Williams spray equation

In combustion, the Williams spray equation, also known as the Williams-Boltzmann equation, describes the statistical evolution of sprays contained in another fluid, analogous to the kinetic theory of gases, named after Forman A. Williams, who derived the equation in 1958.

The sprays are assumed to be spherical with radius ${\displaystyle r}$, even though the assumption is valid for solid particles(liquid droplets) when their shape has no consequence on the combustion. For liquid droplets to be nearly spherical, the spray has to be dilute(total volume occupied by the sprays is much less than the volume of the gas) and the Weber number ${\displaystyle We=2r\rho _{g}|\mathbf {v} -\mathbf {u} |^{2}/\sigma }$, where ${\displaystyle \rho _{g}}$ is the gas density, ${\displaystyle \mathbf {v} }$ is the spray droplet velocity, ${\displaystyle \mathbf {u} }$ is the gas velocity and ${\displaystyle \sigma }$ is the surface tension of the liquid spray, should be ${\displaystyle We<<10}$.

...
Wikipedia