The velocity of a secondary droplet is modeled statistically based on experimental observations. The velocity is given as
 | (6–92) |
where w and v are the normal
and tangential velocity components of the incident droplets, 
is the unit normal vector to the impinged wall surface, 
is the unit vector tangent to the impinged surface and in the plane made by
and the incident droplet velocity, and 
is defined as 
. The normal velocity component w is modeled using a
Nukiyama-Tanasawa distribution
 | (6–93) |
where the mean of the distribution w m is defined as a function of the incident angle α (the angle between the surface normal and the incident droplet velocity) and azimuthal angle ϕ as
 | (6–94) |
The azimuthal angle is defined as the angle made by the tangential
velocity of the secondary droplet and the vector 
, and it lies in the interval [-π, π ]. It is
statistically chosen according to the distribution proposed by Naber and Reitz [60]
 | (6–95) |
Where P is a random number in the interval [0, 1] and γ is a parameter related to the incident angle α by
 | (6–96) |
The tangential velocity of the secondary droplet is described by a Gaussian distribution as
 | (6–97) |
Where the mean 
and variance δ of the distribution are given
as
 | (6–98) |
According to Han et al. [29] , the constants are set to be A = 0.7, B = 0.03, c 1 = 0.1, c 2 = 0.02306.
The term ζ in Equation 6–92 is used to describe the radial distance from the edge of the film to the point of impact at any azimuthal angle ϕ . It is assumed to be proportional to the radial velocity
 | (6–99) |