Flow geometry flattens viscous fingers

In the early 20th century, petroleum engineers noticed that water does not displace oil uniformly but instead penetrates it through a process now known as viscous fingering. When Philip Saffman and G. I. Taylor analyzed the problem in 1958, they realized that instabilities at the interface emerge as long, propagating fingers when a less viscous fluid presses against a more viscous one. Small perturbations at an otherwise flat interface create local pressure gradients that force the less viscous fluid into regions just ahead of each perturbation—the initiation of a positive feedback system that drives the fingers’ growth. (The image here shows an example of air pressing on mineral oil.) Saffman and Taylor also realized they could capture the essential physics of the flow using a two-dimensional channel known as a Hele-Shaw cell, in which fluids are confined between two parallel plates separated by a small gap. In a study combining theory and experiments, Princeton University researchers led by Howard Stone have now found that the introduction of a gentle negative gradient in the gap can suppress the instability. Here’s how: As the gap narrows in a converging cell, the tip of a finger experiences an increased surface tension force that opposes the finger’s advance and effectively overcomes the instability induced by viscous effects. The Princeton team found, and then confirmed experimentally, that the stability condition in a given system is set by just three parameters: the angle of taper, the fluids’ wetting angle, and the flow speed. (T. T. Al-Housseiny, P. A. Tsai, H. A. Stone, Nat. Phys., in press, doi:10.1038/nphys2396 .)—R. Mark Wilson