Gravitational Instability of a Fictitious Front During Mixing of Miscible Fluids

We analyse the stability of a fictitious front between two miscible fluids in an extended geometry. It is found that, contrary to what occurs in a Hele-Shaw geometry, or porous media, both diffusion and viscosity play, when each is considered alone, a singular role. Their mutual presence completely destroys the mathematical structure. We find that the characteristic time and length of the instability scale as τ ∼ ν2/3/(g2/3D1/3), and λ ∼ (νD/g)1/3, respectively (D = diffusion constant, ν = viscosity, g = gravity). We propose experimental protocols to check these scaling laws.