[abi111]

Hi there

I've doing some work on density induced flow. My problem contains a single phase fluid with 2 components (water and a solute). I'm solving the continuity equation along with the advection diffusion, darcy, equation of state (links between the concentration and density) and a viscosity function.

Currently i'm trying to figure out whether the Boussinesq approximation is valid in my case. I've scaled the equations and while doing so, revealed a gap in my Understanding of the physics involved.

The continuity-mass conservation for the fluid phase:
φ∂(ρ)/∂t+∇∙(ρq)=0
scaling it using characteristic diffusive time scale, flux and density: (x0^2)/D, q0, rho0.
The scaling produced:
ε/Pe(∂ρ/∂t)+ε∙ρ∇∙q+∇∙q+ε∙q∇ρ=0
where ε<<1 and Pe<<ε
For that case i can see that the accumulation term has the largest magnitude and therefore (∂ρ/∂t)=0.
But i have diffusion in my system and density does change in respect to time. what's going on?

Thanks a lot!
Avi