GRAVITATIONAL-INSTABILITY OF A FICTITIOUS FRONT DURING MIXING OF MISCIBLE FLUIDS

We analyse the stability of a fictitious front between two miscible fl uids in an extended geometry. It is found that, contrary to what occur s in a Hele-Shaw geometry, or porous media, both diffusion and viscosi ty 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 tau sim ilar to nu(2/3)/(g(2/3)D(1/3)), and lambda - (nu D/g)(1/3) respectivel y (D = diffusion constant, nu = viscosity, g = gravity). We propose, e xperimental protocols to check these scaling laws.