Destabilization of a Saffman-Taylor Fingerlike Pattern in a Granular Suspension

Abstract

We study the Saffman-Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. When using an effective viscosity for the flow of the suspension in the Hele-Shaw cell to define the control parameter of the system, the results for the finger width of stable fingers are found to be close to the classical results of Saffman-Taylor. One observes, however, an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. Classically, the threshold of destabilization is linked to the noise in the cell and is thus difficult to quantify. We show that the grains represent a "controlled noise" and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon et al. allows us to link this perturbation to the value of the threshold observed.

Gas migration regimes and outgassing in particle-rich suspensions

“…Adding particles to the invaded liquid creates a spectrum of gas phase geometries that arise from interactions between gas bubbles, liquid and particles [e.g., 9,10]. If the particles are density matched, increasing the particle fraction causes fingers to thin and branch, due to an increase in effective viscosity, and local perturbations from discrete particles [11,12]. When the suspension approaches the random close packing (RCP, also called maximum random packing), fracture-like patterns may form [12][13][14][15][16][17].…”

Morphodynamics during air injection into a confined granular suspension

“…When looking at the patterns formed during injection we have two limiting situations, the Saffman-Taylor instability [5][6][7], well known for Newtonian fluids and recently also studied for complex fluids [8][9][10][11][12] and the injection of a non-miscible fluid in a saturated porous medium, a problem that has been studied since the 1980s [13,14] and that still attracts much interest today [4,15,16]. Recently, several teams have considered the injection of a air in a reorganizing dense packing of dry grains confined in Hele-Shaw cells [17][18][19][20]46].…”

Sensitivity of Saffman–Taylor fingers to channel-depth perturbations

“…A critical value of 1/B could not be found, but the instability occurred at lower 1/B when the roughness was adjusted from 0.3 % to 3 % of the channel height, suggesting that small, uncontrollable, geometric non-uniformities were the cause of the instability. Early destabilisation due to controlled perturbations of the interface was demonstrated by Chevalier, Lindner & Clément (2007), who studied fingering in a granular suspension in viscous liquid, where the perturbation amplitude was proportional to the grain size. Associated theoretical studies have also explored finger stability (Bensimon 1986), and the effect Sensitivity of Saffman-Taylor fingers to channel-depth perturbations 345 of anisotropy on finger selection (Ben Amar & Brener 1996).…”