Saffman–Taylor Fingers

Plate 10 speaks for itself: “The thin pushes into the thick, and splits.”

The Physics

When a less viscous fluid pushes a more viscous one in a thin gap (a Hele-Shaw cell), the interface is unstable and grows fingers. Flow in the gap obeys Darcy's law.

u = −(b² / 12μ) ∇p

• u: gap-averaged velocity, m s⁻¹
• b: gap thickness, m
• μ: dynamic viscosity, Pa s
• ∇p: pressure gradient, Pa m⁻¹

One steady finger fills about half the channel. Saffman and Taylor, 1958.

Sources

• P. G. Saffman, G. I. Taylor, Proc. R. Soc. A 245, 312 (1958).

On the poster

Plate 010, “Saffman–Taylor Fingers”: the pixel-art plate with its slogan “The thin pushes into the thick, and splits.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.