geometry for (c) vertical (y-direction), and (d) horizontal (z-direction)
Close modal

A fixed flowrate of 30 L/min was applied to both IM and SM to investigate the effect of the flowrate. Figure 5 shows that with a flowrate of 30 L/min, vertical and horizontal (y and z) particle velocities increased at both geometries' outlets. The addition of flowrate to the system helped drug particles to accelerate. Since the SMI nozzle was located along the centerline of the mouth geometry, the average velocity at the center of the profile was higher. However, the velocity increment was more significant (almost two times higher than IM) in the presence of the flowrate of 30 L/min for the SM geometry, as shown in Figs. 5(c) and 5(d). This is mainly due to the geometry of the SM in which the outlet diameter is narrower by 11 mm compared with IM geometry, thus enhancing the impact of the flowrate. The axial velocity increment associated with geometry constriction was consistent with the previous CFD study of Xi and Longest in a constant inhalation rate [63]. They also related the aerosol axial velocity to the drug deposition at the back of the throat. Their study showed that as a result of higher aerosol velocity, a more significant number of particles passed through the mouth (outlet of IM and SM) and were deposited on the back of the throat [63].

Fig. 5
Particles' magnitude velocity at the outlet of IM for (a) vertical (y-direction), and (b) horizontal (z-direction); particles' magnitude velocity at the outlet of SM for (c) vertical (y-direction), and (d) horizontal (z-direction), for nozzle position at x0
Fig. 5
Particles' magnitude velocity at the outlet of IM for (a) vertical (y-direction), and (b) horizontal (z-direction); particles' magnitude velocity at the outlet of SM for (c) vertical (y-direction), and (d) horizontal (z-direction), for nozzle position at x0
Close modal

Slightly different vertical and horizontal velocity profiles are observed when comparing Figs. 5(a) and 5(b) and 5(c) and 5(d). This is because the particles' velocity was reduced due to evaporation and loss of inertia as the particles traveled downstream. However, the asymmetrical velocity profile in vertical and horizontal directions can be attributed to gravity.

Figure 6 represents vertical velocity vector plots along the mouth pathway, that is, in x direction, for the IM and SM. This figure also confirms higher velocity profiles for the SM geometry. As the plume travels along the mouth, uniform profiles were observed in the presence of the flowrate (see Figs. 6(b) and 6(d)), which is more significant in Fig. 6(d) for SM geometry. However, in both IM and SM, velocities along the centerline decreased more rapidly for the case with no flowrate (see Figs. 6(a) and 6(c)) in comparison with near-the-wall locations that are more dominant in Fig. 6(a) for the IM geometry. In fact, the particles' trajectory is influenced by the drag force, which is caused by the surrounding flow field and results in a decrease in the particles' velocity. This effect is more significant at the center of the velocity profile, where the particles have the highest velocity, and when there is no flowrate inside the geometries. In fact, in the absence of a constant flowrate in the system, the aerosol plume is not well formed and developed. Previously, Longest and Hindle also showed that SMI creates an uneven aerosol plume in an open-air environment during the actuation in a zero-flux of air atmosphere [4].

Fig. 6
Particles' magnitude velocity vectors inside IM: (a) without flowrate, and (b) with a flowrate of 30 L/min; and inside SM: (c) without flowrate, and (d) with a flowrate of 30 L/min; at nozzle position of x0
Fig. 6
Particles' magnitude velocity vectors inside IM: (a) without flowrate, and (b) with a flowrate of 30 L/min; and inside SM: (c) without flowrate, and (d) with a flowrate of 30 L/min; at nozzle position of x0
Close modal

Table 3 presents the mouth deposition for both IM and SM geometries as a function of the flowrate (either 0 or 30 L/min) and nozzle position (x0, x1, and x2: see Fig. 1). This table shows an almost 15-fold and 40-fold decrease in mouth wall deposition in the IM and SM geometries, respectively, in the presence of the flowrate. With a fixed flowrate of 30 L/min inside both IM and SM, the particles had less residence time, and consequently, the possibility of deposition on the mouth wall was dramatically reduced. According to Longest et al., a higher inhalation rate resulted in lower particle residence time in the human respiratory tract [3]. Thus, a lack of inhalation increases drug deposition (a waste of drugs inside the mouth region, which leads to increased side effects) [3].

