P.G. Saffman and G. Taylor, The penetration of a fluid into a porous medium or Hele–Shaw cell containing a more viscous liquid, PRSA 245, 312–329, 1958

These authors investigate the stability of a fluid front produced by a less viscous fluid penetrating a more viscous fluid. The experiment was conducted using a Hele-Shaw cell that could be positioned either vertically or horizontally. The pressure gradient in the cell was produced applying either air pressure or air suction. The instability of the front is shown to be velocity dependent. Characteristic finger spacing is observed. The paper mathematically develops the growth of a single finger.

Comments/ Questions:

1) The non-uniqueness of the Darcy flow solution developed was discussed. This was pointed out in contrast to the week 1 reading by G.K. Batchelor which discussed the uniqueness of the Darcy flow solution under certain assumptions

2) Why don’t fingers pinch off but instead stay intact as they grow?

3) What controls the preference of finger growth? Why do some fingers grow at the expense of others? There are no compaction fronts or increase in friction at finger boundaries as in the experiment described in week 2 reading (B. Sandnes et al.)

4) A nice natural example of finger growth was given by George who described the brine pockets in sea ice slowly flowing through the ice and producing ‘salt finger’ in the ocean http://smithsonianmag.tumblr.com/post/58919927616/smithsonian-magazine-icy-finger-of-death

R. Holtzman, M.L. Szulczewski and R. Juanes, Capillary fracturing in granular media, PRL, 108, 264504, 2012.

These authors study the deformation of a non-cohesive granular material due to the injection of a fluid. The experimental set-up involves a thin cylinder filled with water saturated glass beads. Weights are used to varying the confining pressure and a syringe is used to inject fluid into the material at various rates. The bead size is also varied. Three invasion regimes are identified: 1) capillary fingering, 2) viscous fingering, and 3) capillary fracturing. Frictional sliding is the mechanism that controls fracturing of the medium. Competition between viscous and capillary forces controls the type of fingering.

Comments/Questions:

1) There was some discussion about scaling analysis mostly centered on how to properly scale/ non-dimensionalize problems. Some reading on Buckinghams pi theorem was suggested

2) The direction of deformation was discussed. From figure 2 it appears as though viscous fingering does not have a preferential direction where as capillary fingering and fracturing develop asymmetrically

3) This paper was similar to the B. Sandnes et al. paper discussed in week 2 and it was nice to have these two similar papers to compare. The biggest difference mentioned was the investigation of the effects of grain size on the deformation regimes (discussed by R. Holtzman et al. and not B. Sandnes et al.)

4) Everyone was a bit confused on the definition of surface energy and how it is effects deformation style