In this chapter, a range of 1-D models of flashing propellant flow through the twin-orifice system of pMDI were presented. The following existing models were implemented for application to assess their validity for metered pMDI flows: the homogeneous frozen model (HFM), the homogeneous equilibrium model (HEM) and the slip equilibrium model (SEM). A novel hybrid-homogeneous flow model (H-HFM) was also developed. This model has the capability to address liquid metastability and evaporative mass transfer in the spray orifice. Temporal behaviour of solution variables of the propellant flow through the twin-orifice system was presented and it was observed that the trends were similar to the ones obtained by Clark (1991). The duration of the spray is predicted to be different for different flow models due to the large differences in predicted mass flow rate. In general, the predictions of H-HFM were found to be similar to those for HFM. This was due to the small evaporation rate predicted by H-HFM in conjunction with nucleation parameters that were used previously by Senda et al. (1994) for n-pentane/n-heptane mixtures. Results suggest that the magnitude of pressure, temperature and flow quality inside the chamber is almost independent of the implemented orifice flow model. However, the flow quality at the spray orifice exit is greater for HEM and SEM compared with HFM and H-HFM predictions.
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Flow velocity at the spray orifice exit shows inverse relation to the amount of evaporation, so the HFM predicts the highest spray orifice exit velocity, whereas the H-HFM prediction is marginally lower, and the HEM/SEM shows the lowest spray orifice exit velocity predictions. This trend reverses when the near-orifice velocity is considered. Higher pressure at spray orifice exit is predicted for the equilibrium models in which more evaporation is predicted to take place. Thus the flow accelerates more in near-orifice region.
To seek validation, the model predictions of near-orifice velocity were compared against temporal measurement of plume velocity using optical diagnostic techniques (PDA). For three separate sets of measurement, the velocities predicted by HEM and SEM vapour phase were found to be consistently larger than the measured values. The SEM liquid phase velocity on the other hand was consistently well below the plume velocity. The predictions of the HFM and H-HFM models were always in the correct order of magnitude and exhibited the correct temporal trends reported in previous work.
To further assess the model, parametric variations of modelling variables were applied to study their effect on plume velocity and duration. Due to limited data in the literature and lack of data presentation in temporal format, the comparison was made qualitatively. Results show that effect of saturated vapour pressure of the propellant is one of the significant factors which determine the plume velocity and duration. This factor was studied using different propellants and ambient temperatures. As supported by previous works changing in metering chamber volume only influences the plume duration, whereas spray velocity remains approximately unaffected. Model outcomes indicate that reduction of spray orifice cross-sectional area leads to formation of a faster and shorter plume. This trend was also observed by Clark (1991) and Gabrio et al. (1999).
Chapter Four
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4 Chapter Four: Atomisation Model of pMDI
4.1 Introduction
Pressurised metered dose inhalers are distinguished by their unique ability to form a fine aerosol plume with large numbers of droplets predominantly in the size range 1-5 Β΅m. The mechanism responsible for droplet generation from bulk formulation is known to be transient, turbulent and highly complex (Versteeg & Hargrave, 2006; Finlay, 2001; Gavtash et al. 2014), but the details are poorly understood. Two possible effects have been previously identified as candidate mechanisms of liquid bulk disintegration, namely (i) propellant flashing (Finlay, 2001; Clark, 1991; Versteeg et al., 2006; Dunbar, 1997) and (ii) aerodynamic atomisation (Clark, 1991, Gavtash et al., 2014).
Flashing is the process of rapid growth of the gas phase after exposing a pressurised fluid to abrupt pressure drop. The liquid content in the mixture becomes superheated and the vapour nuclei in the mixture rapidly grow up to a point where disintegration of the bulk liquid is caused, generating fine droplets. This mechanism of droplet generation is called flash boiling atomisation. Initial bubble nuclei can be present in the liquid if it is sufficiently superheated (Sher et al., 2008). The twin-orifice arrangement of a typical pMDI allows rapid depressurisation when propellant flows (i) from the metering chamber into the expansion chamber space through the valve orifice, (ii) from expansion chamber through the spray orifice constriction and (iii) when the two phase propellant mixture is expelled into the ambient having atmospheric pressure (Finlay, 2001).
Clark (1991) conjectured that the dominant atomisation mechanism of the pMDI was aerodynamic breakup similar to air-blast atomisation. Propellant is understood to be pre-atomised into liquid ligaments during its passage from the metering chamber to the expansion chamber. Two-phase propellant formulation was understood to enter the spray orifice in the form of liquid ligaments and rapidly expanding propellant vapour. The vapour flow was assumed to deform liquid ligaments and generating smaller liquid segments, which finally exit the spray orifice as small spherical droplets. It was concluded that the propellant vapour pressure and, furthermore, the amount of vapour produced in expansion chamber as a result of evaporation were the most significant controlling factors governing the droplet size. Clark correlated the experimental droplet size data with the peak expansion chamber
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pressure πππ and vapour quality π₯ππ to obtain an empirical correlation for the mass median
aerodynamic diameter (MMAD) as defined by equation β4-1:
πππ΄π· = πΆ
π₯ππ0.46(πππβ ππππ
ππππ )
0.56 β4-1
Where ππππ = ambient pressure. Clark (1991) reported good fit to measured data for
continuous and metered discharge using the constant C = 8.02 and 1.82, respectively. Dunbar et al. (1997); Dunbar and Miller (1997) applied C = 8.02 in combination with a transient CFD model to find the values of droplet size at a particular time using instantaneous values of π₯ππ and πππ. Although Clarkβs correlation has been the most
influential one up to date, the model is empirical. The constant C of equation β4-1 has dimension of length. Equation β4-1 successfully captures the trends that relate formulation parameters to the final size of the droplets, but the length-scale determining physics is not described by the expression. This limits the predictive power of the equation. Other studies (Stein & Myrdal, 2004; Brambilla et al., 1999; Ivey et al., 2014) have developed empirical correlations for spray droplet size requiring measurement of the residual droplet size from binary liquid sprays containing HFA propellant and a non-volatile excipient. Thus none of the existing approaches predicts droplet size from first principles.
The aim of this chapter is to present a novel theoretical approach to the prediction of the size of droplets produced by pMDIs without the need for empirical adjustments. Two separate models are constructed based on (i) aerodynamic atomisation using the linear instability sheet atomisation (LISA) framework (Senecal et al., 1999), and (ii) hybrid-aerodynamic/flashing atomisation using combination of LISA, the approach of (Sher & Elata, 1977) linked with secondary break-up. The hybrid atomisation model enables us to explore the possibility of droplet formation based on either of aerodynamic or flashing modes of atomisation. Since atomisation is strongly dependent on flow rate, velocity and properties of fluid (Lefebvre, 1989), both atomisation models require accurate predictions of the mentioned parameters. According to chapter 3, section β3.7.4.3, HFM and H-HFM were the most successful models in predicting near-orifice spray velocity when
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comparing the predictions against PDA measurements. These internal flow models are used in conjunction with the atomisation models to predict issued droplet size.