Physics Help Forum Density driven flow

 Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum

 Jul 18th 2017, 02:00 AM #1 Junior Member   Join Date: Jul 2017 Posts: 1 Density driven flow I'm doing some work on density induced flow in porous media. 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/dispersion eq., Darcy, the 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: $$φ\frac{∂ ρ}{∂t}+∇\cdot(ρq)=0$$ I've decided to scale my system of equations using a diffusive time scale $x_0^2/D$. The other relevant scaling factors are the flux $q_0$ e and the density is scaled as $${ρ^*}=({ρ}-{ρ_0})/(ρ_{max}-ρ_0)$$ The scaling produced: $$\frac{ε}{Pe}\frac{∂ρ}{∂t}+ε\cdot ρ∇\cdot q+∇\cdot q+ε\cdot q∇ρ=0$$ where $ε\ll1$ and $Pe\ll ε$ For that case I can see that the accumulation term has the largest magnitude and therefore $∂ρ/∂t=0$.It does not make sense to me since density does change in respect to time due to diffusive processes. Clearly i'm missing something basic here. Any ideas? Thanks!

 Tags density, driven, flow, mass transport, porous media

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post campbell9035 Thermodynamics and Fluid Mechanics 4 Feb 15th 2017 05:01 PM alexgeek Kinematics and Dynamics 2 Jan 20th 2011 02:40 PM simonsam86 Thermodynamics and Fluid Mechanics 5 Sep 1st 2009 03:39 AM physicsquest Kinematics and Dynamics 7 Apr 27th 2009 11:06 PM abaset Advanced Mechanics 0 Feb 18th 2009 10:49 AM