In the early 20th century, petroleum engineers noticed that water pumped into porous, oily rock does not displace the oil uniformly but instead penetrates it through a process now known as viscous fingering—the tentaclelike flow of one fluid into another. When Philip Saffman and G. I. Taylor analyzed the problem in 1958, they realized that instabilities at the fluids’ interface naturally emerge as long, propagating fingers. Small perturbations at an otherwise flat interface create local pressure gradients that force the less viscous fluid into regions just ahead of each perturbation. As the fluid speed locally increases, so do the pressure gradients, and the positive feedback drives the fingers’ growth.
Saffman and Taylor also realized that they could capture the essential physics of the flow in porous rock using a two-dimensional channel known as a Hele–Shaw cell, in which the different fluids are confined between two parallel glass plates separated by...
