In this study, we investigate the problem of the effects of droplets dispersion dynamics on ignition of polydisperse spray in turbulent mixing layers using probability density function. Studies of this problem have been found to be instrumental in developing understanding of turbulent combustion including the ignition of turbulent gaseous diffusion flames. The parameters used to describe the distribution of droplet sizes are the moments of the droplet size distribution function which are allowed to vary in the fourth vector (x,y,z,t). In our analysis we applied the Homotopy Analysis Method. This method contains a certain auxiliary parameter which provides a way to control the convergence region and the rate of convergence of the series solutions.

partial differential equations, polydisperse fuel spray, laminar boundary layer, Homotopy Analysis Method