Nature Phys.http://doi.org/jbg (2012)

A flowing, low-viscosity fluid penetrating a thicker one tends to form elongated patterns, resembling fingers, in the direction of the flow. Such 'fingering instabilities' can cause inefficiencies in oil-recovery processes and in microfluidic set-ups; for instance, when air is used to flush a liquid out of a channel, traces may be left behind. Now, Talal Al-Housseiny and colleagues show that fingering instabilities can be easily avoided by creating a depth gradient in the direction of the flow. Using a Hele-Shaw cell (a shallow rectangular channel) with varying depth, the researchers demonstrated that finger-like patterns disappear when the capillary number — the ratio of viscous to surface-tension forces — is below a critical value, which depends on the viscosity ratio of the displaced and displacing fluids, the contact angle of the fluid interface with the cell's wall, and the gradient in fluid depth. With appropriate flow rates, microfluidic channels that are tapered should then be easier to clean perfectly with a flush.