## 2 Methods  
### Zero-Dimensional Spray Model  
The zero-dimensional spray model simulation was performed to assess the applicability of CFD for the inhalation exposure assessment of biocide spray. The zero-dimensional spray model has been developed to predict the biocide concentration results from consumer spray products. The spray model was developed considering the effect of ventilation and the force balance acting on particles by the aerosol diameter size. The spray model [4] is as follows:  
\[\frac{dA_{air}}{dt}=-q_{vent}A_{air}(\delta)-v_{s}(\delta)S\frac{A_{air}}{V}+R_ {release}f_{airborne}P(\delta,0)d\delta \tag{1}\]  
\[\frac{dA_{air}(\delta)}{dt}=-q_{vent}A_{air}(\delta)-v_{s}(\delta)S\frac{A_{air} }{V} \tag{2}\]  
\[C_{air}(t)=\frac{1}{V}\int A_{air}(\delta,t)d\delta \tag{3}\]  
where \(q_{vent}\) is the ventilation rate, \(A_{air}\) is the total mass of sprayed aerosol/particle (kg), \(\delta\) is the aerosol diameter, \(S\) is the surface area of the room for deposition effect, \(V\) is the room volume, \(R_{release}\) is the rate of release of mass in aerosol particles, \(f_{airborne}\) is the rate of non-volatile aerosol from volatile aerosol, \(P(\delta,0)\) is the particle mass distribution function at time t determined from the initial distribution \(P(\delta,0)\), \(v_{s}\) is terminal velocity, which is decided by \(\delta\). \(V\), \(\delta\) and \(R_{release}\) are input parameters for the zero-dimensional simulation. The input parameters are obtained based on the measurement results. Equations (1)-(3) represent the total mass of sprayed aerosol/particle during spraying, the total mass of sprayed aerosol  
Figure 1: Research flow chart. The CFD and PSD mean computational fluid dynamics and particle size distribution, respectively. aerosol/particle after spraying and the total concentration in the room, respectively. The first term of Equation (1) represents the removal mechanism by ventilation. It is assumed that the concentration of non-volatile aerosol is dispersed instantly. The second term of Equation (1) represents the removal mechanism by the force balance effect depending on particle size. As a result, the space concentration is calculated through the mass according to each aerosol diameter. The model, represented by ordinary differential equations, can quickly predict the aerosol concentration in indoor spaces. The input parameters used in the zero-dimensional spray model are classified into aerosol characteristics and spatial characteristics. In this study, in the case of spatial characteristics, a 30 m\({}^{3}\) chamber with a controlled air supply was used in the experiment. Air was supplied from 51 inlets with a diameter of 0.03 m. The total air flow rate is 30 m\({}^{3}\). The aerosol input parameters of the zero-dimensional model consist of the particle size distribution (PSD), mass generation rate, exposure factor, etc. The PSD is an important input parameter that affects the results of the zero-dimensional spray simulation and CFD simulation because the particle/aerosol behavior depends on particle diameter size. To set the PSD measurement results equally for CFD and zero-dimensional models, the PSD data were converted to a Rosin-Rammler curve. The Rosin-Rammler curve can describe the PSD by using parameters such as the mean aerosol/particle diameter and spread number. The Rosin-Rambler equation is as follows [25]:  
\[Y_{d}=1\ -\ e^{-\left(\frac{d}{d}\right)^{n}} \tag{4}\]  
where \(Y_{d}\) is the cumulative mass fraction, bigger than a given particle/aerosol diameter \(d\), \(\overline{d}\) is the mean of particle/aerosol diameter and \(n\) is the spread number. In other words, the PSD was described by the Rosin-Rammler function. The mean diameter of the particle/aerosol and the spread parameter were determined by curve fitting the experimental results to the Rosin-Rammler function.