Table 3

Particle deposition data for both IM and SM

GeometryFlow rate (L/min)Nozzle position on x-axisMouth wall deposition (kg)Deposition fraction of particles with diameter >5 μm on mouth wall (%)
IM0x01.27 × 10–797
30x06.82 × 10–11100
0x13.97 × 10–797.3
30x12.75 × 10–11100
0x25.12 × 10–799
30x22.23 × 10–11100
SM0x03.93 × 10–764.5
30x01.5 × 10–8100
0x17.96 × 10–775.11
30x16.97 × 10–9100
0x28.19 × 10–776.1
30x22.08 × 10–998.9
GeometryFlow rate (L/min)Nozzle position on x-axisMouth wall deposition (kg)Deposition fraction of particles with diameter >5 μm on mouth wall (%)
IM0x01.27 × 10–797
30x06.82 × 10–11100
0x13.97 × 10–797.3
30x12.75 × 10–11100
0x25.12 × 10–799
30x22.23 × 10–11100
SM0x03.93 × 10–764.5
30x01.5 × 10–8100
0x17.96 × 10–775.11
30x16.97 × 10–9100
0x28.19 × 10–776.1
30x22.08 × 10–998.9

Figures 7(a) and 7(d) shows velocity path lines inside IM and SM geometries. Recirculation regions were formed inside both geometries (see Fig. 7(a) for IM and Fig. 7(c) for SM) near the SMI nozzle when there was no flowrate. The presence of recirculation flows was also discussed in other studies as one of the leading causes of an increase in particle deposition inside the human respiratory tract [63,64]. In a CFD study by Koullapis et al., recirculation zones are found near the mouth wall due to the geometry curvature [65]. However, no studies showed strong recirculation regions around the nozzle when moving the nozzle position further along the x-axis, forcing particles to flow backward toward the inlet. As demonstrated in Figs. 7(b) and 7(d), the flowrate in the system removed recirculation regions inside both the IM and SM geometries, resulting in lower particle deposition, as reported in Table 3.

Fig. 7
Particles' magnitude velocity path line at 0.03 s for IM: (a) without flowrate, and (b) with a flowrate of 30 L/min; and for SM: (c) without flowrate, and (d) with a flowrate of 30 L/min, at the nozzle position of x2
Fig. 7
Particles' magnitude velocity path line at 0.03 s for IM: (a) without flowrate, and (b) with a flowrate of 30 L/min; and for SM: (c) without flowrate, and (d) with a flowrate of 30 L/min, at the nozzle position of x2
Close modal

Table 3 also shows that particle deposition on the mouth wall for both IM and SM was increased when the nozzle position was changed from x0 to x1 and x2 within the mouth on the x-axis. Despite the shorter distance of the inhaler device's nozzle from the outlet in the x1 and x2 positions, particle deposition on the walls of IM and SM increased when there was no flowrate. This is due to a number of particles traveling in the opposite direction (toward the inlet), which can be called the “backflow” of an aerosol plume. The plume backflow was caused by the interaction of the high-speed aerosol plume exiting from the nozzle and zero-flux of air inside the mouth geometry that forms recirculation flows around the nozzle. During the recirculation, larger particles (higher mass) are likelier to travel in a straight line rather than follow the recirculation trajectory due to their higher inertia, leading them to leave the recirculation region and deposit on the mouth wall. As seen in Fig. 8(a), recirculation flow increases the particles' residence time in the system, which, in turn, leads to higher particle deposition on the wall of IM and SM. Milenkovic et al., through a CFD approach using DPI devices, reported that a slow flow field is developed by recirculation flow that results in a higher residence time for drug particles inside the mouth area [66]. The presence of backflow is evident from Fig. 8(b) at the beginning of actuation (0.03 s). However, with a fixed flowrate in the system, that backflow field significantly disappeared (see Fig. 7(b)).

