Evaluation of Soft Mist Inhaler Aerosol Velocity, Size, and Deposition Inside the Mouth—A Computational Fluid Dynamics Study

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 [2–4]. 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 [9–11].

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].

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 [39–41]. 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.

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.

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.

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].

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

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

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, α_k = 0.31, σ_ω = 0.5, and σ_k = 0.85 [52].

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]).

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].

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].

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, C_c is the Cunningham correction factor; d_p is the particle diameter, and $μ$ is the absolute viscosity. Injection characteristics used in this simulation are given in Table 1.

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].

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.

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.

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 $NRMSE(%)=(∑i,j=1N(ui−uj)2)/N(∑i=1N(ui)2)/N×100$ 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].

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.

The numerical results of particles' velocity at the outlets of both the IM and SM geometries when the nozzle position was at x_0, 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.

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].

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].

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].

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.

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)).

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.

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 × 10⁻⁵kg 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 × 10⁻⁵kg/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.

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.

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.

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.

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.

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

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

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

Notations

C_p =

specific heat constant, J/kg K

C_u =

model constant

$dp$ =

particle diameter, μm

$DV$ =

diffusion coefficient, m²/s

g_i =

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

$u′i$ =

fluctuating velocity, m/s

$x′$ =

dynamic shape factor

$YV$ =

mass fraction of water vapor in the mixture

Greek Symbols

α_k, β^*, β, σ_k, σ_ω =

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

μ_air =

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

τ_ij =

Reynold stress tensor, m²/s²

$ω$ =

turbulent frequency, s^–1

$F$ =

anisotropic correction factor

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