why do we assume a constant turbulent diffusivity for all species in a reacting flow?

surely hydrogen is diffused more than, say, oxygen by tubulence. i.e. due to the fact it is lighter.

why dont we use a different turbulent Schmidt number for each species?

i dont know

This is because turbulent diffusivity is not a preperty of a particular fluid, but that of the turbulent flow.

hi agg,

ok. but still in reality would you not expect lighter species to be transported more than heavier ones by turbulence?

That is true. Hence for example in LES dynamic models are used to account for the differences (if my understanding is correct). A constant is an approximation (and has worked) to simplify the model.