Fig. 8
(a) Particle residence time at the beginning of actuation inside IM and (b) particles' magnitude velocity for the backflow near the SMI nozzle inside IM; at nozzle position of x2 for zero-flux of air
Fig. 8
(a) Particle residence time at the beginning of actuation inside IM and (b) particles' magnitude velocity for the backflow near the SMI nozzle inside IM; at nozzle position of x2 for zero-flux of air
Close modal

Table 3 shows that moving the nozzle position from x0 to x1 and x2 in both geometries, especially in the SM geometry, increases deposition on the mouth area for particles with diameters higher than 5 μm. Despite the nozzle position, with a fixed flowrate (30 L/min) in both geometries, an increase in deposition fraction for particles with a diameter greater than 5 μm was observed. This observation is consistent with the result of previous CFD analyses. For example, Longest and Hindle showed that particles with a diameter >5 μm primarily reside at the exterior edge of the SMI plume due to their greater inertia [4]. The flowrate adds to their inertia, and consequently, their chance of deposition increases. In fact, particles with a diameter >5 μm have a reduced possibility of deposition in the lower airways [4]. This table also demonstrates that a greater number of fine particles, that is <5 μm, traveled from IM and SM geometry outlets to human lungs. Smaller particles, with a diameter of approximately 3–5 μm have a better chance of deposition in the lungs due to their good lung penetration efficiency and less loss from exhalation in adults [64].

Figure 9 shows the effect of different SMI nozzle angles on particle deposition with no flowrate inside the IM. Increasing the SMI nozzle angle from 0 deg to 10 deg and 20 deg increased particle deposition in the mouth area, and this increment was more significant while the nozzle was positioned at x2. It was found that stronger recirculation regions increased particle residence time and backflow effect. This resulted in higher deposition rates inside the IM geometry. In contrast, particle deposition on the mouth wall decreased when a fixed flowrate of 30 L/min was applied in the IM. This shows that the flowrate helped particles to pass the outlet. Histograms in Fig. 9 also show that the flowrate was more influential than the nozzle position.

Fig. 9
Comparison of mouth wall deposition inside IM at x0 and x2 for different SMI nozzle angles with and without flowrate of 30 L/min
Fig. 9
Comparison of mouth wall deposition inside IM at x0 and x2 for different SMI nozzle angles with and without flowrate of 30 L/min
Close modal

Table 4 presents the particle deposition mass and fraction on the mouth wall and for particles that passed the outlet of IM as a function of nozzle angle (10 deg and 20 deg), nozzle position (x0 and x2), and flowrate (either 0 or 30 L/min). Considering the total mass flowrate (1.5 × 10−5 kg in 1.5 s), when the nozzle angle is 20 deg and the SMI nozzle is at x0 for a case of 0 L/min (i.e., no flowrate), a total mass of 0.44 × 10−5 kg/s is lost in the human mouth. Moving the nozzle position as well as applying a fixed flowrate of 30 L/min allowed more particles to exit the IM geometry. In contrast, increasing the SMI nozzle's angle decreased the number of particles leaving the mouth outlet. The deposition fraction of particles with a diameter >5 μm on the wall and the mass fraction of particles that passed the outlet of the IM decreased when the nozzle angle increased to 20 deg. The decrease in the deposition fraction for particles with a diameter >5 μm when changing the SMI angle to 20 deg is attributed to the reduced chance of particle impact on the IM wall for the lower side of the aerosol plume. However, an upward trend was still observed in the total mass deposition for particles with a diameter >5 μm on the mouth wall and the mass of particles with the same diameter range that passed the outlet of IM. This shows that moving the SMI nozzle forward along the x-axis and applying a fixed flowrate of 30 L/min has a more substantial effect on particle deposition than increasing the SMI nozzle angle.

Table 4

Data for particles that pass the outlet for different SMI nozzle angles inside IM

