INSIGHTS IN EROSION INSTABILITIES IN NONCONSOLIDATED POROUS-MEDIA

We investigate the different flow regimes in nonconsolidated porous me dia. The porous bulk is soaked with water, which is then pumped out of it, across the boundary defined by the particles at the edge of the b ulk. Experiments are carried out on sand and glass beads soaked in dis tilled water and placed in a circular Hele-Shaw cell, the flow being r adially convergent. We show, for a given value of flow velocity (the y ield velocity), the existence of an unstable regime where the fluid-po rous interface is deformed and branches upstream in the bulk. When thi s velocity is further increased, two cases arise depending on the valu e of the yield velocity: Either a second threshold is passed, global f luidization of the porous bulk sets in, and the flow becomes stable or the instability persists and the canal arborescence continues to grow . The driving mechanism of this instability is thus the permeability c ontrast across the edge of the porous bulk; when this contrast diminis hes, the flow becomes stable. A force balance on the boundary particle s predicts the threshold value for the fluid velocity, beyond which th e flow is unstable. Using a Saffman-Taylor inspired linear perturbatio n analysis [Proc; R. Sec. London, Ser. A 245, 312 (1958)], a dispersio n function is:found (predicting the wavelength dependence of the insta bility growth amplitude), taking into account the particle arch format ion in the porous bulk. We then find the velocity of propagation of th e receding front, predicted to be proportional to the particle velocit y beyond the front, itself described by a Bagnold concentrated suspens ion flow [Proc. R. Sec. London, Ser. A 225, 49 (1954)]. This front vel ocity is successfully confronted with experimental measurements. A scr eening effect characteristic of Laplacian growth phenomena is seen in the experiments as testified by flow rate conservation between the dif ferent branches of the arborescence and direct dye visualization. The topologies obtained are fractal and the measured dimension D-f = 1.6-1 .7 compares favorably to the calculated dimension from the branching a ngle distribution. [S103-651X(98)10610-4].