Turbulent Schmidt number

Danby

I understand that we make the assumption of a constant schmidt number (Sc) for all species. This is justified that at high Reynolds number molecular diffusion is small compared to turbulent diffusion.

when we use a turbulent model for species however we then use the tubulent schmidt number (Sct). but this also has a single value - same for all species.

surely Sct should be different for each species as tubulence will effect light species differently to heavier ones?

Can someone please expalin what i dont understand. Thanks