Flow rate (L/min)Nozzle position on x-axisSMI nozzle angleMass of particles that passed the outlet (kg)Mass fraction of particles that passed the outlet with a diameter >5 μm (%)Deposition fraction of particles with diameter >5 μm on mouth wall (%)
0x010 deg1.13 × 10–53692
0x020 deg1.06 × 10–534.589
0x210 deg1.39 × 10–536.199
0x220 deg1.32 × 10–535.692
30x010 deg1.43 × 10–537.126
30x020 deg1.42 × 10–53723
30x210 deg1.46 × 10–536.958
30x220 deg1.45 × 10–536.854
Flow rate (L/min)Nozzle position on x-axisSMI nozzle angleMass of particles that passed the outlet (kg)Mass fraction of particles that passed the outlet with a diameter >5 μm (%)Deposition fraction of particles with diameter >5 μm on mouth wall (%)
0x010 deg1.13 × 10–53692
0x020 deg1.06 × 10–534.589
0x210 deg1.39 × 10–536.199
0x220 deg1.32 × 10–535.692
30x010 deg1.43 × 10–537.126
30x020 deg1.42 × 10–53723
30x210 deg1.46 × 10–536.958
30x220 deg1.45 × 10–536.854

Figure 10 shows the effect of nozzle angle on the particle size distribution with a flowrate of 30 L/min inside the IM. Figure 10(a) shows that when the SMI nozzle angle is 0 deg, (the inhaler mouthpiece is positioned correctly in the mouth), particles with a diameter >5 μm primarily reside at the upper and lower sides of the aerosol plume. When the SMI nozzle angle increased to 20 deg, see Fig. 10(b), particles with a diameter >5 μm residing at the upper side of the plume deposited on the IM wall. However, particles with a diameter >5 μm residing at the lower side of the aerosol plume exit the IM outlet toward the throat. This explains the decrease in the deposition fraction of particles with a diameter >5 μm at the SMI nozzle angle of 20 deg reported in Table 4.

Fig. 10
Particle size distribution inside IM at x0 and with a constant flowrate of 30 L/min at (a) SMI nozzle angle of 0 deg and (b) SMI nozzle angle of 20 deg
Fig. 10
Particle size distribution inside IM at x0 and with a constant flowrate of 30 L/min at (a) SMI nozzle angle of 0 deg and (b) SMI nozzle angle of 20 deg
Close modal

Figure 11 shows that by changing the SMI nozzle position in the mouth along the x-axis from x0 to x1 and x2, the average velocity of drug particles at the outlet of both the IM and SM increased. Figures 11(a) and 11(b) show that the drug particles' average velocity at the outlet for IM increased from 0.173 m/s to 0.390 m/s as the nozzle's position changed from x0 to x1, respectively. Moving the nozzle further forward from the mouth inlet along the x-axis to x2 increased the outlet drug particles' average velocity to 0.519 m/s due to fewer interactions of the drug particles with air. However, the velocity increment when the nozzle moved from x0 to x1 was more than twice that of when the nozzle moved from x1 to x2. As shown in Fig. 8(b), the backflow of the drug particles noticeably affected the sensitivity of the velocity increment in IM.

Fig. 11
Particles' magnitude velocity at the outlet of IM for (a) vertical (y-direction), and (b) horizontal (z-direction); particles' magnitude velocity at the outlet of SM for (c) vertical (y-direction), and (d) horizontal (z-direction), for different nozzle positions with and without flowrate of 30 L/min
Fig. 11
Particles' magnitude velocity at the outlet of IM for (a) vertical (y-direction), and (b) horizontal (z-direction); particles' magnitude velocity at the outlet of SM for (c) vertical (y-direction), and (d) horizontal (z-direction), for different nozzle positions with and without flowrate of 30 L/min
Close modal

Figures 11(c) and 11(d) show that the average velocity of drug particles at the outlet of the SM increased from 0.190 m/s at the nozzle position of x0 to 0.660 m/s at the nozzle position of x2. The aerosol particles' velocity decreased nonlinearly along the x-axis due to their entry into a stabilized atmosphere that imparts a drag force onto each aerosol. We also observed that at the beginning of the actuation, due to the zero-flowrate of the continuous phase in the mouth, some of the drug particles flowed in the opposite direction (along the negative x-axis). When the SMI nozzle is positioned further inside the mouth (x1 or x2), the system tracks more drug particles flowing backward (see Figs. 8(a) and 8(b)), and consequently, the sensitivity of the velocity increment is reduced. While comparing the aerosols' horizontal (z-direction) and vertical (y-direction) velocity profiles at the outlets, no noticeable change was observed along the centerline. The horizontal velocity profile, however, showed a slightly higher aerosol velocity near the mouth wall. This asymmetric velocity profile in the y- and z-direction was not unexpected due to the turbulent flow inside the system. Applying a constant flowrate when moving the SMI nozzle to x1 and x2 removed backward flow and increased the particles' average velocity at both IM and SM outlets. This increment was more noticeable for SM due to its narrower diameter. The vertical and horizontal velocity profiles comparison did not show any significant difference for both IM and SM.

