Modelling multi-component nucleation and growth of aerosol droplets in an inhaler device.
| dc.contributor.author | Stephenson, Paul | |
| dc.date.accessioned | 2023-04-18T03:03:44Z | |
| dc.date.available | 2023-04-18T03:03:44Z | |
| dc.date.issued | 2022 | en |
| dc.description.abstract | Inhalers which use multi-component droplet nucleation and growth may be used to deliver drugs to the lungs. However, little research has been completed to model and optimize the processes involved in these devices to generate droplets and efficiently deliver drugs. This thesis aims to build a model of nucleation and growth of multi-component droplets for use in modelling evaporation-condensation inhaler devices, and of hygroscopic growth of these droplets in the airway after inhalation, and to apply these to a new evaporation-condensation inhaler design. First, the Maxwell model of droplet growth by diffusion-driven condensation was adapted to model multiple condensing components, and was implemented in MATLAB. This was used to model growth of a solitary multi-component droplet. All material properties except diffusion coefficients were modelled using relationships from the VDI Heat Atlas (2010). A literature survey showed the required diffusion coefficients were not available. The Fuller-Schettler-Giddings method (Fuller, Schettler and Giddings 1966) was implemented to estimate the diffusion coefficient as a function of molecular mass and structural descriptors. This method was implemented in a MATLAB code and validated for species for which experimental data was available. The equilibrium droplet composition reached after sufficient time, predicted by this multi-component Maxwell model, was shown to agree with vapour-liquid equilibrium calculations. The more sophisticated Stefan-Fuchs droplet growth model, which includes convective flow effects and unimolar diffusion, was implemented. The Stefan-Fuchs model was chosen for all further modelling due to its inclusion of unimolar diffusion and convective effects in the rare circumstances where there is a non-negligible difference in velocity between the droplets and vapour. Discrepancies were found between different sources for the value of activity coefficients of water in water – glycerol mixtures. No experimental data suitable for determining activity coefficients of water, propylene glycol and glycerol in a mixture were found. The Stefan-Fuchs growth model was used to show that activity coefficient values had minimal effect on droplet equilibrium size and composition for the size of droplets expected in the inhaler device, and therefore, it could be assumed that the activity coefficients were equal to 1. Activity coefficient was shown to have an impact on droplet growth in slow growing conditions, which may be present in the airway, however, activity coefficients of 1 were retained due to the uncertainty of estimating activity coefficient with the UNIFAC model (Fredenslund, Jones & Prausnitz 1975). A challenge was developing a numerical heat transfer model that did not give an unphysically high peak in temperature during the early stages of droplet growth with practical timesteps. Various models were considered to limit the rate of heat transfer in the first timesteps. A method which partitions the heat released between vapour and droplet in proportion to their heat capacities, such that they had the same temperature, was chosen. Another challenge was implementing a nucleation model which correctly predicted the very large nucleation rates expected for glycerol. It is well documented that classical nucleation theory under-predicts nucleation rates for alcohols, especially glycerol. A new nucleation model based on collision theory, proposed by Fisenko et al., 2021, was implemented. This model assumes critical nuclei form when three glycerol molecules collide. Droplet number densities and diameters produced using this model were much closer to experimental results, however, more research is needed to further validate this nucleation model in a wider range of conditions. The Stefan-Fuchs model, with heat partitioning and the collision theory based nucleation model described above, was implemented into ANSYS Fluent 2020 R2 using user defined scalars (UDS) to model the aerosol droplet number density and droplet mass, and user defined functions (UDF) to modify these scalars according to the nucleation of new droplets, and growth by condensation of existing droplets. Source functions were also implemented to deplete the surrounding vapour to maintain mass continuity. These were used in conjunction with the built in particle transport and deposition mechanisms of the discrete phase model (DPM). This model was used to simulate a new inhaler device. The model predicted a mass mean diameter (MMD) of 0.86 µm, count median diameter (CMD) of 0.75 µm and a droplet number density of 4.10×10¹⁴ droplets/m³ at an air flow rate of 1.1 L/min. Experimental results from collaborators at the University of Applied Sciences, South