Modeling turbulent fluxes in RANS (Reynolds-Averaged Navier-Stokes) equations is a nontrivial task. Unlike molecular diffusion, turbulent scales are tipically not well separated from those over which mean properties vary, and therefore the very common analogy between them is a poor one. When the interest lies in simulating the initial stage of a process (e.g. the zone close to a nozzle discharging material) some modifications to the diffusion coefficients must be done in order to represent the process adequately. Moreover, when the turbulent dispersion of a puff of material or a burning kernel needs to be predicted, it is necessary to consider that not all of the turbulent eddies are effective in diffusing the material. Eddies much larger than the puff primarily convect it in a random way, and this must also be included in the diffusion process if the puff growth is to be computed accurately. In this work, lagrangian simulations are performed in a simplified turbulence configuration. Then, dispersion statistics are used to obtain an expression for the turbulent diffusivity appropriate for simulating the growth of a puff and related phenomena, such as the kernel produced after a spark discharge.