4 Conclusions

A CFD study investigated the effects of flowrate and SMI nozzle position and angle on the particles' velocity profile, size distribution, and deposition in the mouth area. We modeled the simple mouth geometries and did not consider the throat region in our study to mimic the geometries employed in the available experimental study. The CFD results were first validated against experimental data and showed that the CFD model could simulate aerosol particle transport and deposition inside the mouth. Our results showed that mouth geometry (IM and SM) significantly affects the velocity of aerosol particles and particle deposition on the mouth wall. With a fixed flowrate of 30 L/min, the aerosol velocity at the outlet of both geometries increased while the mouth wall deposition decreased. The deposition fraction of larger particles that is >5 μm, increased with a fixed flowrate of 30 L/min. We found that recirculation regions and backward flow were the main reasons for the increase in the particles' residence time, leading to higher particle deposition in the absence of the flowrate. By moving the SMI nozzle further forward in the mouth along the centerline (x-axis), the velocity at the outlet of both IM and SM increased, and this increment was more significant for SM geometry. Particle deposition on the mouth wall increased by moving the nozzle position to x1 and x2. The flowrate inside the IM geometry decreased particle deposition significantly. This shows that flowrate is a more effective parameter on particle deposition than the nozzle's position. Also, wrongly positioning the SMI by changing the SMI's nozzle angle inside the human mouth increased the particle deposition in the mouth and, consequently, decreased the mass of particles that passed the outlet of the IM geometry. However, a sufficient flowrate of 30 L/min as an inhalation rate can make the effect of the SMI's nozzle angle less significant. Although the geometries modeled in this study were simple and limited only to the mouth area, the results can be used to design a new add-on (such as a sensor or a mouthpiece) that can notify patients (primarily children or the elderly) when they use an SMI inhaler in the wrong position.

Acknowledgment

The authors gratefully acknowledge the supercomputer and technical assistance provided by Lakehead University.

Funding Data

  • Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. 11-50-14050129; Funder ID: 10.13039/501100000038).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

Notations

Notations
Cp =

specific heat constant, J/kg K

Cu =

model constant

dp =

particle diameter, μm

DV =

diffusion coefficient, m2/s

gi =

gravitational acceleration in the xi-axis direction, m/s2

hs =

enthalpy of species, J

k =

turbulent kinetic energy, m2/s2

kg =

air conductivity, W/m K

P =

time-average pressure, Pa

PrT =

turbulent Prandtl number

Se =

air energy source term, W/m3

SV =

water vapor source term, kg/m3

ScT =

turbulent Schmidt number

t =

time, s

ui =

velocity at a single point, m/s

Ūi =

mean velocity, m/s

ui =

fluctuating velocity, m/s

x =

dynamic shape factor

YV =

mass fraction of water vapor in the mixture

Greek Symbols

Greek Symbols
αk, β*, β, σk, σω =

coefficients of shear stress transport model

δij =

Kronecker delta

ε =

dissipation rate, m2/s3

λi =

normally distributed random number

μ =

absolute viscosity, kg/m s

μair =

viscosity of air, kg/m s

ν =

kinematic eddy viscosity, kg/m s

νt =

turbulent viscosity, kg/m s

ρ =

mixture density, kg/m3

ρair =

air density, kg/m3

ρp =

particle density, kg/m3

ρ0 =

unit density, kg/m3

τij =

Reynold stress tensor, m2/s2

ω =

turbulent frequency, s–1

F =

anisotropic correction factor

Abbreviations

Abbreviations
CFD =

computational fluid dynamic

DPI =

dry powder inhaler

DPM =

discrete phase model

IM =

idealized mouth

NRMSE =

normalized root-mean-square error

pMDI =

pressurized metered dose inhaler

SM =

standard mouth

SMI =

soft mist inhaler

URANS =

unsteady Reynolds averaged Navier–Stokes

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