Stability of solutal advective flow in a horizontal shallow layer

Experimental and numerical investigation of a density-driven instability during a horizontal miscible displacement

“…In Figure 6a the instability onset time is plotted against the Pe number, for various experimental conditions. Each data series represents experiments carried out for the same h and ∆ρ, while the only varying parameter affecting Pe was the flow rate, q. T c shows a weak proportional decrease according to ∼ 1/Pe, a finding in accordance with previous studies in similar systems 24 . For systems without advection, scaling laws of similar structure have been proposed: either for the stationary Rayleigh-Taylor instability 38 or for a solutal system, based on the Rayleigh-Bénard scaling laws 46,47 .…”

“…However, the vortex dissipation only sets in later (t 0 + 14 s), due to the above-discussed delay in the pattern evolution. This kind of dynamic vortex interaction is not observed in previously studied rectilinear cases of the instability 24,32,36 . We strongly suspect that the shear induced by the lateral walls ( du x dy ) might contribute to the phenomenology of the resulting vortex pattern.…”

“…value of λ is defined as the average distance between two dark regions in the shadowgraph image across the cells's width (see embedded sketch in Figure 7). In contrast with previous studies that propose scalings using exclusively the advective flow contribution 24 expressed by Pe or using exclusively the gravitational effect 36 , here, it appears more appropriate to combine both contributing forces, resulting in the Pe −0.23 Ra −0.14 term. This reinforces the argument that two different mechanisms act to promote the onset of the instability.…”

“…We have conducted experiments in a horizontally placed rectilinear geometry shown in Figure 2. In contrast to previous experimental or numerical studies 24,32,36 , where the 7 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”

“…It has been observed that when a fluid 1 of density ρ 1 and viscosity µ 1 is injected into a miscible fluid 2 of density ρ 2 and viscosity µ 2 , a tongue-like profile is created in the contact zone of the two fluids, where an abundance of instabilities may occur [13][14][15] ; whether they are convective [16][17][18] , viscous 19,20 , wetting-front 21 , or even Marangoni-driven 22,23 . When this displacement takes place in a gravity field and µ 1 ≥ µ 2 , then a buoyancy-driven convective instability dominates the dynamics of the system 16,24 . Generally, when a denser fluid is superimposed on top of a lighter fluid, the horizontal interface is gravitationally unstable, resulting in the well-known Rayleigh-Taylor instability 25,26 .…”