The governing differential equation is a so-called diffusio-integral differential equation.The integral terms account for the particle-particle interactions, called coagulation, and is a summation over the entire particle size distribution.
There is also an additional convection term due to the effect of external forces on the particle motion.
External forces include gravitational, thermophoresis, and inertial forces.
Then explanation about terms :
Term 1. Convection
-Free convection: using Buosinessq and or Bouyancy
The results of Walsh et al., (2006) about deposition of aerosol particle on the wall, indicate that for a given inlet and wall temperature, free convection impacts the velocity profiles to a larger degree than the temperature profiles, and thus changes in the particle deposition profiles due to free convection are linked more tightly to differences in residence time rather than to differences in the local temperature gradients.
-Forced convection
Term 2. External forces
-Gravitational force or Body force refers to behaviuor in x-y-z directions.
-Thermophoresis refers to the behavior in which aerosol particles suspended in a gas acquire a velocity in the direction of decreasing temperature due to collisions with the surrounding gas molecules.
-Inertial force
Term 3. Diffusion
Term 4. Coagulation ( , )
Term 5. Particlegrowth
Term 6. Internalsources
Verify what regime of flow that used: Turbulent or Laminar (Calculate Reynold number first to make decision about this)
Equations that include in this thesis (both particles-solid-aerosol and gas-air) : [1]. Continuity Equation, [2]. Momentum Equation, and [3]. Energy Equation.
The FPM solves for the evolution of moments of the size distribution. Because the FPM uses lognormal size distributions to represent the particle size distribution within each mode, each of which is represented by three parameters (total mass, mean size, standard deviation), three integral moments are solved for each mode. The modal parameters can be calculated from these three integral moments. For multicomponent simulations, an additional mass moment is solved for each additional chemicals species.
