The wall film mass equation is

(6–100)

where ρ _l is the liquid density, h is the film thickness, is the surface gradient operator, is the mean velocity of the film, is the wall velocity. is the mass source per unit area due to impingement, re-entrainment, or vaporization.

The motion of the wall film particles on the wall is governed by the momentum equation

(6–101)

where is the pressure due to impingement, is the pressure difference across the film, is the shear stress on the gas side of the wall film, is the film viscosity evaluated at the mean film temperature , and are the momentum and liquid mass source terms (per unit area), respectively, due to impingement, is the unit vector normal to the wall, is the unit vector in the direction of , is acceleration due to gravity.

Based on Han et al. [29] , the incident droplet velocity of a sticking or spreading particle is treated as

(6–102)

where w _p,0 and v _p,0 are the normal and tangential velocity of the incident droplet. , ϕ , , are defined in the wall impingement model section.

The wall film energy equation is

(6–103)

where C _vl is the liquid specific heat, T _l is the mean film temperature, T _s is the gas temperature at the film surface, T _w is the wall temperature, λ is the heat conductivity of the liquid film, and are the energy and mass source terms due to impingement. Note that is computed based on the internal energy of the incident droplets.