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24 OctOber 2021 Inhalation underlying insight into the behavior of the mix- tures and the reason for the departure from ideal behavior. It is also not predictive, in the sense that it could not be generalized to mixtures with additional or alternative components—new exper- iments would be necessary. Physically-based models, on the other hand, utilize an expression that incorporates some of the under- lying physics and/or chemistry of the mixture to represent the thermophysical property. While these still have fitted parameters that allow the expres- sion to adequately represent experimental data, the values of these parameters can have fundamental physical meaning relating to the theories under- pinning them. In addition, these expressions can become predictive if the physically-based model is well-matched to the behavior of the mixture. is means that it still gives reliable physical property values if there is little or no experimental data for a mixture at a condition of interest. In engineering CFD packages, properties of mix- tures will typically be calculated from simple mixing rules or empirical relationships [10]. ese may not be based on any experimental evidence, and if they are, they will only be strictly valid for the range of experimental conditions. Saturated vapor pressure (SVP) As previously discussed, the SVP is one of the most important properties of a formulation of which to have good knowledge and understanding. If a liquid mixture or solution contains molecules that do not interact, then a suitable expression for the mixture SVP is Raoult's law, given in Equation 1: SVP = Σ i x i P vi (1) in which x i is the mole fraction of species i in the mixture and P vi is the SVP of the pure species i at the temperature of interest. For solution formula- tions containing HFAs and ethanol, Equation 1 is not suitable because it would predict a flat, inclined surface, rather than a curved surface, for Figure 1. Instead, the modified Raoult's law is needed, given in Equation 2: SVP = Σ i γ i x i P vi (2) where γ i is the activity coefficient for species i in the mixture. is is now an appropriate physically-based model, since it is based on the thermodynamic equi- librium between the vapor and liquid phases in a two-phase system, under the simplifications of an ideal vapor phase and an incompressible liquid phase [17] and the activity coefficients have physical meaning beyond the scope of Equation 2. using either a proprietary instrument or laser-based test system. A range of compositions and tempera- tures can be tested, and a suitable number of repeat measurements can be made to generate a dataset that can support decision-making or be used as input for a model or model-fitting exercise. Property modeling: Representation and prediction Once property data has been measured, or if exist- ing data has been identified, it will then need to be recalled: for comparison of two or more for- mulations, or as input into a simulation exercise. Of course, this can include the need to evaluate a property at a temperature or composition that was not part of the matrix of experimental con- ditions. Two families of expressions are typically fitted to experimental data to provide a continuous function of temperature, composition, pressure or other independent variables, to represent the thermophysical property. ese are known as empirical (or phenomenological) models and physically-based models. Importantly, any func- tion used must minimize the error between the actual experimental property data and representa- tions of the property by the function. An example of a phenomenological model to represent the SVP of HFA134a/ethanol mixtures across the full composition range and at pMDI relevant tempera- tures is shown in Figure 1, from reference 16. e normalized SVP is represented by a polynomial in both ethanol mole fraction and temperature with 6 fitted coefficients, which fits closely to the exper- imental datapoints from that work and provides useful interpolation and extrapolation. However, this empirical expression does not provide any Figure 1 Normalized saturated vapor pressure for HFA134a/ethanol mixtures: Experimental data points and empirical surface fitted to those. From reference 16, used with permission. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 Temperature (−) Ethanol Mole Fraction (−) ∏v 255 260 265 270 275 280 285 290 295 300 305