Batchelor scalar microscale (${\eta }_B=({\alpha }^2\nu /ϵ{)}^{1/4}$)

At the Batchelor scalar microscale, molecular diffusion rate $\alpha /r^2$ balances the smooth Kolmogorov strain rate $(ϵ/\nu {)}^{1/2}$. For $\alpha \ll \nu$ this scale is much smaller than the Kolmogorov length scale.