Westphalia showed a MMD of 0.79 µm and a droplet number density of 1.24×10¹⁴ droplets/m³ under the same conditions. Given the difficulties in measuring droplet concentration experimentally, and in predicting heat flux to the evaporating liquid in a practical inhaler, this agreement was acceptable. Sensitivity studies were then completed to examine the effect of variation of total flow rate, vapour flow rate and tank liquid composition on the aerosol outlet parameters. CMD was found to decrease with increasing flow rate, with a CMD of 0.84 µm recorded at 0.44 L/min which steadily decreased to a CMD of 0.63 µm at 4.4 L/min. This agreed with experimental results produced by Mikheev et al., 2018, who measured a decrease in CMD from 0.2 µm to 0.1 µm when flow rate was increased from 1.2 L/min to 2.4 L/min. Variation in vapour flow rate at the heater from 3 mg/s to 2 mg/s produced similar distribution parameters at both flow rates, except for total particle mass (TPM). TPM has been shown to increase approximately linearly with increasing heater power (Floyd et al., 2014), which is advantageous in evaporation-condensation inhaler design, as adjusting this power can be used to adjust the mass of drug delivered to the user without significantly affecting droplet size. Variation in tank liquid had a similar effect, with minimal change observed in aerosol distribution parameters, except for droplet composition. This is also advantageous, as tank liquid composition can be adjusted without significantly affecting particle size and therefore deposition rates in the airway. The experimental particle size distribution was then combined with the simulated droplet number density and composition to best represent an accurate distribution of droplets entering the human airway. The upper airway from the mouth down to the middle of the trachea was obtained from CT scan data and branches of the airway down to generation 23 were produced using the Lung4Cer program (Kitaoka, 2012). The distribution entering the airway was scaled and droplet number density adjusted to maintain the same TPM entering the airway from the device. The experimentally measured particle size distribution from the device produced optimal deposition in the alveoli of 44.3 mg/s at a steady inhalation flow rate of 1.1 L/min. Droplet size distributions in which the MMD was scaled by factors ranging from 0.5 to 1.5 times gave TPM values from 40.7 mg/s to 44.0 mg/s. The effect of varying droplet water content on deposition rate was examined. For this study the glycerol mass fraction was held constant and propylene glycol mass fraction was varied to accommodate the changes in water content. The deposition rate of glycerol to the alveoli was then monitored. Results showed that a water content of less than 0.05% produces a glycerol deposition rate of 0.67 mg/s compared to 0.87 mg/s at 2.5% water content. Deposition rates fell to 0.82 mg/s for a droplet water content of 6% and remained constant at higher water contents. The deposition rate of a generic therapeutical compound was estimated assuming a 5% mass fraction of compound exiting the Boxvape device at 1.1 L/min. Estimated total deposition over a 3 s CORESTA puff was 0.3 mg. During the work, collaborators at the University of Applied Sciences, South Westphalia observed a previously unreported phenomenon of periodic starting and stopping of nucleation, resulting in bands or strata containing droplets, separated by droplet-free vapour. This phenomenon was recreated in ANSYS Fluent using the nucleation and vapour-droplet mass transfer models described above. A free-falling 2.8 mm diameter parent drop, in the boundary layer of which this periodic nucleation phenomenon had been observed, was modelled. The frequency of commencement and cessation of nucleation was predicted by the CFD model, agreeing with experimental results to within 14%. The modelling gave insights which contributed to an explanation of the phenomenon. Bands of droplets nucleate and grow in regions of high supersaturation. Depletion of vapour in this region occurs faster than diffusion can replace it until convection of this band moves the droplets downstream. Diffusion of vapour continues and another region of high supersaturation is established, in which a second band of droplets forms. The process repeats cyclically. | en |
| dc.identifier.uri | https://hdl.handle.net/10092/105353 | |
| dc.identifier.uri | http://dx.doi.org/10.26021/14448 | |
| dc.language | English | |
| dc.language.iso | en | en |
| dc.rights | All Right Reserved | en |
| dc.rights.uri | https://canterbury.libguides.com/rights/theses | en |
| dc.title | Modelling multi-component nucleation and growth of aerosol droplets in an inhaler device. | en |
| dc.type | Theses / Dissertations | en |
| thesis.degree.discipline | Mechanical Engineering | en |
| thesis.degree.grantor | University of Canterbury | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |
| uc.bibnumber | 3258356 | |
| uc.college | Faculty of Engineering | en |