Family-Vicsek scaling of detachment fronts in granular Rayleigh-Taylor instabilities during sedimentating granular/fluid flows

Abstract

When submillimetric particles saturated with a fluid form a compact cluster on the top on a confined clear fluid of the same nature, they fall by detaching from the lower boundary of the cluster, and this separation front between particles and fluid is unstable. Particles detach and fall in the clear fluid region, giving rise to growing fingers of falling particles. We study this problem using both experiments and hybrid granular/fluid mechanics models. In the case of particles from 50 to 500 microns in diameter falling in air, we study the horizontal density fluctuations at early times: the amplitude of the density difference between two points at a certain horizontal distance grows as a power law of time. This happens up to a saturation corresponding to a power law of the distance. The way in which the correlation length builds up to this saturation also follows a power law of time. We show that these decompaction fronts in sedimentation problems follow a Family-Vicsek scaling, characterize the dynamic and Hurst exponent of the lateral density fluctuations, respectively z ∼ 1 and ζ ∼ 0.75, and show how the prefactors depend on the grain diameter. We also show from similar simulations with a more viscous and incompressible fluid, that this feature is independent of the fluid compressibility or viscosity, ranging from air to water/glycerol mixtures. a

Pneumatic fractures in confined granular media

“…Granular fingering instabilities have also been studied in closed vertical cells, where gravity drives the flow as heavier beads fall down from a granular layer at the top of a lighter fluid layer [48][49][50][51][52][53]. When the beads detach at the front, they form fingers of falling granular material surrounding fingerlike bubbles of rising fluid.…”

Dynamic Development of Hydrofracture

“…In this way the hydrodynamics evolve 5 intrinsically with irreversible micro deformation in a solid matrix through the use of the Kozeny- 6 Carman porosity-permeability relation. The solution procedure adopted for this coupled problem is based on the same basic 9 principles that were successfully used in simulations to model instabilities in fluid filled granular grains falling in a gas [J. L. Vinningland et al, , 2007bVinningland et al, , 2009aVinningland et al, , 2009bVinningland et al, , 2010, or a fluid 13 [Niebling et al, 2010a[Niebling et al, , 2010bVinningland et al, 2012], and in situations of aerofracturing, i.e. 14 injection of gas in granular media [Niebling et al, 2012a[Niebling et al, , 2012b.…”

Microseismic Emissions During Pneumatic Fracturing: A Numerical Model to Explain the Experiments

“…Particularly, if the fluid flow is pressurized, it can induce rapid porosity changes inside the porous medium which is in contact with the fluid, like fracturing and channeling (Benson et al, ; Bouchut et al, ; J. A. Eriksen, Toussaint, et al, ; Farquharson et al, , ; Galland et al, ; Gidaspow, ; Goren et al, , ; Johnsen, Chevalier, et al, ; Johnsen et al, ; Johnsen, Toussaint, et al, ; Kunii & Levenspiel, ; Trulsson et al, ; Vinningland et al, , , , ). This type of brittle deformation is visible in nature (e.g., volcanic activities and tremors), and in engineering (ground improvements, CO 2 sequestration, and fracturing applications; Agency, ; Aochi et al, ; Charléty et al, ; Cuenot et al, ; Dorbath et al, ; Gao et al, ; Schuring et al, ).…”

“…Fluid flow inside granular media is a very common phenomenon in nature and in industrial applications. Particularly, if the fluid flow is pressurized, it can induce rapid porosity changes inside the porous medium which is in contact with the fluid, like fracturing and channeling (Benson et al, 2008;Bouchut et al, 2016;Farquharson et al, 2016Farquharson et al, , 2015Gidaspow, 1994;Goren et al, 2010Goren et al, , 2011Johnsen, Chevalier, et al, 2008;Johnsen et al, 2006;Kunii & Levenspiel, 1991;Trulsson et al, 2012;Vinningland et al, 2007aVinningland et al, , 2007bVinningland et al, , 2010Vinningland et al, , 2012. This type of brittle deformation is visible in nature (e.g., volcanic activities and tremors), and in engineering (ground improvements, CO 2 sequestration, and fracturing applications; Agency, 1994;Aochi et al, 2011;Charléty et al, 2007;Cuenot et al, 2008;Dorbath et al, 2009;Gao et al, 2014;Schuring et al, 1996).…”