State-space model for airborne particles in multizone indoor environments

A state-space model is presented to predict the concentration and the fate of particulate matters (PM) in multizone indoor air. By introducing vector-matrix notation, the ordinary differential equations to describe the dynamic behavior of PM in multizone buildings are expressed as the state equation. The state equation is solved analytically and the dynamical evolution of PM is discussed quantitatively and qualitatively. The equilibrium point of the dynamic system is asymptotically stable. The minimum decay coefficient of PM concentrations is computed by the formula, which is found to directly link the minimum decay rate with the eigenvalues of the state matrix. The analytical solution based on the eigen structure shows that the evolution modes of indoor PM are mainly determined by the eigenvalues of state matrix. The detailed quantitative analysis on the diluted ventilation and interzonal transport via the central air-conditioning system indicates that the penetration efficiency of filter Pi and the integrated loss-rate coefficient kij integrating the remove mechanisms of natural ventilation, leakage and particle deposition have significant impact on dynamical behaviors of particles, such as the decay rate of concentrations and the ability of interzonal infection via HVAC system, etc.