Instabilité gravitationnelle de deux fluides miscibles

When a heavy fluid P is placed (at time t=0) above a light fluid L, a diffuse interface is formed, of width Δ=(Dt) 1/2 , where D is a mural diffusion coefficient. There is no interfacial tension P/L. The interface is mechanically unstable for all wave vectors q<Δ -1 , with a growth time τ(q). For inviscid fluids, the dominant instability shows up when τ(q≅Δ -1 )=t.This characteristic size Δ 1 for the primary droplets of the mixing process (∼1 μm). But, when viscosity is allowed, the dominant instability shows up at a larger scale q *-1 (∼100 μm), analysed long ago by S. Chandrasekhar, and independent of Δ 1