# The Ability to Control VOC Emissions from Multilayer Building Materials
## 1 Introduction
### State of Knowledge-Emission Modelling
The [PERSON] model [15] takes into account both material diffusion and mass transfer through the air boundary layer. As the authors themselves claimed, a general characteristic equation is developed which would reduce to that of [PERSON] et al. [10] when the gas phase mass transfer coefficient becomes infinite. The [PERSON] model [15] shows a good agreement with the experimental data, while the model of [PERSON] overestimated the concentration of the emitting VOC in the air. When building their model, used until today, [PERSON] [15] needed basic parameters of the mass transfer process, i.e., they used the experimental data of mass transfer: the diffusion coefficients of VOCs \(D_{m}\) in the materials, the initial concentrations in the materials \(C_{o}\) and the material-air partition coefficients \(K_{ma}\) (verified by the CFD method) from [PERSON] et al. [16]. Another study by [PERSON] [17] looked at the effect of air velocity on the amount of emissions (measured as chamber \(C(t)\) in the air) due to an increase in the VOC diffusion coefficient in the material. For a material with a diffusion coefficient \(D_{m}>10^{-10}\) m\({}^{2}\)/s, the VOC emission rate increased with increasing velocity, with air velocity having a significant effect on VOC emissions. For a material with a diffusion coefficient of \(D_{m}<10^{-10}\) m\({}^{2}\)/s, the VOC emission rate increased with the increase in air velocity only in a short period of time <24 h. The source publications in the diagram (Figure 11, Appendix A) show reference to the research by [PERSON] [9] and the more recent publication by [PERSON], [PERSON] and [PERSON] [18], which describes a new quick method for measuring two key parameters, \(K_{ma}\) and \(D_{m}\), as well as convective mass transfer coefficient (\(h_{m}\)). Compared to traditional methods, it has the advantage that the \(K_{ma}\), \(D_{m}\) and \(h_{m}\) factors can be obtained in one experiment simultaneously, making it convenient to use. The frequently cited research on the theoretical dependence of the VOC emission rate from building materials on temperature was carried out by the team of [PERSON], [PERSON], [PERSON] and [PERSON] [19] focused on the example of formaldehyde. Their validated correlation \"shows that the logarithm of the emission rate by a power of 0.25 of the temperature is linearly related to the reciprocal of the temperature\". The emission rate at temperatures other than the test condition can be obtained using the correlation, greatly facilitating engineering applications. However, theoretical work on the procedures for determining the parameters of physical emission models is still ongoing. For example, [PERSON], [PERSON] et al. [20] used the Least Square and Global search algorithm with multi-starting points to achieve a good agreement in the normalised VOC concentrations between the model prediction and experimental data. They estimated the effects of experimental uncertainty of chamber-measured concentration. Returning to the work of the [PERSON] [15] team, their new approach was based on the fact that they adopted some known empirical relations for the determination of the mass transfer coefficient in the gas phase. For laminar flow, it was assumed [13] (1):  
\[Sh=0.664\cdot Sc^{1/3}Re^{1/2} \tag{1}\]  
where \(Sh=hl/D_{a}\) is [PERSON]'s number, \(Sc=\
u/D_{a}\) is [PERSON]'s number, \(Re=ul/\
u\) is [PERSON] number, \(\
u\) is the kinematic viscosity of air, \(u\) is the velocity of air above the material, \(l\) is the characteristic length of the material, \(D_{a}\) is the VOC diffusion coefficient in the air and \(h\) is the gas phase mass transfer coefficient (m\(\cdot\)s\({}^{-1}\)). Apart from these uniform initial condition models, [PERSON] and [PERSON] [21] also developed a model for the two-layer system with the assumption thatan initial condition is given by a general non-uniform concentration profile in each material layer. This model was useful for studying the effects of adopting different initial VOC concentrations in the emitting layers.