Dear all,

i'm concerned with fluid dynamic simulations on a µm-scale. Since the modelling software can't handle calculations on a µm-sized grid i used the idea of dynamic similarity to set up a m-sized model that behaves the same way as the µm-sized example. This works really well so far.

Now i want incorporate a diffusive scalar transport equation. My software therefore requires the input of a diffusivity coefficient D. I chose D = 2.1e-9, which equals to oxygen being dissolved in water. This, again, works fine for the simple µm-sized test model.

To get the same result in my m-sized model, i tried:

- keeping the same Schmidt number on both scales (as the idea of dynamic similarity is that on both scales the dimensionless numbers should be the same)

- having the same diffusion velocity (210 µm/s and 210 m/s)

- having the same diffusion velocity (210 µm/s on both models, as my m-sized model behaves like it is µm-sized)

- using the Stokes-Einstein equation

But the different approaches yield diffusion coefficients between 1.44e-15 to 2.1e3.

**The question: If i want to use my m-sized model to simulate the same scalar transport as on the µm-sized scale, how do i scale my diffusivity coefficient?**